Measurement of theDisappearance of Muon Neutrino
in 250 km Long Base Line
Experiment

UNI VE

KY O

O

ITY
RS

T

Takahiro Inagaki

8
ED 1

97

JAPAN

ND

FO

KYOTO

U

Department of Physics, Faculty of Science
Kyoto University

2

Abstract
This thesis presents the results of the first accelerator experiment of the neutrino oscillation
with 250 km long base line. Muon neutrinos are generated by 12 GeV proton synchrotron,
travel 250 km, and are detected in Super-Kamiokande, to measure reduction during thetravel.
From June 1999 to June 2000, 2.29× 1019 protons on target have been accumulated. The
distribution of produced pions is measured by a gas Cherenkov detector. The measurement
provides the neutrino energy spectra and the flux ratio at far/near site. The direction of
the neutrino beam and the stability of the flux are monitored by a near neutrino detector.
Measurements of the secondary muon and the proton profile in beam line hold the stability
on spill-by-spill basis. These measurements confirm that the neutrino beam is stable enoughto extrapolate the number of neutrino events from near to far detector. The absolute valueof the event rate is derived from the measurements at 1kt water Cherenkov detector in thenear site. The extrapolation shows the expected number of events in Super-Kamiokande+3.8
is 37.8−4.0.
Data of the corresponding period at Super-Kamiokande are analyzed. Super-Kamiokandeobserves 28 fully-contained events in 22.5 kt fiducial volume, with negligible background ofo(10−3 ). Comparing the expectation and the observation, the probability of no change is
9.6%. The most likely explanation of this reduction is the neutrino oscillation. Assuming
the hypothesis of νµ → νx oscillation with large mixing angle, the best estimation of ∆m2
is around sevral of 10−3 eV2 . This is consistent with the recent assertion of the atmospheric
neutrino observations.

Contents
1 Introduction
1.1 Neutrino Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Neutrino Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Oscillation formula . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Atmospheric neutrino observations . . . . . . . . . . . . . . . . . .
1.2.3 Solar neutrino observations . . . . . . . . . . . . . . . . . . . . . .
1.2.4 Reactor neutrino experiments . . . . . . . . . . . . . . . . . . . . .
1.2.5 Accelerator neutrino experiments . . . . . . . . . . . . . . . . . . .
1.2.6 Summary of the neutrino oscillation measurements . . . . . . . . .

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2 Overview of the K2K Experiment
2.1 Concept of the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Analysis of the Muon Neutrino Disappearance . . . . . . . . . . . . . . . .
2.3 Components Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 History of K2K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Experimental Components
3.1 Neutrino Production Beam Line . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Accelerator and proton beam line . . . . . . . . . . . . . . . . . . .
3.1.2 Proton beam monitors . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Production target and focusing devices . . . . . . . . . . . . . . . .
3.1.4 Decay volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Pion monitor (PIMON) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Goal of PIMON . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Cherenkov technique for pion identification . . . . . . . . . . . . . .
3.2.3 Cherenkov technique for simultaneous measurement of (pπ , θπ ) . . .
3.2.4 Analysis strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Design of PIMON . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 Hardware of PIMON . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Muon Monitors (MUMONs) . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.3.1 Goal of the MUMON . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Hardware set up of the MUMON . . . . . . . . . . . . . . . . . . .
Data Acquisition System of Beam Line Monitors . . . . . . . . . . . . . . .
Near Neutrino Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 1kt water-Cherenkov detector (1kt) . . . . . . . . . . . . . . . . . .
3.5.2 Muon Range Detector (MRD) . . . . . . . . . . . . . . . . . . . . .
3.5.3 Fine grain detector (FGD) system . . . . . . . . . . . . . . . . . . .
3.5.4 Data acquisition system of near neutrino detector . . . . . . . . . .
Far neutrino detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Detector features . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . .
Global Positioning System (GPS) . . . . . . . . . . . . . . . . . . . . . . .
3.7.1 Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.2 Stability check . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Monte Carlo Simulations
4.1 Pion Production and Decay to Neutrino (beamMC) . . . . . . . . . . . . .
4.1.1 Proton injection to the target . . . . . . . . . . . . . . . . . . . . .
4.1.2 Pion production in the target rod . . . . . . . . . . . . . . . . . . .
4.1.3 Simulation of the particle tracing through the magnetic field and the
decay section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 Simulated neutrino beam . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Neutrino interaction simulation (neutMC) . . . . . . . . . . . . . . . . . .
4.2.1 Neutrino interaction around 1 GeV . . . . . . . . . . . . . . . . . .
4.2.2 CC quasi-elastic, and NC elastic scatterings . . . . . . . . . . . . .
4.2.3 Single-meson production . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Multi-pion production . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.5 Coherent pion production . . . . . . . . . . . . . . . . . . . . . . .
4.2.6 Experimental constraint of the CC total cross section . . . . . . . .
4.2.7 Nuclear effect for hadrons . . . . . . . . . . . . . . . . . . . . . . .
4.2.8 Uncertainty of the neutrino interaction . . . . . . . . . . . . . . . .
4.3 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Simulation of MRD . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Simulation of water Cherenkov detector (1kt, SK) . . . . . . . . . .

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5 Analysis Strategy
5.1 Overview of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Operation of the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Good Beam Spill Selection . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.4
3.5

3.6

3.7

2

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6 Proton and Secondary Particle Measurement
6.1 Pion Distribution Measurement using PIMON . . . . . . . . . . . . . . . .
6.1.1 PIMON measurement . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Cherenkov photon distribution . . . . . . . . . . . . . . . . . . . . .
6.1.3 Subtraction of electro-magnetic shower contribution . . . . . . . . .
6.1.4 Extraction of the pion energy and angular distribution . . . . . . .
6.1.5 Prediction of the neutrino energy spectrum . . . . . . . . . . . . . .
6.1.6 Systematic error of the energy spectrum and Far/Near ratio . . . .
6.2 Stability of the Proton Beam . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Proton beam profile measurement . . . . . . . . . . . . . . . . . . .
6.2.2 Injection angle dependence . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Injection point dependence . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 Profile width and divergence dependence . . . . . . . . . . . . . . .
6.2.5 Systematic errors due to the proton targeting . . . . . . . . . . . .
6.3 Stability of the Muon Profile Center . . . . . . . . . . . . . . . . . . . . . .

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7 Neutrino Beam Measurement
7.1 Neutrino Event Selection at MRD . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 Overview of the MRD analysis . . . . . . . . . . . . . . . . . . . . .
7.1.2 Overview of the track finder . . . . . . . . . . . . . . . . . . . . . .
7.1.3 Neutrino event selection . . . . . . . . . . . . . . . . . . . . . . . .
7.1.4 Selection efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Check of MRD Performance and its Stability . . . . . . . . . . . . . . . . .
7.2.1 Hit efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2 Tracking efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3 Reconstruction resolution . . . . . . . . . . . . . . . . . . . . . . .
7.2.4 Cosmic ray measurement . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Neutrino Profile at MRD . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1 Vertex profile of fully-contained (FC) events . . . . . . . . . . . . .
7.3.2 Stability of the neutrino profile . . . . . . . . . . . . . . . . . . . .
7.3.3 Profile reconstruction test by Monte Carlo simulation . . . . . . . .
7.3.4 Conclusion of the neutrino beam direction . . . . . . . . . . . . . .
7.4 Muon Distribution at MRD . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.1 Observed muon spectrum and angular distribution . . . . . . . . .
7.4.2 Stability of the muon distribution . . . . . . . . . . . . . . . . . . .
7.5 Neutrino Event Rate at MRD . . . . . . . . . . . . . . . . . . . . . . . . .
7.5.1 Event rate stability . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5.2 Calculation of the neutrino interaction rate at MRD . . . . . . . . .
7.5.3 Systematic errors at MRD . . . . . . . . . . . . . . . . . . . . . . .

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8 Measurement of the Neutrino Event Rate at 1kt Detector
8.1 Neutrino Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Overview of the 1kt analysis . . . . . . . . . . . . . . . . . . . . . .
8.1.2 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.3 Selection efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.4 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Neutrino Event Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.1 Event rate calculation . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.2 Event rate stability . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.3 Systematic errors at 1kt . . . . . . . . . . . . . . . . . . . . . . . .
8.2.4 Summary of the neutrino event rate at 1kt . . . . . . . . . . . . . .
8.3 Constraint of the Low Energy Neutrino Spectrum . . . . . . . . . . . . . .
8.3.1 Total photo-electron distribution . . . . . . . . . . . . . . . . . . .

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9 Neutrino Event Measurement at Super-Kamiokande154
9.1 Neutrino Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
9.2 Observed events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
10 Comparison of Near and Far Event Rate
10.1 Key Issues of the Near Site Measurement . . . . . . . . . . . . . . . . . . .
10.2 Estimation of the Expected Number of Events . . . . . . . . . . . . . . . .
10.2.1 Extrapolation formula . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SK
10.2.3 Systematic error for Nexp
. . . . . . . . . . . . . . . . . . . . . . .
10.3 Cross-check of the Expected Number of Events From MRD. . . . . . . . .
10.4 Observed Number of Events at SK . . . . . . . . . . . . . . . . . . . . . .
10.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.5.1 Statistical significance . . . . . . . . . . . . . . . . . . . . . . . . .
10.5.2 Physics Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . .

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11 Conclusion

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A MRD Track Finder
A.1 Noise hit rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Cell fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.3 Fragment fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.4 2-D fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.5 3-D fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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B Neutrino Profile of Vertex-Contained Events at MRD
B.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2 Profile of vertex-contained (VC) events . . . . . . . . . . . . . . . . . . . .
B.3 Stability of the profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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C TDC fit

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D Experimental Test of the Vertex Reconstruction at 1kt

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E Analysis of June 1999 Run
E.1 PIMON analysis results in Jun.99 run. . . . . . . . . . . . . . . . . . . . .
E.2 Neutrino Profile at MRD . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.3 Muon Distributions at MRD . . . . . . . . . . . . . . . . . . . . . . . . . .

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F Comparison Between MRD and 1kt
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F.1 Event Rate Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
F.2 Discussion about RM RD/1kt . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
G Various Distributions of the Observed Events in SK

5206

Chapter 1
Introduction
1.1

Neutrino Mass

In the Standard Model of the weak interactions, neutrinos are considered as the massless
leptons. In this case, three different neutrinos, νe , νµ , and ντ are identified by the correspondence to e, µ, and τ in the weak interaction. Then, the neutrinos are only expressedas the eigenstate of the weak interaction.
However, if the neutrinos have non-zero mass, they can be also expressed as the eigenstateof the mass. If the weak eigenstate is not equal to the mass eigenstate, the mixing causes theflavor change as that is observed in the quark sector. Furthermore, when three generationsof leptons are mixed, one phase parameter may lead a CP violation. Thus, the observationof the non-zero neutrino mass and the existence of the lepton mixing make a significant
extension beyond the Standard Model.
Direct mass measurement of the neutrinos has been performed by precise measurementof the decay kinematics. However, no experiment has found the finite mass over the measurement error. The most sensitive measurement of the νe mass was the electron spectrum
measurement in the tritium beta decay (summarized in [1] and [2], and recent results arereported in [3]).
33+−
1 H → 2 He + e + ν¯e(1.1)

If ν¯e has a finite mass, the end-point of the electron energy spectrum shifts due to the
4-momentum conservation. Various experiments have been analyzed, and they give only
the upper limit of several eV. In addition, the arrival time spread of the neutrinos fromSupernova-1987A provides the upper limit of mνe at a few 10 eV [4].
The best limit of the νµ mass was obtained from the muon momentum measurement of
the pion decay at rest in PSI [5]. Based on this measurement and the average for the pionmass, PDG evaluated the mass limit of mνµ < 190 keV in 90% confidence level [1].
6

Neutrino
νeνµντMass limit (by PDG [1])Experiment
3 eV
tritium β decay [3]190 keV (90% C.L.)
pion decay [5]18.2 MeV (95% C.L.)
tau decay [6]Table 1.1: The present limit of the each neutrino mass, evaluated by Particle Data Group.
The present limit of the ντ mass was obtained from the kinematics of the tau decay in
ALEPH detector [6]. Two separate limits were derived by fitting the distribution of visibleenergy versus invariant mass inτ − → 2π − π + ντ
τ − → 3π − 2π + (π 0)ντ

(1.2)
(1.3)

The two results are combined to obtain a 95% confidence level upper limit of mνµ <18.2 MeV. Table 1.1 summarizes the mass limit referred by PDG [1].

1.2

Neutrino Oscillation

Another experimental search of the finite neutrino mass is the search of the ”neutrino
oscillation”. This is the phenomenon that a neutrino changes its flavor, caused by themixing between the flavor eigenstate and the mass eigenstate, when the neutrino has a nondegenerate mass. In following sections, the principle of the oscillation and the observation
results are explained.

1.2.1

Oscillation formula

A flavor eigenstate |ναi(α = e, µ, τ ) is generally expressed by a mixing of mass eigenstate|νi i(i = 1, 2, 3) as follows;|να i =

Xi

Uαi|νi i(1.4)

where Uαi is the element of the unitary matrix U (Maki-Nakagawa-Sakata matrix [7]),corresponding to Cabbibo-Kobayashi-Maskawa matrix [8] in quark sector. When lepton
sector consists of 3 generations, there are for free parameters, the 3 × 3 matrix U can beparameterized by three mixing angle θ12 , θ23 and θ13 , and one CPV phase δ;
c12 s12 0c13
0 s13 e−iδ
1
0
0




−s
0
1
0
U =  0 c23 s23  
12 c12 0 
0
0 1−s13 eiδ 0c13
0 −s23 c23






7



c12 c13s12 c13s13 e−iδ=  −s12 c23 − c12 s23 s13 eiδ c12 c23 − s12 s23 s13 eiδ s23 c13 s12 s23 − c12 c23 s13 eiδ −c12 s23 − s12 c23 s13 eiδ c23 c13

(1.5)

d
|ν(t)i = H0 |ν(t)i
dt

(1.6)





where cij = cos θij and sij = sin θij .
When neutrinos are generated and interacted by weak interaction, they are identified as
the flavor eigenstate. On the other hand, the time evolution of the state is described as
the mass eigenstate in following Schrödinger equation;iwhere H0 is Hamiltonian for the free neutrinos. When neutrinos have common
momentumq2p, this equation can be solved as following energy eigenstate with Ei = p + m2i ,|νi (t)i = e−iEi t |νi (0)i

(1.7)

Thus, ν1 , ν2 , ν3 have different time evolution.
Assume the neutrino is generated as pure να , probability for observing νβ after finite
time t (or at distance L) is expressed as follows;
P (να → νβ ) = |hνβ |U H0 U † |να i|2= δαβ − 2

X
i<j

Re

"

∗
∗
Uβi
Uαi Uβj Uαj∆m2ij L1 − exp −i
2p

!!#

(1.8)

where ∆m2ij ≡ m2i − m2j is the difference of mass squared. If U has non-zero mixing angle
θ and non-zero ∆m2, the second term of this formula changes the probability dependingon the distance L. This phenomenon is called ”Neutrino Oscillation”.
As mentioned in following sections, the atmospheric neutrino observations indicate ∆m2atm ∼O(10−2 ∼ 10−3 ) eV2 , whereas the solar neutrino observations indicate ∆m2sol < O(10−4 ) eV2 .
Then, ∆m2ij is approximated as follows;∆m212  ∆m223 ' ∆m213(1.9)

In this case, the contribution of ∆m212 term becomes negligible and the oscillation probability relevant to the experiment can be expressed by following formula;
P (νµ → νµ ) '≡P (νµ → νe ) '≡P (νe → νe ) '1 − cos4 θ13 · sin2 2θ23 · sin2 Φ23
1 − sin2 2θµµ · sin2 Φ23
sin2 θ23 · sin2 2θ13 · sin2 Φ23
sin2 2θµe · sin2 Φ23
1 − sin2 2θ13 · sin2 Φ23
8(1.10)(1.11)(1.12)

Experiments

L

Eν

∆m2

results

15 ∼ 13000 km

0.1 ∼ 100 GeV

10−4 ∼ 10−2 eV2

exist
no

1.5 × 108 km

0.2 ∼ 15 keV< 10−4eV2

exist

0.02 ∼ 1 km

3 MeV

> 10−3eV2

noanalysisAtmospheric neutrino observations
νµ /νe → νµ /νeSolar neutrino observations
νe → νe

Reactor neutrino experimentsν¯e → ν¯e

Accelerator neutrino experiments
CHORUS
NOMAD
CDHSW
CHARM
LSND
KARMENK2K

νµ → ντ

0.8 km20 ∼ 30 GeV> 1eV2no [30, 31]

νµ → νµ , νe0.1, 0.9 km

1 ∼ 1.5 GeV> 0.3eV2

no [32, 33]ν¯µ , νµ → ν¯e , νe
ν¯µ → ν¯eνµ → νµ , νe0.03 km0.02 km
250 km< 53 MeV< 53 MeV
1.3 GeV> 10−1eV2> 10−1eV2> 10−3eV2exist [34]
no [35]this thesis

Table 1.2: Comparison of the various neutrino oscillation experiments.

whereΦij ≡ ∆m2ij · L/4p = 1.27 · ∆m2ij [eV2 ] · L[km]/Eν [GeV](1.13)

gives the oscillation pattern depending on the baseline distance L and the neutrino energyEν . These expressions can be regarded as the 2 flavor oscillation with the effective mixing
angle θµµ and θµe.
If the neutrino oscillation is actually observed, it proves the fact that the neutrinos haveat least two different mass eigenstates, and at the same time, proves the existence of themixing between the mass eigenstate and the flavor eigenstate. Taking a long base-line L
and using the low energy Eν neutrinos, the search of the oscillation has a good sensitivity
to find non-zero ∆m2ij much less than eV2 . Various experiments have been performed tofind the oscillation as summarized in Table 1.2. They are explained in following sections.
9ν x ) oscillation
100

0.1

10
1

0.01

0.1
SuperKamiokande
Kamiokande
Soudan-2
MACRO

10

-4

10

0.01
-3

10

0.5
2
sin (2 θ )LSNDallowed
CHOOZ
excluded

10

-5

0

Bugey 95
CCFR96-4

10

1∆ m 2 (eV 2 )∆ m 2 (eV 2 )allowed regions-3ν x ) oscillation(ν e
KARMEN2
excluded(ν µPalo Verdeexcluded
LMA

SMA
SuperK exclusion#
day-night asymmetry

-6

10
10

-7

LOW

-8

SK+GALLEX+SAGE+Homestake
allowed
VAC

10

-9

10

-10

10

-3

10

0.01 0.1
sin 2 (2 θ )1Figure 1.1: Allowed region of νµ → νx oscillation (left), and νe → νx oscillation (right).
The right figure refers to [1]101.2.2

Atmospheric neutrino observations

Atmospheric neutrinos are produced by the decay of pions, kaons, and muons, which areproduced by the collision of high energy cosmic ray protons injected to the upper atmosphere. The peak energy of these neutrinos is at about 1 GeV, and their energy spectrum
extends to the order of 100 GeV. The main production process around sub-GeV range isfollowing sequential pion decay;(−)

π ± → µ± νµ(1.14)µ± → e± νµ νe(1.15)(−)(−)

Therefore, the flux ratio of (νµ + ν¯µ )/(νe + ν¯e ) is ideally 2. Considering the finite atmospheregeometry, the simulation predicts the ratio with 5% uncertainty, whereas the absolute flux
has about 20% uncertainty.
This ratio has been measured in several underground experiments. Super-Kamiokande [9,10], Kamiokande [11, 12], and IMB experiments [13, 14] use water-Cherenkov type neutrino
detectors. Soudan-2 [15], Fréjus [16], and NUSEX [17] experiments use iron-calorimeter
type detectors. In each detector, neutrino events are identified by the containment of theinteraction vertex. Observed events are classify ed to the µ-type events Nµ or the e-type
events Ne , by the Cherenkov ring pattern in the water-Cherenkov type detectors, or the hit
distribution of the charged particles in the iron-calorimeter type detectors. The measured
event ratio (Nµ /Ne )meas are compared to the simulated value as follows;R≡(Nµ /Ne )meas(Nµ /Ne )M C

(1.16)

Table 1.3 summarizes the results R in these experiments. Historically, Kamiokande and
IMB gave the significantly lower R value, which is called ”atmospheric neutrino anomaly”.
On the other hand, in NUSEX and Fréjus experiment, R value was consistent to 1, while
the data statistics are poor. Recently, Super-Kamiokande and Soudan-2 experiments has
been performed with higher statistics. They show lower R values, which are consistent
results with Kamiokande measurement.
Existence of the neutrino oscillation was clearly proved by the zenith angle dependenceof the R value in Kamiokande and Super-Kamiokande experiments [10]. The upward-goingneutrinos are originally produced at the atmosphere of opposite side of the globe and travel more than 10000 km distance through the earth, while the downward-going neutrinos
travel only several 10 km from the upper atmosphere. Since the observed charged particles generally conserve the induced neutrinos’ direction, the zenith angle of the observed
Cherenkov ring distributions corresponds to the oscillation baseline L in the Formula 1.10
and 1.11. Figure 1.2 shows the distributions of µ-like and e-like events for 4 energy ranges.
”sub-GeV (multi-GeV)” indicates the events that the visible energy is less (more) than11

Experiment
Super-K (sub-GeV)
Super-K (multi-GeV)
Kamiokande (sub-GeV)
Kamiokande (multi-GeV)IMB (Evis < 0.95 GeV)
IMB (Evis > 0.95 GeV)
Soudan-2Fréjus
NUSEX

exposure
33 kt-yr
33 kt-yr
8.2 kt-yr
8.2 kt-yr (FC)
6.0 kt-yr (PC)7.7 kt-yr
7.7 kt-yr
3.9 kt-yr
2.0 kt-yr
0.74 kt-yr

R
0.63 ± 0.03stat ± 0.05syst [10]0.65 ± 0.05stat ± 0.08syst [10]+0.06 stat0.60−0.05± 0.05syst [12]+0.08 stat0.57−0.07± 0.07syst [12]0.54 ± 0.05stat ± 0.12syst [13]+0.07 stat1.1−0.12± 0.11syst [14]0.64 ± 0.11stat ± 0.06syst [15]1.00 ± 0.15stat ± 0.08syst [16]+0.320.96−0.28[17]

Table 1.3: Summary of the measured R values in various experiments. (sub-GeV) and(multi-GeV) represent the energy range. In Super-Kamiokande and Kamiokande, they aredefined that the visible energy is less and more than 1.33 GeV, respectively. In IMB, theevents are separately analyzed with the threshold of 0.95 GeV in visible energy.

1.33 GeV. Each data sample is arranged to two energy ranges by their reconstructed momentum. The figures also show the simulation without any oscillation (hatched box), andthe best fit with νµ → ντ oscillation (bold line). The interpretation of the low R value has
two choices, one is the νµ → νe oscillation, the other is the νµ → ντ oscillation. The resultsof the zenith angle distribution shows the deficit in upward-going µ-like events, while e-likeevents shows flat distributions. Therefore, latter νµ → ντ scenario is strongly favored. The
allowed region of the mixing angle and ∆m2 are;sin2 2θµτ > 0.88,

1.5 × 10−3 < ∆m2 < 5 × 10−3 eV2in two flavor oscillation,and0.4 < sin2 θ23 < 0.7, 1.5 × 10−3 < ∆m223 < 5 × 10−3 eV2
sin2 θ13 < 0.35

in three flavor oscillation,

at 90% confidence level, as shown in Figure 1.1 (left).
In addition, the flux of upward-going muons has been analyzed in Super-Kamiokande[18] and MACRO experiment [19]. Since the upward-going muons are produced by the highenergy νµ interaction in the underground, their zenith angle distribution also represents
the νµ oscillation. Both experiments showed the deficit in vertical direction comparing to
the horizontal direction, which gave the consistent parameter region in νµ → νx oscillation.
12

Figure 1.2: Zenith angle distribution of the µ-like and e-like events [10].

1.2.3

Solar neutrino observations

Solar neutrinos are produced by the nuclear interactions inside the sun. They are electron
neutrinos with several 100 keV up to 15 MeV energy. Distance between the sun and theearth is 1.5 × 108 km. Therefore, the sensitivity of νe → νx oscillation reaches down to∆m2 ∼ 10−11 eV2. Two detection methods are used to analyze the solar neutrinos.
One is the measurement of the integrated amount of isotopes produced by the neutrino
reactions as follows;νe + 37 C` → e− + 37 Ar(1.17)(1.18)

in Homestake experiment [20], andνe + 71 Ga → e− + 71 Ge(1.19)

in SAGE experiment [21], GALLEX experiment [22] and GNO experiment [23]. The results
are summarized in Table 1.4. They show significantly lower neutrino flux comparing to theStandard Solar Model (SAM) of Bah call and Pinnsonneaut model (BP) [24].
13ExperimentHomestake
SAGE+GALLEX+GNO
Kamiokande
Super-Kamiokandeobservation
Ethres.
Ar radioactivity 814 keV
Ge radioactivity 233 keVwater Cherenkov 7.0 MeV
water Cherenkov 6.5 MeV

Measured / BP2000
0.34
0.58
0.55
0.48

Table 1.4: Results of the solar neutrino measurement, which are the measured flux overprediction given by BP2000. These comparisons are refereed from [24].

The other is the water-Cherenkov-type neutrino detector, which observe the Cherenkov
photons from following elastic scattering.
νe + e− → νe + e−

(1.20)

Kamiokande experiment [25] and Super-Kamiokande experiment [26] gave the results (Table 1.4) that also showed lower flux than expectation of SSM of BP model.
Recently, Super-Kamiokande has presented the energy spectrum of the recoil electrons
and the flux difference between the daytime and the nighttime [27] which can be affected by
the matter effect of the earth. They gave the constraint to the oscillation parameters. As
a result, νe → νx oscillation with considering the MSW (Mikheyev-Smirnov-Wolfenstein)effect only could explain all the measurement. The allowed parameter region is 3 × 10−5 <∆m2 < 1 × 10−4 eV2 and 0.5 < sin2 2θ < 0.9, as shown in Figure 1.1 (right).

1.2.4

Reactor neutrino experiments

Several experiments [28, 29] have been performed to measure reactor-produced ν¯e . The
mean energy of ν¯e was about 3 MeV. The detectors were located with the distance of a few
10 m to 1 km far from the reactor core. ν¯e is interacted by the inverse β-decay reaction ;ν¯e p → e+ n

(1.21)The detectors were filled with the liquid scintillator 1. The events were identified by thecoincidental detection of the prompt e+ signal (boosted by the two 511-keV annihilation
γ rays), and the delayed signal due to the n capture in the detector nuclei. The signal-tobackground rate was estimated by comparing the data in reactor-ON and reactor-OFF.
All the experiments found no evidence of the ν¯e disappearance. The most sensitive
result around ∆m2 = 10−3 ∼ 10−2 eV2 was carried out by the CHOOZ experiment[28]. It
1

In Krasnoyarsk experiment, the detector was a hexagonal prism filled with granulated polyethylene.

14gave us the exclude region of ν¯e → ν¯x oscillation. With the assumption of Equation 1.12,
parameters are restricted to approximately ∆m213 < 7 × 10−4 eV2 for maximum mixing,
and sin2 2θ13 < 0.10 for large ∆m2, as shown in Figure 1.1.

1.2.5

Accelerator neutrino experimentsνµ (ν¯µ ) oscillation has been searched using the accelerator-produced neutrinos. The experiments which have the most sensitive results are listed below, and summarized in Table
1.2.
• νµ → ντ , in ∆m2 > 1 eV2 region.
Two experiment, CHORUS and NOMAD has searched ντ events from the oscillationin the 800 m base line. Almost pure νµ beam with about 25 GeV average energy is
produced from the π + decay in the production beam-line. In CHORUS detector, ντ
events can be identified by the τ observation in the emulsion target. No τ candidate
was found [30]. In NOMAD detector, ντ events can be analyzed by the kinematic
distribution of the τ decay. An the result, there was no evidence for an oscillation
signal [31]. Both experiments exclude the νµ → ντ oscillation down to sin2 2θµτ <4 × 10−4 (90% C.L.) at large ∆m2.
• νµ → νx , in ∆m2 > 0.3 eV2 region.
Two old experiments, CDHSW and CHARM were performed using the νµ beamin CERN Proton-Synchrotron. The average energy of beam was 1 to 1.5 GeV. In
each experiment, two similar detectors were placed on the near site (about 130 m
from the π + production target) and the far site (about 900 m). Comparison of theobserved events in near and far detector enable us the analysis of νµ oscillation.
Both experiments reported no evidence of the oscillation was found [32, 33]. They
excluded 0.3 < ∆m2 < 90 eV2 region for maximal mixing, and sin2 2θ > 0.05 regionat ∆m2 = 2.5 eV2 .
• ν¯µ → ν¯e , in ∆m2 > 10−1 eV2 region.
Two experiments, LSND and KARMEN, has searched for µ+ decay-at-rest ν¯µ → ν¯etransitions by the reaction ν¯e p → e+ n. Since the ν¯µ is produced from stopped µ+ , it
has a energy distribution according to Michel spectrum (Eν¯µ < 53 MeV).
The LSND neutrino detector is located 30 m far from the proton beam target. The
detector consists of a large tank of mineral oil with a small admixture of scintillator,
which enables us to tag the ν¯e interaction using the Cherenkov photons and the 2.2
MeV gamma rays from the subsequent neutron capture.
The KARMEN detector is located at a distance of 17.7 m from the production target.
The neutrinos are detected in a rectangular tank filled with a liquid scintillator, whose
15

wall is coated Gd2 O3 in order to detect efficiently thermal neutrons. The ν¯e event is
identified by the delayed coincidence of the positron and γ emission of either of thetwo neutron capture process p(n,γ)d or Gd(n,γ).
Present results of these two experiments have fairly same sensitivity in the oscillation
analysis. They show the opposite result each other. LSND reported the positive
evidence of ν¯e appearance with a oscillation probability of (0.25 ± 0.06 ± 0.04)%[34]. On the contrary, KARMEN found no indication of the oscillation signal, andexcluded many of the (sin2 2θ) − (∆m2) space where LSND defined as an allowed
region [35]. Assuming the exclusion from the KARMEN and reactor experimentresult, the remaining allowed region is a narrow band shaped area between (sin2 2θ =4 × 10−2 , ∆m2 = 0.2 eV2 ) and (2 × 10−3 , 1 eV2 ), as shown in Figure 1.1.

1.2.6

Summary of the neutrino oscillation measurements

As shown in previous section, there are three positive measurement of the neutrino oscillation.
1
2
3

Atmospheric neutrino observations ∆m2 = 10−3 ∼ 5 × 10−3 eV2Solar neutrino observations∆m2 ≤ 10−4 eV2LSND∆m2 = 0.2 ∼ 1 eV2If the neutrino has only three flavors (or closes with three generations), 3 neutrino mass
eigenvalues can not explain these three different ∆m2. Or fourth generation or other exotic
reduction scenario may be introduced to the Standard Model. Thus, these three cases must
be carefully investigated as long as the fact is surely confirmed.
KamLAND experiment [36] will attempt to analyze the disappearance of ν¯e from nuclear
power stations along the more than 100 km distance. It will cover the parameter range ofcase-2 (∆m2 > several × 10−6 eV2).
The parameter range of case-3 will be investigated by the further measurement of KARMEN, and by MiniBooNE experiment [37] in Fermilab.
In order to confirm the parameter range of case-1, accelerator experiments, K2K experiment [38] has been performed since 1999. K2K experiment is the first terrestrial “longbase-line” experiment with artificially produced νµ beam. If the ∆m2 exists over 2 × 10−3
eV2 , K2K is expected to provide significant evidence of the νµ oscillation, and to give
constraint on the parameter space.
Entire understanding of the neutrino oscillation will imply the finite neutrino mass andthe non-zero lepton mixing, which overtake the Standard Model.
This thesis is the report of the result for νµ disappearance in K2K experiment.

16

Chapter 2
Overview of the K2K Experiment
2.1

Concept of the Experiment”K2K experiment” (KEK-PS-E362 [38]) was proposed and have been performed, in order
to investigate the neutrino oscillation asserted by atmospheric neutrino observations. The
experiment uses muon neutrinos, which are produced by the pion decay in flight as;
π + → µ+ νµ(2.1)

Large amount of pions are produced by hadron interactions of the high energy proton beam,provided by 12 GeV proton synchrotron (KEK-PS) in High Energy Accelerator Research
Organization (KEK). Generated neutrinos travel through the 250 km distance and areobserved at Super-Kamiokande detector (SK). Neutrinos are also measured just after the
production by near neutrino detectors, which are located 300 m downstream of the target
in KEK. Comparison of both observations gives us evidence (or exclusion) of the neutrino
oscillation.
Main characteristics of K2K experiment are;• Sensitivity around ∆m2 = 10−2 ∼ 10−3 eV2 range.
As described in previous chapter, atmospheric neutrino observations have asserted
the oscillation parameter ∆m2 is in this range. Since the mean energy of the neutrinos
is 1.3 GeV, 250 km base line is the appropriate (Formula 1.10).
• Large far detector.
One of the difficulty of this type of experiment is low statistics due to the small
cross section of neutrinos and due to the small acceptance for 250 km far site. The
most massive neutrino detector, SK gains enough statistics of the events. In thisexperiment, expected events at SK is typically 0.4 events per day without oscillation.
17

200mν µ

Beam dump& MUMON

Super-Kamiokande
250km
KEK

π

    
    
&    
Target    





    HORN
magnets
    

p





          




Line      ν








    

























 

















 
 detectors
 
 


Near

Beamν
 PIMON




Dec
yvolu
m ea

ction

80m

extra

To SK

       
           12GeV-PS   Figure 2.1: The schematic view of K2K experiment.

• Simultaneous measurement at the neutrino production site and at the far
site.
The neutrino beam properties can be experimentally measured before oscillation.
Comparison of the observation in both site enable us to cancel most of the neutrino
flux uncertainty as well as cross section uncertainty.
• Accelerator-produced neutrinos.
Neutrino beam can be controlled and monitored by the measurement of protons,
pions and secondary muons.
Basically the neutrino oscillation is studied by the comparison of the neutrino event
distribution at near detector and the far detector. The analyzed quantities are mainly
listed below;
 Number of νµ events.
This (and next) kind of analysis is called ”νµ disappearance”. When deficit of theneutrino event rate is observed at the far site comparing to the observation at thenear site, this proves the existence of the neutrino reduction mechanism, which isprobably the neutrino oscillation (or some exotic scenario like neutrino decay).
18 Energy spectrum distortion of νµ events.
When the observed neutrino reduction is caused by the neutrino oscillation, the reduction probability depends on the neutrino energy as shown in Formula 1.10. Therefore,
measured energy spectrum of νµ at the far detector differ from the expected spectrum that is obtained from the measurement at the near site. This distortion patternstrongly proves the oscillation of νµ → νx mode. By fitting the distortion patternwith Formula 1.10, the two oscillation parameters θ and ∆m2 can be determined.
 νe event appearance. 1
When mixing angle between νµ and νe is not equal to zero, some νµ may oscillate toνe . This oscillation mode is studied by searching for the electron production by νeevents at the far detector.
 Events from neutral current (NC) interaction.
When the νµ oscillation is observed, the study of the number of NC interaction gives
the distinction of νµ → ντ or νµ → νsterile .
This thesis focused on the study of the number of event comparison between the nearsite and the far site. So far, event statistics is not enough to discuss about the energy
spectrum.

2.2

Analysis of the Muon Neutrino Disappearance

As emphasized in previous section, νµ disappearance is investigated by means of the comparison of the observed number of νµ events in both sites. For the comparison, near detector
measurement is expressed by following “number of expected event at SK”;
SK
Nexp
=

near
Nobs
Φf ar · σf ar · Mf ar·· SKnear Φnear · σnear · Mnear

where,
near
Nobs
near , SKΦnear , Φf ar

σnear , σf ar
Mnear , Mf ar: number of observed events at near detector: event selection efficiency: expected neutrino flux
considering the angular acceptance difference: neutrino cross section: fiducial mass.

SK
SK
This expectation Nexp
and the observed number of events Nobs
are compared.
1

Present studies and results of νe appearance mode is described in other thesis [39].

19

(2.2)

2.3

Components Design

K2K experiment was designed and constructed with satisfying following key issues.
• Similar near detector to the far detector.
A water-Cherenkov-type detector named “1-kilo-ton detector (1kt)” was constructed
as a near detector, to avoid uncertainty of the neutrino cross section. Then, σnear
and σf ar in Formula 2.2 are strictly canceled, and the large part of the uncertaintyof near and f ar are also canceled.
• Experimental measurement of Φf ar /Φnear .
The flux ratio of Φf ar /Φnear basically obeys the L−2 dependence where L < 300m at
near site and L = 250km at far site from the production point of neutrinos. However,the decay point of pions depends on their energy and geometry of the decay volume.
In addition, neutrinos are focused to the forward direction due to the Lorentz boostof pions, and the directional distribution depends on the pion direction and energy
distribution. There has been large uncertainty in hadron interaction process at thisenergy range, and the simulation of pion production is not reliable enough to predict
the neutrino flux.
Then, the experimental measurement of pion energy and angular distribution is performed using the ”pion monitor (PIMON)”. The result can be compared to various
Monte Carlo simulations with different hadron interaction models. The confirmed
pion production model provides the neutrino energy and angular distribution. And
finally, the flux ratio of Φf ar /Φnear is obtained.
• Neutrino beam pointing to SK.
The neutrino beam should be pointed to SK. The neutrino beam has a broad profile
due to the pion divergence and the smearing by the pion decay. Figure 2.2 shows the
expected profile broadness at SK site, and the energy spectrum estimated by Monte
Carlo simulation (which is described in Chapter 4). According to these figures, thepointing accuracy of 3 mrad is needed to keep the neutrino flux and the spectrum
shape.
Direction of the neutrino beam is generally derived from the pion direction, which isdetermined by the two focusing magnets, named “HORN magnets”. Direction of theneutrino beam is confirmed at the near detector. Muon Range Detector (MRD) with
7.6 m ×7.6 m of transverse area, effectively measure the spatial profile of ±10 mrad
range. In addition, secondary muons are measured by Muon monitor (MUMON) on
spill-by-spill basis. The muon profile center also confirms the neutrino beam direction.
These components, that is, HORN magnets, MRD, and MUMON should be alignedwith enough accuracy. Positions of SK and KEK were measured using Global Posi20

1200

2

Number of neutrinos / cmnumber of neutrinos/ cm

2

x 10 31400

1000

Arbitrary unit                           neutrino         (at super-Kamiokande)          5    flux vs radius  
x10 12 
  
 10 
  
  
  8
  
Profile at SK  6
  
  4
  
  2
  

 


 off


  02468 10mrad

Spectrumat SK
center4mrad off
8mrad off
12mrad off

800

600

400

200

0

0

0.5

1

1.5

2

2.5

3

3.5

radius (km)

0

1

2

3

4 GeV

Figure 2.2: Left: Neutrino spatial profile at SK site. Right: Energy spectrum of the
expected neutrino at SK site, without oscillation. Both figures are made by the Monte
Carlo simulation.

tioning System (GPS) survey within 0.01 mrad accuracy [40]. Table 2.1 shows the
position of the production target in the beam line (KEK) and center of the SK watertank. Following this survey point, these components were carefully aligned within
0.1 mrad accuracy.
• Time synchronization.
Expected signal rate at SK is about 0.4 event per day (no oscillation), on the other
hand, the fully-contained events from atmospheric neutrino is about 8 events perday. The most effective way to identify beam associated neutrino events is timesynchronization with the KEK-PS. Simultaneous reception of GPS signal at both site

Latitude
000
Target at KEK 36 09 14.9531 (N)000
SK center36◦ 25 32.5862 (N)distance from KEK to SK
downward tilt◦

Longitude
altitude above sea000
140 04 16.3303 (E)70.218 m
000◦
137 18 37.1214 (E)371.839 m
249.83 km
000
1◦ 04 30◦

Table 2.1: The positions of the production target at KEK and the center of SK water tank,measured by GPS survey [40].

21provides the time calibration with the order of 100 ns precision. Two GPS receivers
are prepared at each site. Since the proton beam is provided by fast-extraction with
1.1µs spill width, we obtain the order of µsec time window for event selection in every
2.2 sec repetition cycle. Thus, the background rate is suppressed to the order of 10−5comparing to the signal rate.
Considering these issues, following components were designed and constructed.
∗ KEK-PS and proton beam line,
which accelerate protons and bent them toward the direction of SK.
∗ Proton beam monitors,
which measure the intensity and profile of the proton beam along the proton beamline, to monitor the beam stability.
∗ Target and two HORN magnets,
where pions are produced by the hadron interaction, and are focused by toroidal
magnetic field of two HORN magnets.
∗ 200 m long decay volume,
where π + decay to νµ and µ+ . After the decay volume, an iron and concrete beam
dump stops all charged particles and only neutrinos are pass through the earth toreach the near detectors and SK.
∗ Pion monitor (PIMON),
which is occasionally put in the secondary beam line, in order to measure the pion
momentum and angular distributions. The obtained distribution provides the energy
spectrum shape of the neutrino beam and the flux ratio Φf ar /Φnear .
∗ Muon monitors (MUMONs),
which measure high energy muons above 5.5 GeV, in order to confirm the neutrino
beam pointing on spill-by-spill basis.
∗ Near neutrino detectors,
which consist of following detectors.
– 1-kilo-ton water Cherenkov detector (1kt),
which is a miniature detector of SK. The obtained neutrino events are used forthe comparison to the events in SK.
– Muon Range Detector (MRD),
which has a large coverage and a largest neutrino event rate, The results are used
for the neutrino profile determination and also give the neutrino beam stability.
22

1995

Proposal [38] was approved at KEK.
Components design was started.
1996
Civil construction was started.
1998
Detector components were placed.
Civil construction finished.
Feb., 1999 Proton beam was extracted to the target.
Mar., 1999 Horn has been operated.
June, 1999 We started stable data taking with 200 kA. horn current
Oct., 1999 We started stable data taking with 250 kA. horn current
Table 2.2: The history of K2K experiment.

– Fine grained detector system (FGD),
which has a water tubes with scintillation fiber tracker as a neutrino interaction
target. This is used for the neutrino energy reconstruction, and the study of theneutrino interaction.
∗ Super-Kamiokande detector (SK),which is used as the far neutrino detector.
Figure 2.1 shows the location of these components. In the next chapter, detailed structure
and performance of them are described with this order.

2.4

History of K2K

Table 2.2 summarizes the history of K2K experiment. Stable data taking has been
performed since June 1999. In this thesis, we analyzed the data with 100 days from June
1999 to June 2000 corresponding to 2.29 × 1019 protons on target.

23

Chapter 3
Experimental Components
K2K experiment consists of the accelerator, neutrino beam line, near detector systems,
and 250km far site detector, Super-Kamiokande. The brief explanation of the purpose andperformance in this experiment are described in following sections.

3.1

Neutrino Production Beam Line

3.1.1

Accelerator and proton beam line

KEK-12GeV Proton Synchrotron (KEK-PS) in High Energy Accelerator Research Organization (KEK) is used [41]. Its specifications are summarized in Table 3.1. More than
7 × 1012 protons per one cycle are accelerated up to 12 GeV in kinetic energy. Each
extracted beam spill has 9 bunches in 1.1µs spill length. The repetition cycle is 2.2 second.
After protons are accelerated to 12GeV, they are extracted by the kicker magnet system
at ”EP1-A” section. Kicker magnets changed the proton orbits inside the PS and four
septum magnets separate them to the extraction line. All the 9 bunches are extracted justin one cycle of 1.1µs, named ”single turn extraction.” This fast extraction is effective to
our neutrino experiment to distinguish the beam-associated events from the backgrounds.
The extracted beams are collimated and lead to the target section by the proton beamline named ”EP1 neutrino beam line” (shown in Figure 3.1). In this beam line, protons
are bent about 90 degree to the West-North-West at the final section, pointing to SK [40].
61 quadrupole magnets and 44 dipole magnets are used in this 400 m section.

3.1.2

Proton beam monitors

In order to control and monitor proton beam, beam monitor systems are used along thebeam line, as shown in Figure 3.1. With these monitors, following issues are monitored;
24

Accelerator components

Operation mode for K2K
Typical intensity in main ring
Typical intensity after extraction
Number of bunches
Bunch repetition
Total spill length
Repetition cycle

Pre-injector (750 keV, Cockroft-Walton acc.)
LINAC (40 MeV)
BOOSTER (500 MeV)
Main ring (12 GeV in kinetic energy)
fast extraction (single turn) to EP1-A
7 × 1012 protons per spill
6 × 1012 protons per spill
9
about 120 ns
1.1µs
2.2 sec

Table 3.1: Specification summary of KEK-PS for K2K experiment.

80m




































































Near
detectors

      y v o lu m  
Deca
e

200m

Beam dump& MUMON(TGT)  C,S          C,S     S       
C,S
S
S
C,S
S
     S    C,S             (V39)              &          C,S   
Target                  
 magnets
                 
HORN
           C,S       C : CTbeam intensity
S : SPIC
beam profile                          
C,S                   C,S   
















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









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

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
S
TGT-CT
3
3

4
4
C,S
S
TGT-SPIC2
1211 21211 4343 4343 65 65 V39-SPIC
 
 

2121  2121 4343  4343  6565 6565    Profile monitor 


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
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


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            2212121  2212121 43434343  43434343  656655 656655 proton
S
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

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 
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"21212121 9 21212121 9 434343 . 434343 '' 656565, '' 656565 '' 
"C,S
2nd-HORN

#
#
#
#

$

$
$



78
78
78
78
78
78
77 8
77 
8
8
87877 8
87877 1st-HORN
#
#$
#$
$
$
$#$##
78
78
78
78
78
78
&%&% &%&% 99&%&% 99:: 0/0/ 43 -.- 0/0/ 43  ('('( 65+,+  ('('( 65  ('('( *)*)*)  *)*)*)  *)*)*)  *)*)*)  
#
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77 8
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S 
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 
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
pions
line C,S
 
 
 
 
 
 
 
 
   (Target)    beam    
S  











































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


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 C,S






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
S
S
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
C,S






PIMON
 
 
 
12GeV-PS
Figure 3.1: Location of the neutrino production beam line components and monitors.
Lower-left figure shows a magnification view of the target area.

25

Figure 3.2: Oscilloscope photograph of the typical beam time structure from CT. Bunch
structure is clearly shown while it is smeared due to the time constant of CT. Signals areusually measured with integration during the one spill gate time (1.3µs) by ADCs

• Proton beam intensity, and transport efficiency.
• Proton beam profile, in particular, at the target section.
Intensity monitors
Proton intensity is measured with 13 Integrated Current Transformers (CT), which picksup the wake field when protons pass the coils. Figure 3.2 shows the typical signal shape of
the proton beam. The signals are lead to the control room several 10 m to 100 m far outof the radiation area, and connected to the charge integration ADCs with full beam spillgate of 1.3µs. The CT’s inner diameter is about 12cm, which is the same size as the beam
pipe and large enough to contain the proton beam. Most of the CTs are placed along thevacuum pipe. One CT named ”TARGET-CT” is placed in front of the target. The protontransport efficiency is monitored by CTs.
The CTs were calibrated by pulsed current source. The result shows the ±10% systematic
error, due to the noise induced at 100 m long coaxial cables.
Profile monitors
Proton profiles are measured by 27 Segmented Plate Ionization Chambers (SPIC), shownin Figure 3.3. SPIC is the ionization chamber consist of three copper foiled capton sheetswith 1 cm gap. Central plane is the anode (negative high voltage) and the outer ones are
26

to ADC

to ADC

Protonbeam

Protonbeam-HV

Figure 3.3: The schematic view of the Segmented Plate Ionization Chamber (SPIC).

the horizontal and the vertical readout cathodes. Size of the sensitive area of the SPICs
is 4.1 cm square for one most downstream SPIC ”TARGET-SPIC”, and 16 cm square forother ones. They sufficiently cover whole proton profiles. The thickness of the sheet is
28µm. The gap is filled with helium. The electrons are collected by high voltage (typically−1000 V) between the copper cathodes and anodes. Cathodes are 32 of separated stripes
with 1.27 mm and 5 mm pitch for ”TARGET-SPIC” and others, respectively. The signals
are read by charge sensitive ADCs.
Obtained proton profiles are continuously monitored. In particular, V39-SPIC andTARGET-SPIC which are located between final bending magnet ”V39” and the target,
are used to obtain proton emittance (profile and divergence), with 128 cm in free space(shown in Figure 4.1).
The further description about the SPIC is in [42].

3.1.3

Production target and focusing devices

Pions are generated from the hadron interaction of 12 GeV protons at the target. In orderto focus these pions toward SK, two toroidal horn magnets provides the magnetic field asshown in Figure 3.4. ”1st-HORN” has the aluminum target rod inside, in order to achieve
high focusing efficiency, overcoming a rather large beam spot size. ”2nd-HORN” is thereflector which is located at 10 m downstream of the 1st-HORN.
Electrical current is supplied along the beam axis between inner and outer conductors,
which wakes the toroidal magnetic field between them, and also partially inside of the target
rod. When current Ihorn (kA) is supplied, the strength of the magnetic field B (kGauss) at
27

Figure 3.4: Schematic view of the two horn magnets.

radius r (cm) is given by;
B=

Ihorn
,
5·r

where,(r ≥ R : rod radius)(3.1)

Hence, the maximum magnetic field is 33 kGauss at R = 1.5 cm rod surface at Ihorn = 250
kA. This field focuses the positive charged particles to forward direction and sweeps out
the negative particles. Thus π + is selectively collected to get almost pure νµ . In addition,
protons are also focused along the target, which improves the targeting efficiency. This twohorn system enhances neutrino flux above 0.5 GeV by 22 times of one with no current case(see Figure 3.5).
1st-HORN is 0.70 m in diameter and 2.37 m in length. Target, inner, and outer conductors are made of aluminum alloy 6061-T, which is chosen for the reason of the lightdensity, strength and electrical conduction. The length of the target rod is 66 cm. The
diameter is 2 cm in June 1999 run, and 3 cm since Oct. 1999. The target corresponds to 1.7
interaction length [1]. Monte Carlo simulation (described later) shows almost all protons
interact in the target, including elastic scattering. 2nd-HORN is 1.65 m in diameter and2.76 m length, in order to focus spread low energy pions. Except the target, central region
is vacant to avoid loss due to pion’s secondary interaction. Both horn conductors are kept
thin as much as strength requirement permitted.
Both horns have perfect cylindrical symmetry except four current feeders attachments
at the front side. Pulsed electrical current is supplied to both horns. The peak current is
200 kA in June 1999 run and 250 kA since Oct. 1999. The pulsed cycle is synchronizedwith the beam extraction of 2.2 sec. repetition period. The total pulse length is about 3
ms and the timing of the current peak is adjusted to the beam timing, which is quite flat
during the beam spill (1.1µs). The current is made by the HORN power supply with 6 mF
28

Arbitrary unit of neutrino flux

with
HORN current

without
HORN current
0

1

2

3

4

5

Neutrino energy (GeV)

Figure 3.5: Expected neutrino flux at the Super-Kamiokande site in Monte Carlo simulation, with (solid) or without (hatched) horn current. Target diameter is 30 mm and current
is 250 kA. Above 0.5 GeV, enhance factor is about 22.

capacitors and the thyristor switches. The pulsed operation is needed to avoid the thermalmelt down and to reduce continuous electrical power. The current is measured by CTs putin the each power feeders, with Flash-ADC readout.
Magnetic field inside of the HORN was measured using coils for pro-to-type of the 1stHORN (target rod is 2 cm diameter). The radial distribution is roughly consistent with thedesign and the azimuthal symmetry is confirmed within the measurement error of 15% [43].
The only non-symmetry structure in the azimuthal direction is four current feeders, which
are commonly used both this pro-to-type HORN and the actually used one. Therefore,±15% error is quoted as the azimuthal uniformity of the field in following analyses.
Further detailed issues about the horn systems are described in [44, 45].
Proton targeting and the pion focusing is also monitored by a large SPIC type ionizationchamber, which is installed at the entrance of the decay volume (about 7 m downstreamof 2nd-HORN). The coverage is 2(h) × 1.5(v) m and it contains 192 and 160 channels forhorizontal and vertical projection. It is used for monitoring to be kept the spatial symmetryof charged particles.

3.1.4

Decay volume

Focused pions (mainly π + ) are sent to the 200 m long decay volume which start at 19 m
downstream from the target. The diameter is 1.5 m in the first 10 m section, 2 m in thefollowing 90 m section, and 3 m for the remaining 100 m section. It is filled with helium29

at 1 atm. to avoid pion absorption loss and ”un-controllable” pion production in the gas.
In the decay volume, π + decays to µ+ and νµ .
π + → µ+ νµ(3.2)

Because π + is strongly boosted, νµ is also emitted towards the Super-Kamiokande withinsome decay angle of several 10 mrad order. The neutrino profile is broad more than several
km at Super-Kamiokande site.
Finally all the charged particles are stopped at the beam dump just after the end of thetunnel. The dump is consist of 3.5 m iron block, 2 m concrete and about 60 m soil (seeFigure 3.15). Only the neutrino can pass through this shield to the near neutrino detector
and SK.

3.2

Pion monitor (PIMON)

3.2.1

Goal of PIMON

Most of neutrinos come from well-known two-body decay of pions, as Formula 3.2. Therefore, neutrino flux in each acceptance can be predicted from the measurement of pion
momentum and angular distributions.
When pions with momentum pπ decays to neutrinos, the energy of the neutrinos is;Eν =m2π − m2µ2(Eπ − pπ )(1 + γ 2θ2 )(3.3)

where β = pπ /Eπ and γ = Eπ /mπ are the Lorentz factors, and θ is the polar angle ofneutrino with respect to the pion direction in the laboratory flame. The neutrino flux dΦ
in small solid angle dΩ is;
N
dΦ
=
2
dΩ
4πγ (1 − β cos θ)2(3.4)

where, N is the number of decayed pions. The decay probability is basically given as afunction of the pion velocity. In realistic case, the geometrical constraint of pion decay
volume is considered. Pion flight and decay is traced using Monte Carlo simulation.
Pion monitor (PIMON) intends to measure 2-dimensional distribution of pion momentum (Pπ ) and divergence (θπ ) space just after the HORN magnets. From this (Pπ , θπ )distribution, the neutrino flux at both detector and their ratio can be obtained with previous formula.
30

arbitrary unit

10e+, e-

6

10

5

10

4

ProtonThreshold for
n=1.00242

Threshold for
n=1.00024

Pion +
Pion Muon

0.996 0.9965 0.997 0.9975 0.998 0.9985 0.999 0.9995

Particle β
Figure 3.6: β distribution of protons, pions, muons and e± after the 2nd-HORN. In thisfigure, (radius) < 60 cm, and tan θ < 50 mrad from the beam axis, are required.

3.2.2

Cherenkov technique for pion identification

The most severe requirement for PIMON is the pion identification from the large background of protons and electrons. Figure 3.6 shows the beta distribution of protons, pions,
muons and e± after the PIMON site, in Monte Carlo simulation. Protons dominate overpions by about factor 2.
Cherenkov photon measurement distinguishes the pions from protons. Since our beamenergy is 12 GeV in kinetic energy, proton momentum is naturally less than 13GeV/c.
Then Cherenkov threshold is set at over the threshold of 13GeV/c protons. Electrons andpositrons remain to the main background for high energy pions.

3.2.3

Cherenkov technique for simultaneous measurement of(pπ , θπ )Cherenkov photons is emitted as the corn shape with half opening angle of;cos θc =

1
nβ

(3.5)

around the particle direction. Therefore, particle direction is obtained from the ring direction. And, Cherenkov ring radius gives the particle momentum.
In order to collect these Cherenkov photons, a spherical mirror is used. Figure 3.7
explains the characteristic of the spherical mirror. The spherical mirror focuses the light31

with an incident angle to a fixed position of the focal plane. That is, all the Cherenkov
photons from the charged particles with certain momentum and certain direction gathers
to the unique point on the focal plane, independent of its emission point. When a pion
with velocity β (= ppi /Epi ) and radial angle θπ on the vertical direction, emitted Cherenkov
photons are focused on y-axis of the focal plane at;
y = L · tan(θπ ± θc )


= L · tan θπ

v
u
u
±t

n2
1 + (mπ /pπ )2



− 1

(3.6)

where, L is the focal length, which is the half of the curvature radius of the spherical mirror.
Most of pions have only the radial divergence rather than the azimuthal angle, because
the magnetic field of HORN does not give any azimuthal momentum. It is necessary
to know only the radial divergence, in order to obtain neutrino flux with Formula 3.3.
Therefore, PIMON can concentrate to measure radial divergence.
If simple circular spherical mirror is used, many Cherenkov rings with various central
positions are overlapped, as shown in Figure 3.8-A. This image is hard to analyze. To avoid
this difficulty, a ”pie-shaped” mirror is used. The mirror is the part of the spherical mirror,
as shown in Figure 3.8-B. Since the divergence of pions is dominated in vertical direction,
the rings are aligned along the vertical axis. The photon distribution on vertical axis ismeasured to obtain (pπ , θπ ) distribution with Formula 3.6. It is assumed that obtainedpion distribution is valid for all the azimuthal part, because the HORN magnets and beamline is designed azimuthal symmetric.
Cherenkov photon distributions are observed by photo detectors. They are verticallyaligned at the focal plane. The photo detectors suffer hard radiation damage in the beamline area. Therefore, the photo detectors should be kept as far away from the beam line aspossible. For this reason, the spherical mirror is placed with a 30 degree angle to the beamaxis, to deflect Cherenkov photons to the photo detectors. This makes small sphericalaberration acceptable for the analysis.
Considering these characteristics, PIMON was designed as shown in Figure 3.9. Using
this mirror optics, observable Cherenkov photon distributions are simulated as shown in
Figure 3.10. These distributions are obtained with certain refractive indices, and the realistic pion distributions simulated by our standard Monte Carlo simulation (this called“beamMC”, described in Chapter 4).
Designed refractive indices are provided by gas. In order to obtain high refractive index,
freon gas R-318 (C4 F8) is used. The refractive index n of certain gas is given by following
Lorentz-Lorenz formula;n2 − 1
Nα
=
2
n +2
30
32

(3.7)

Sphericalmirrorat Focal plane

Focal planeθcθπSphere center

y+
y−

L

2L
at Focal plane

θ’c
θ’π

Sphere center

y+’
y−’

Figure 3.7: Focusing optics of the spherical mirror.

Spherical mirror

Focal planeπSuperposition ofmany rings.
Hard to analyze.

A) Circular mirror

Rings are aligned
along the y-axisπ

PMT array
1-dimentional
read-outB) Pie-shaped mirror

Figure 3.8: Advantage of the pie-shaped mirror.

33

15

230

0

mm

64

34
ng

l
ca

le

Fo

Blind

48

24

470

th

900

Spherical
mirrorTop view

200

2750

190

2100

Beam window 910
Beam line
Beam center527

Beam view
200

2

33

600

910

Photo detector
20 PMTs110

Laser light

Figure 3.9: The schematic view of PIMON.

34

Arbitrary photon intensity

n=1.0021

n=1.0011

3000

1500

2000

1000

1000

500

0

0
-25

0

25
y (cm)-25

n=1.0006

025
y (cm)

n=1.0004

800

400

600
400

200

200
0

-25

0

25
y (cm)

0

-25

0

25
y (cm)

Figure 3.10: Y-directional slice of the typical Cherenkov photon distribution in Monte
Carlo simulation, in various refractive indices. Horizontal axis of there figures is the vertical
position at the focal plane. Only pions are simulated to emit the Cherenkov photons.

35

Pressure (atm.) Refractive index
0.18
1.000240.31
1.000410.34
1.000480.42
1.00058
0.53
1.000740.68
1.00095
0.92
1.00129
1.24
1.00176
1.70
1.00242

Cherenkov threshold for pion (GeV/c)
6.4
4.9
4.5
4.1
3.6
3.2
2.7
2.4
2.0

Table 3.2: Freon gas pressure set in PIMON measurement in Nov. 1999. Refractive indices
are calibrated by primary proton measurement described in Section 3.2.6.

where N is the number of molecules or atoms per unit volume, α is the polarizability of themolecules or atoms, and 0 is the dielectric constant of vacuum. N is given as N = P/kT
with the pressure P , the temperature T and the Boltzmann constant k. When (n− 1)  1,this formula is written as;
n−1=

α P
20k T(3.8)

After all, n − 1 is proportional to the gas pressure P at fixed temperature.
Gas pressure can be controlled by an external gas system. Changing the gas pressure,
Cherenkov photon distributions are measured with different Cherenkov threshold. Table
3.2 summarizes the freon gas pressure, refractive index, and the Cherenkov threshold, which
are used in our measurement.

3.2.4

Analysis strategy

Observed Cherenkov photon distributions (typically shown in Figure 3.10) are superpositions of Cherenkov rings from particles of various momentums and divergences, as shownin Figure 3.11.
Reconstruction of the pion population in (pπ , θπ ) bins
Several Cherenkov photon distributions are obtained with various refractive indices listed
in Table 3.2. They are fitted as weighted sum of the contributions from particular (pπ , θπ )36

(A) Cherenkov photon(C) Neutrino flux

distribution(B) Pion (p π , θ π )distributionθ π (mrad)

+

+

+50

0

=

=

2 3 4 5 6
p π (GeV/c)-50

Figure 3.11: Analysis strategy of PIMON. It explains one-to-one correspondence between(ppi , θπ ) plane and Cherenkov photon distribution, and (ppi , θπ ) plane and neutrino energy
spectrum.

bins, with considering following χ2;
χ2 =

X
k




numberof
X PMT(distobs
j −

j=1

P50

n=1 W (n) · dist(n)j )
σj2

2




(3.9)
k

where, k is the identifier of the measurement with certain refractive index, j is the PMT
number, n is the identifier of each pion kinematic bin, and W (n) is a pion population in
the n−th kinematic bin. By minimizing this χ2 , the best combination of pion populations
W (n) is obtained.
Prediction of the neutrino flux
Determined pion kinematic distribution gives the neutrino flux with Formula 3.3 and Formula 3.4. Neutrino flux from each (pπ , θπ ) is obtained using the pion tracing simulation
with known decay volume.
Reconstruction test using Monte Carlo simulation
Monte Carlo study of our reconstruction method was performed [46]. The reconstructedresults agreed well with the MC true distributions. Small discrepancies are assigned to thesystematic errors of fitting method in Chapter 6.1.6.
37

3.2.5

Design of PIMONAs shown in Figure 3.1, PIMON is located at downstream of the 2nd HORN magnet, andin front of the decay volume. PIMON is designed to be retractable. It is rolled into thebeam-line only during the PIMON measurement run. Otherwise, it is hidden at the escapeposition to avoid from disturbing the beam and its radiation damage.
To consider realistic circumstance of PIMON, the requirements are summarized;• Measure pions in large background of protons and electrons.
• Measure (pπ , θπ ) distribution of a few 1012 pions per every spill.
• Measure intense photons with fast spill structure. The instantaneous photon intensity
is up-to 109 photons in 1.1µs.
• Need large acceptance for the pion beam. Most of the pions are spread to 50 cm fromthe beam axis at the PIMON site.
• Keep minimum material along the beam line. To reduce the effect of beam interaction,
beam window should be thin.
• Stand against severe radiation in the primary beam line.
• All systems and monitors are remotely controlled. Mechanical reliability of operationis needed. Because it is very hard to access to PIMON site due to the hard radiation
during the running period.
Considering these issues, PIMON apparatus was designed and constructed. Figure 3.9
shows the schematic view of PIMON.

3.2.6

Hardware of PIMONAs shown in Figure 3.9, PIMON mainly consists of a gas volume and control system, aspherical mirror, photon detectors, a monitoring system, and a readout system. These
sub-sections show the performance and calibration of them.
Gas vessel
Gas vessel is made from 5 mm thick stainless steel except for the beam window. The beam
window is placed at the beam entrance and exiting point at the cylinder part of the vessel.
The size is about 65 cm wide and 90 cm high. They are made from 1 mm aluminum(Al-6061), in order to reduce interaction in the window. This thickness corresponds to0.01 radiation length and 0.0025 interaction length. PIMON must stand with the pressure38

Figure 3.12: Wavelength dependence of the refractive index of freon R-318. The horizontal
axis shows the wavelength, and the vertical axis shows the index at 1 atm. These data arereferred from [47].

change between the −1 atm. (vacuum) and +1.1 atm. (maximum index). Resistance testof the window was performed using water. It was confirmed that they have enough strength[46].
A 50µm thick aluminum foil is set 23 cm in front of the mirror. This foil defines thefiducial area of the Cherenkov photon emission that is free from the beam window convex
and concave.
All surface of the inner wall is painted black in order to reduce scattered light. An opticalslit in the middle of the mirror and the PMTs also reduces the scattered light.
As described in previous section, PIMON is occasionally installed from the escape position. Gas vessel is set on a movable support. It is remote-controlled with a position meter.
The alignment of the vessel and mirror optics is ensured by the geometrical survey within
1 mm accuracy.
Gas system
The gas supply system consists of freon gas bottles and a buffer tank, connected to PIMON
by 100 m pipe with 1 inch diameter. Used gas is recirculated to the buffer tank using arecirculation pump. In addition, two vacuum pumps are prepared to set low pressure below
1 atm. The supply system is heated, because freon R-318 has low vapor pressure of about
2.3 atm. at 20 degree.
Refractive index of the freon gas is shown in Figure 3.12. There is wavelength dependenceof the refractive index. Wavelength of the observed Cherenkov photon is determined by theemitted wavelength distribution (proportional to λ−2 ), mirror reflectivity, transparency ofthe quartz window on PMT surface, and the quantum efficiency. In our case, it is assumed
that 160 to 300 nm is the dominant wavelength range.
39

<< Top view >>


















































He-Ne laser

λ0

double slit

screenvacuumLaser beam
expanderPMT

gas

Microscopedconvex lens

stripe image
on the screen

filled the gas

Figure 3.13: The schematic view of the interferometer.

The refractive index of freon gas is measured by two methods.
• One is the measurement using an interferometer as shown in Figure 3.13. He-Ne
laser light is expanded through the beam expander. It goes to a vacuum vessel thatis separated into two regions inside. One part of it is kept at vacuum (∼ 1 torr) andthe other is being filled with gas with a constant rate. Laser light passes a double
slit and a convex lens to make stripe image on the screen in front of a microscope.
The stripes slide proportional to the gas pressure. The number of stripes which passthrough the one fixed point on the screen is counted by eyes or a photo-multiplier.
This number N is related to the refractive index n by the following formula;
N=

n−1
λ0 /d

(3.10)

where λ0 is the wavelength of the laser (632.8 nm), d is the length of the vacuum
vessel (16 cm).
Obtained refractive index itself cannot be used for Cherenkov photon calculation,
because wavelength of used laser light is different from that of Cherenkov photons.
Although, this measurement is used to confirm the gas purity of the freon gas stored
in the buffer tank.
• The absolute value of the refractive index is obtained by the measurement of theCherenkov photons emitted by primary protons. Gas pressure of PIMON is set at2.11 atm. and Cherenkov photon distribution is measured as Figure 3.14. It clearlyshows the inner two steep peaks made by primary protons with 12 GeV kinetic energy,
and two low peaks from pions. The refractive index is calculated from the distanceof two peaks using the Formula 3.6. As a result, the refractive index is n = 1.00294
at 2.11atm.
40

CT normalized ADC counts

Two peaks due to primary protons
1.2

n=1.0030

1
0.8
0.6
0.4
0.2
0
10 20 30 40 50 60 70 80
PMT position number (1 unit / 0.875cm)

Figure 3.14: Cherenkov photon distribution measured by PIMON, in 2.11 atm. Two peaks
around the center part is made from the 12 GeV proton.

Spherical mirror
The spherical mirror is shown in Figure 3.9. The radius of curvature is 6 m and the size is
60cm × 15 cm. The thickness is about 8 mm. It is made of Pyrex glass, which is partiallycoated with Al and frosted by sand to make a pie-shape. It covers about 12 degree of
azimuthal part of the beam. The mechanical hardness for the radiation and heat-up of themirror material was tested with intensive proton beam at KEK-Booster [46]. The opticsof the mirror was confirmed using an LED [46]. The absolute reflectivity is assumed about
more than 90% for Al coat, although the value is not used in the PIMON analysis because
absolute pion intensity is not used for analysis.
PIMON has a mirror monitoring system using a dye laser to check the partial radiation
damage. Light from a 410 nm dye laser is lead to the PIMON by quartz optical fiber.
The light is directed towards the mirror and reflected to the PMT array. The reflectivity
is monitored from the pulse height of the PMTs. We compared the reflectivity on the
beginning of the run with that after first-year run. The result indicated that the partial
reduction of the reflectivity suffered no damage within ±6% during 1999 run.
Photo detectors
Twenty photo-multiplier tubes (PMTs) are used as the photon detectors at the focal planeof the spherical mirror. Signal of each PMT is lead by a 100 m long cable to a charge
sensitive ADC placed in the data acquisition room outside.
41

PMTs are Modified-R5600-01Q type made by HAMAMATSU Photonics Corporation.
Notable characteristics are following;• Small size.
The size is 15.5 mm in diameter of the outer socket and 8 mm in diameter of thephoto-cathode. This size enables us to align 20 PMTs along the vertical direction
with 35 mm steps.
• Quartz window.
This is adopted for radiation hardness instead of standard BK7 glass. The radiation
hardness is tested by the exposure at KEK-PS-K3-beamline [46, 48].
• Multi-Alkali(Sb-Na-K-Cs) photo-cathode material.
This is selected due to the wide dynamic range for intense light. An utilizing MultiAlkali photo-cathode does not saturate up to 10µA, whereas a Bialkali photo-cathodesaturates at 0.1µA [49].
• Low gain.
PMTs should observe large amount of Cherenkov photon (∼ 109 photons instantly).
Low gain PMT is required not only to adjust signal level to ADC but to avoid thesignal saturation. The PMTs are modified to reduce the multiplication in each dynodestep. Typical gain in our operation is 300 in Jun.99 run and 20 ∼ 50 in Nov.99 run.
Gain of PMT was relatively adjusted and calibrated using Xe lamp before the experiment.
A Xe lamp with a diffuser was put in front of the PMT array. It provided isotropic light withorder of 107 (105 ) photons in 500 ns per one PMT for Nov.(Jun.) run. Then, suitable highvoltage was set by interpolation of the measurement with several high voltages. Relative
ratio of this gain has 5%(10%) systematic error for Nov.(Jun.) run, mainly due to theuncertainty of the measurement of Xe light profile [46].
In addition, the gain ratio was also confirmed using Cherenkov photon during the run.
Movable PMT holder enables each PMT to slide to the next PMT. Assuming Cherenkov
photon intensities were stable after proton intensity normalization, the ratio of the signal
gave us a gain ratio between the overlapped PMTs. The results were roughly agreed withthe ratio from Xe lamp measurement, although this measurement have about 20% error
due to the beam stability.
The linearity of each PMT was checked by the Cherenkov photon measurement withthe correlation of the proton beam intensity and the observed signal. In Nov. run, nosaturation was observed because of the low gain. In Jun.99 run set, PMT saturation wasobserved. The non-linearity was fitted with a 2nd polynomial function and corrected formeasured signals. The uncertainty of the non-linearity correction of about 4% is compiled
as a systematic error in June run.
42

µ monitor room
µ monitor (Si)µ monitor (IC)

11m

Fe

6m

8m

decay pipe
(He filled)

hole
earth

top view
3.5m
stairway
6.5m

5m
concrete

7m

12m
stairway
5m
2m
concrete

5.5m

Fe

decay pipe
(He filled)

4m

Figure 3.15: Left: the beam dump of the neutrino beam line and the muon monitor pit.
Right: schematic view of muon monitors, Silicon Solid Detectors (SSD) array and ionizationchamber (µ-SPIC in the figure)

3.3

Muon Monitors (MUMONs)

3.3.1

Goal of the MUMON

Muon monitors (MUMONs) measure the secondary muons after the beam dump. Thesemuons are come from π + → µ+ νµ decay in the decay volume. Since pion is a spin-lessparticle, muon profile center and neutrino’s are same. This fact enables us to monitor theneutrino beam direction on spill-by-spill basis.
MUMONs are set at the downstream of the 3.5 m iron and 2 m concrete shields, as
shown in Figure 3.15. These materials correspond to about 5.5 GeV energy loss for aminimum ionizing particle. Due to this energy loss in the shield, only 2.1% of muons canbe reached at the MUMON site (see Figure 3.16), which are roughly 104 muons per 1cm2 .
This amount of shield is needed to stop all the charged hadrons.
MUMON measurement reflects the properties of high energy pions and neutrinos. Figure
3.16 shows pions and neutrinos which is in the same kinematic region as high energymuons reached to the MUMON site. The corresponding pions are restricted at the forward(θπ < 15 mrad) and high energy (pπ > 5.5GeV/c) phase space. Its fraction is small dueto the small spatial acceptance and high energy threshold. But the high energy pions are43

Pions / 50M p.o.t.

20000
17500
15000

105
104
103

0

7500

2

4

6

8

10

12

Pion momentum (GeV/c)

MUMON canobserve

10000

5000
2500
0

Corresponding pions

10

12500

neutrinos

Muons / 10M p.o.t.

22500

10

10

Corresponding neutrinos

8

10

6

10

0

2

4

6

8

10

0

(GeV/c)

1

2

3

4
5
E ν (GeV)

Figure 3.16: Left: Muon momentum distributions before the beam dump, with marking
the threshold energy to survive to the MUMON site. Right-upper: Momentum spectrumof generated pions. Shaded area is the pions whose produced muons reach to the MUMON
site. Right-lower: Energy distributions of generated neutrinos in the beam line. Shaded
area corresponds to the shaded pions in right-upper figure. All the figures are based on theMonte Carlo simulation.

more sensitive to the overall beam direction than low energy ones. For example, when misssteering caused by incident proton profile change, or horn trouble occurred, muon profile
measured by MUMON always indicates the beam center movement. Thus, MUMON profile
works as the good monitoring of the overall beam steering towards the Super-Kamiokande.
In addition, intensity stability is also the confirmation of the proton targeting [50, 46].
In summary, objective purposes of the MUMON are mainly following two issues;
1. Monitor profile center to confirm neutrino direction on spill-by-spill basis. The requirement of the beam aiming is described in Chapter 6.3, that is ±1 mrad for 1% fluxchange. At the MUMON position of 220 m distance from the target, measurement
must be done with a precision of better than 20 cm.
2. Monitor intensity stability to confirm neutrino beam production on spill-by-spill basis.

3.3.2

Hardware set up of the MUMON

Two type of MUMON detectors are prepared, as shown in Figure 3.15. One is a large
Ionization chamber (ICH), and the other is a Silicon Pad Detector (SPD) array. ICH gives
44

the horizontal and vertical projection of the muon profile of 1.9m × 1.75m area. SPD gives
the 2-dimensional information of the muon profile of 2.8m × 2.8m area.
Ionization chamber (ICH)ICH is a segmented ionization chamber like SPIC in the proton beam line. The crosssection is 190cm × 175 cm square, in order to measure broad muon profile at the beam
bump. From technical reason, the ICH consists of six modules of 60cm × 90 cm squareplates. Three plates are in x and two plates are in y direction. Each module has parallel
three copper-plated G10 board. Central one is the negative voltage anode in both side,and the outer ones are the x and y readout cathodes. The gap is 1 cm whose accuracy is
100µm kept by the insulated spacer. The supplied high voltage is 500 V (minus voltage).
Each readout cathode is segmented to 5 cm strip lines to measure muon profile. Strips areconnected to make 180 cm long strip in x and y. Since the electric field on edge strips are
deformed in each modules, the edge strips are not used in the analysis. In the consequence,
there are 30 available strips in x projection and 28 strips in y projection.
The whole modules are installed in gas vessel filled with argon gas. One minimum ionizing
particle generates about 100 ion pairs in this 1 cm gap filled with argon gas. Average muon
density is about a few ×104 /cm2, then, each 5cm × 180 cm strip has the order of 100 pC
signal in every spill. Each signals are recorded by usual charge sensitive ADC in control
room.
ICH is basically uniform conversion factor among each channel. Only the distortion of gap
spacing may cause non-uniformity. The uniformity is calibrated using stable muon beamitself [46]. During the stable run, whole vessel of ICH is horizontally or vertically moved
to place next parts where originally occupied by neighbor parts. Ratio of two observed
signals gives the ratio of the conversion factor. First, rough distortion is calibrated, whichis expressed as the relative factor of each sub-block with 6 (for x) or 8 (for y) channels.
Next, the factor of each individual channel is calibrated. During the measurement, muon
intensity is quite stable, monitored by SPD.
The obtained relative factors are shown in Figure 3.17. This calibration was performed
several times during the long running period. They show the relative factor has been stablewithin several %. These factors are used to correct the observed muon distribution. With
this correction, profile becomes continuous as shown in Figure 6.10.
Silicon Pad Detector (SPD) array
As shown in Figure 3.15, 17 small-type SPD (size: 1 cm × 2 cm, depletion layer 300µm,
shaded in the figure) are installed along the horizontal and the vertical axis, and 9 largetype SPD (size: 3.4 cm × 3.05 cm, depletion layer 375µm) are installed as diagonal array.
When one muon make ionization loss in the depletion layer, 2.3 × 104 free electrons and45

relative constant

1.3

1.3

1.2

1.2

1.1

1.1

1

1

0.9

0.9

0.8

0.8

0.7

10

20

0.7

30

channel x

10

20

30

channel yFigure 3.17: Relative constant of the gain of each ICH channel, for horizontal (left) andvertical (right) directions measured in June 1999, Nov. 1999, and Jan. 2000. Error bars
are the spill-by-spill fluctuation only.

hole pairs are created in small-SPD and 2.9 × 104 pairs in large-SPD. They are collected by
the bias voltage of 100 V for small-SPDs and 70 ∼ 80 V for large-SPD. Observed signals areorder of 100 pC for small-SPD, and order of 1 nC for large-SPD, without any amplification.
They are read out by charge sensitive ADCs.
Uniformity of the sensitivity of small-SPDs was measured using the LED light in the test
bench. The result shows the uniformity is within ±6%.
For large-SPDs, the uniformity was measured using the muon beam. All the large-SPDs
were once aligned along the beam axis. From the comparison of observed charge, relative
factors are obtained, although they have 10% level uncertainty form the z dependence ofthe muon intensity [46].

3.4

Data Acquisition System of Beam Line Monitors

Data of all the detectors in beam line are taken with the common trigger signal of beam
spill. Two trigger signals are provided from the accelerator. They are synchronized withthe timing of the kicker magnet.
• One trigger signal comes 1.1 ms before the beam extraction. This signal is used forthe timing on HORN magnet.
46

• The other signal comes 120µs before the beam extraction. This signal is used as thebeam spill trigger for the data acquisition (DAQ) of beam line monitors and neardetectors. Simultaneously 16-bit spill number is distributed to the each DAQ site
to identify the each spill. The beam timing is recorded by the GPS time recording
system described in Section 3.7, in order to take the time synchronization to the far
detector measurement.
Signals from each detector, CTs, SPICs, (PIMON during the PIMON run), MUMONs
are measured by charge sensitive ADCs on spill-by-spill basis. The gate width of ADCs
are 1.2µs for CTs, and 2µs for other monitors. There are four DAQ system rooms and six
front-end computers (PCs) along the beam line. One general DAQ program controls eachdata acquisition process in each computer. In total, about 10000 channels of the data arecollected and recorded [45].

47

3.5

Near Neutrino Detectors

Near neutrino detector system is located at 80 m downstream of the beam dump (300 m
downstream of the production target). The neutrino beam is tilted 18.8 mrad downward
from the local horizontal plane, due to the curvature of the globe. Therefore, a detector
hall of 16 m in depth and 24 m in diameter was excavated. The detector system consistsof 1-kilo-ton water Cherenkov detector (1kt), Muon Range Detector (MRD), and Fine
Grain Detector system (FGD) as shown in Figure 3.18. They are described in following
sub-sections.

Veto/Trigger
counter

Muon Range Detector
Lead Glass
SciFi

1kt
Water Cherenkov
Detector
Neutrino Beam

Figure 3.18: K2K near detector system. Neutrino beam direction is from right to left inthis figure.

3.5.1

1kt water-Cherenkov detector (1kt)

Structure of 1kt
One-kilo-ton water Cherenkov detector (1kt) is located most upstream at the detector hall.
It consists of the cylindrical tank of 10.8 m diameter and 10.8 m height, filled with 1000
ton pure water. The inside of the tank is optically separated for an inner volume of 8.6 m
diameter and 8.6 m height, and an outer volume.
48






68020inchPMTs



1,000 ton Water Cherenkov Detector

Tyvek
8" PMTTop Inner   volume
 
 inner-PMT     (20-inch) Outer    
   volume
Black seat

20inch PMT

Barrelanti 8inch PMT

20" PMTouter-PMT (8-inch)

ν bea

m

BottomFigure 3.19: Left: The schematic view of 1kt barrel. Right: The schematic view of theinner structure.
The inner volume is used to detect neutrinos. In the inner volume, 680 photo-multipliertubes of 20-inch diameter (inner-PMTs) are equipped. 456 PMTs are on the barrel wall,
112 PMTs are on the top and 112 PMTs are on the bottom. The PMTs with 70cm grid
spacing are exactly same as those of SK. The photo-cathode of all 680 PMTs covers about
40% of the surface area of the inner volume. The remaining area of the surface is coveredby black polyethylene sheet, which suppresses the reflection of Cherenkov photons.
The outer volume is used to veto the incoming particles from outside. Sixty-eight 8inch PMTs (outer-PMTs) with 140cm spacing are placed on the outer surface of the inner
structure. 42 PMTs are located upstream of the beam direction, and 26 PMTs are at
the bottom. The surface of the outer volume is covered with the white polyethylene sheet(Tyvek), in order to collect Cherenkov photons effectively.
The 20-inch PMT has a long flight length of the multiplied photo-electron, which could
be affected by a magnetic field. Therefore, 1kt detector equips “compensation coils” surrounding the water vessel, which compensate magnetic field of earth.
Cherenkov light
A neutrino interacts with Oxygen or Hydrogen nuclei in the water, and it generates muon,
pion, electron and/or recoil nucleus (described in Chapter 4.2). Cherenkov photons are
emitted by the charged particle traveling in the water at the velocity faster than the light
velocity in water. They are emitted on a cone with respect to the particle direction. Its half49

Particle Threshold momentum (MeV/c)
e±
0.57
±
µ
118
π±
155
p
1045
Table 3.3: The Cherenkov threshold momentum in the water.

opening angle θ is expressed with the particle velocity β and the refractive index n = 1.34
for water.
cos θ =

1nβ

(3.11)

Table 3.3 shows the momentum of Cherenkov threshold in water.
The number of Cherenkov photons emitted by a single-charged particle per unit path
length per unit wavelength is given by;
d2 N
2πα
1
= 2 1− 2 2
dxdλ
λ
nβ

!

(3.12)

where α is the fine structure constant (∼ 1/137). The particle with β = 1 emits about 340
photons per 1cm in the wavelength from 300 to 600 nm, which is the sensitive range of ourPMT.
20-inch PMT
The 20-inch PMTs are used to detect Cherenkov photons. Specifications of the PMTs are
summarized in Table 3.4, and other documents [51]. The PMT can distinguish the single
photo-electron. The timing resolution is typically 2 ns.
Gain calibration
A gain of each PMT is adjusted and calibrated using the scintillator that is flashed by
Xe light with fiber (Scintillator ball) [52, 53]. The signal from each PMT is adjusted togive the same response after correcting the solid angle of each PMT and non-uniformity of
Scintillator ball surface. The uncertainty on the gain of PMT is less than 5.7%, including
the reproducibility [52].
The energy scale is calibrated by using the cosmic ray muons, which are triggered by ascintillation counter placed on the top of the tank. Muons emit Cherenkov photons, which
50

Photo-cathode area
Shape
Window material
Photo-cathode material
DynodesQuantum efficiency
Sensitive wavelength
Typical gain
Dark current
Dark pulse rate
Cathode non-uniformity
Anode non-uniformity
manufactured

50cm in diameter
Hemispherical
Pyrex glass, 4 ∼ 5 mm
Bialkali (Sb-K-Cs)
11 stages, Venetian blind type
22% at λ = 390 nm
300 nm to 600 nm, peak at 390 nm
107 at ∼ 2000 V
200 nA at gain 107
3 kHz at gain 107
less than 10%
less than 40%
Hamamatsu Photonics K.K.

Table 3.4: The specifications of the 20-inch PMT.

can be calculated by the flight length in water by Formula 3.12. We made the Monte Carlosimulation of cosmic ray muons with suitable transparency, scattering, and the reflectionof the water and PMT surfaces. The simulation gives the relation between the number ofphoto-electron and the energy deposit in the water. We analyzed two data samples. One isthe data of through-going muons which is penetrated through the bottom of the tank. The
other is the data of muons stopping inside of the tank. Figure 3.20 shows the comparisonof the data and the simulation of both analyses, after adjustment of the energy scale. The
discrepancy of the energy scale from both analyses is 5%. We adopt the energy scale fromthe analysis of through-going muons. These calibrations are performed by monthly basis.
Time variation of these calibration results are within 5% level. From these results, ±5%error is assigned as the uncertainty of the energy scale in Chapter 8.2.3.
Water purification system
Cherenkov photons are attenuated and scattered by impurities like small dust, bacteria andmetal ions in the water. These impurities are removed by a water purification system. The
system supplies 20 t/hour of pure water. The water temperature is maintained around10◦ C. Water purity is always monitored by the measurement of the electrical resistance(∼ 10 MΩ/cm). The temperature and the purity were stable during the the running
period.
Water transparency is directly obtained from the cosmic ray measurement several times
in long running period. The attenuation length is measured to be over 50 m, and stable51

stopping muons
eventseventsthrough-going muons
100

120

100

80

DATA
80

simulation

60

60
40
40

20
20

0

16

18

20

22

24

26

28

30

32

0

34

1

1.5

2

2.5

3

3.5

4

Reconstructed momentum (MeV/c / cm)

photo-electron / cm

Figure 3.20: Result of the energy scale calibration using cosmic ray muons. The left figure
is a distribution of the total number of photo-electron per 1 cm path length for throughgoing muons. The right figure is a distribution of the reconstructed momentum (calculated
from the sum of ADC count), divided by the range, for muons which stop inside of theinner volume. In both figures, data (dots) and the simulation (boxes) are overlaid. Only
statistical errors are shown.

52

20-inch PMT
x 12

SCH
ATM

Analog Timing Module

x 19
x 228

ATM
GONG

20-inch PMT
x 12

SCH
ATM
interface
SUN

x 19
x 228

SMP

ATM

SMP
SMP

20-inch PMT
x 12

Super Memory Partner

SCH
TRG

ATM

VME

x 20
x 224

online CPU

SMP

GONG

ATM
GONG
TRIGGER

8-inch PMT

PROCESSOR
x 12

SCH
ATM

x 68

TRIGGERx8
HIT INFORMATION from ATM
ATM
GONG

TKO

PMT x 748

ATM x 66

SMP x 4

online CPU x 1

Figure 3.21: The schematic diagram of 1kt data acquisition system.

during the whole run. This good transparency causes negligible effect in 1kt measurement.
Data acquisition system
Figure 3.21 shows the diagram of the data acquisition system of 1kt detector. The dataacquisition system consists of following four parts.
• Front-end electronics.
The front-end electronics records the charge (ADC) and the timing (TDC) of theanalog signals from inner and outer PMTs, and generates the discriminated pulses
for trigger logics. At the front-end electronics, buffer-amplifiers have been used for
impedance match since Jan. 2000. In 1999 run, the impedance mismatch caused
the reflection pulse. Thus, 110 m long cable was used in order to delay the reflection
signals to outside of the ADC gate, instead. Analog-to-digital conversion is performed
by a specified TKO module named ”ATM (Analog Timing Module)”[54], which is53

also used at Super-Kamiokande detector. In the ATM, analog signal is divided tofour. One of them is lead to a discriminator, two of others are lead to two ADCs, andthe other is used to take the analog sum (called “PMTSUM”) of all the signals in
the module. The threshold of the discriminator is equivalent to typically 0.3 photoelectron equivalent signal. The discriminated pulse is sent to two independent TDCs,
and also used for ADC gate. Two sets of TDC and ADC are prepared to handle
multiple events. Both ADC and TDC have 12 bit data, and the conversion factor isabout 0.4 ns/count and 0.15 pC/count for TDC and ADC, respectively.
Data are stored in FIFO memories in ATM, and sent to the rear-end electronics
through SCH (Super-Control-Head) when GONG (GO/NotGo) module receives thetrigger. In ATM, the signal “HITSUM” which corresponds to the number of hit
channels is generated with voltage of about −10 mV per hit and with the width of
200 ns.
One ATM board has 12 channels, and in total 66 ATM are used.
In 1kt detector, all the PMTSUM signals of inner PMTs are summed-up and put
into a Flash-ADC (FADC) module. Sampling frequency is 500 MHz and the dynamic
range is 8 bit. This is used to identify multiple events in one beam spill by counting
the number of steep peaks of the PMTSUM signals.
• Trigger electronics.
The trigger is made by Trigger Processor module. When linear sum of HITSUM
signals exceed to the threshold of −450 mV, which corresponds to about 40 hits at
inner PMTs in 200 ns time window, the trigger pulse is distributed to each ATM
through TRG module. In 1kt detector, the event trigger is permitted being sent
during the beam spill. TRG module records the trigger type and the trigger time.
• Rear-end electronics.
The read-end electronics save the digitalized data temporarily on four SMP modules
in one VME crate. The data on SMP are read-out by the on-line computer with dataon the TRG and data on the FADC.
• On-line computers.
On the on-line computer, data are sorted to build an event, and sent to the hostcomputer of near detector system.
Further details of the electronics are also described in [55].
Timing calibration
Hit timing information of PMTs are important to reconstruct the vertex point and theCherenkov ring. Timing calibration was performed using a laser light [52]. Light from a54

dye laser (λ ∼ 390 nm) was put into a optical fiber and lead to a diffuser ball, which was
installed in the middle of the water tank. The light intensity was continuously changed
using ND filters. We obtained the response of the hit timing as a function of the observed
charge, which is called ”T-Q map”, for each of 680 PMTs. This T-Q map was used for thetiming correction in the off-line analysis.
ATM calibration
ATM calibration gives a correction of non-linear response of TDC and ADC in ATM. With
the correction, the responses of TDC and ADC are kept linear within 1 count for full range
[55].

3.5.2

Muon Range Detector (MRD)

Design of the muon range detector
Muon range detector (MRD) is the range type calorimeter for neutrino-induced muons. It
consists of 12 iron absorber sandwiched with 13 vertical and horizontal drift tube layers(see Figure 3.22). The size of the layer is approximately 7.6m × 7.6 m. In order to get agood energy resolution, 4 iron plates at the upstream side are 10 ± 0.17 cm thick, and 8iron plates at the downstream side are 20 ± 0.2 cm thick. The total thickness of 2 m covers
up to 2.8GeV/c muons. The total mass of iron amounts to 864 tons. When the materialsof the drift tubes (mostly aluminum) are included, it amounts to 915 tons.
Figure 3.22 shows the schematic view of the drift-tube module used in MRD. These drifttube modules are originally constructed and used in VENUS detector[56] at TRISTAN.
There are 829 modules, which has 8 cells of 5cm × 7 cm cross section. One drift-tube layer
is arranged by 25 modules of 7.6 m length with a 2 cm gap between two modules. For
some layers two short modules are combined side-by-side to make 7.6 m sensitive length.
Table 3.5 summarizes the detail order of drift-tubes and iron layers. In total, there are6632 drift cells for charged particle detection. They are aligned as XX or YY pairs in one
layer between iron plates. Therefore, in ideal case, the shortest track that penetrates oneiron produces four hits in both X-view (top-view) and Y-view (side-view). Typical muontrack is shown in Figure 7.1.
The drift-tubes are filled with P10 gas, which is the mixture of 90% argon and 10%
methane. Gas circulation system [57] supplies purified P10 gas continuously. Gas quality
has been measured using a gas chromatography every week, in order to keep lower noise
rate. When the contamination level becomes higher, purifier is operated to regenerate thegas.
Each drift-tube has a 70µm diameter tungsten wire. Before construction, wire tension
was measured by searching for the resonant frequency under a certain magnetic field [57].
55LayerTubes 1X
Tubes 1YIron 1
Tubes 2YTubes 2X
Iron 2
Tubes 3Y
Tubes 3X
Iron 3
Tubes 4Y
Tubes 4X
Iron 4
Tubes 5Y
Tubes 5X
Iron 5
Tubes 6Y
Tubes 6X
Iron 6
Tubes 7Y
Tubes 7X
Iron 7
Tubes 8Y
Tubes 8X
Iron 8Tubes 9Y
Tubes 9X
Iron 9Tubes 10Y
Tubes 10X
Iron 10
Tubes 11Y
Tubes 11X
Iron 11
Tubes 12Y
Tubes 12X
Iron 12
Tubes 13Y
Tubes 13X

z-pos(cm)

436.2

478.5

520.3

562.6

609.8

662.0

713.6

764.5

815.2

867.0

917.9

968.6

H × W × t(cm3 )modules × length(cm)
25 × 760

763 × 750 × 10
25 × 760

763 × 750 × 10

25 × 760

763 × 750 × 10

25 × 760

763 × 750 × 10

25 × 760

763 × 750 × 20

25 × 760

763 × 750 × 20

25 × 760

780 × 755 × 20

25 × 760

710 × 755 × 20

25 × 760

709 × 755 × 20

25 × 760

709 × 755 × 20

modules × length(cm)
25 × 760
25 × 760
25 × 760
25 × (505 + 245)
25 × (505 + 245)
25 × 760
25 × (290 + 474)
25 × (290 + 474)
23 × (474 + 290)
23 × (474 + 290)

6 × (300 + 474) + 9 × (290 + 474)
+8 × (474 + 290)
25 × 760

674 × 755 × 20

25 × 505

674 × 755 × 20

25 × 505

1 × (760) + 16 × (300 + 505)
1 × (760) + 16 × (300 + 505)

Table 3.5: Arrangement of the drift-tubes and iron layers in MRD.
56

shield covershield cover

mm
50
mm
15

0
245

mm
250

m
15m

m
0m
760

70m m

2.5m m

35m m
50m m

shield box forfront-end electronics
teflon tubes#
forgasanode w ire(70 m
C ross sectionalview)

Figure 3.22: The schematic view of Muon Range Detector (left) and its drift-tube (right,[58]).
In addition, a cosmic ray test was performed as a whole test of the drift-tube system at
the assembly hall.
In MRD, 2.7 kV negative high voltage is supplied to each wire. The efficiency plateau
is around 2.5 kV [57]. The time-to-drift-distance relation was investigated by using cosmic
ray data. This study confirmed the VENUS parameterization of the relation:x = 2.11 × t2 + 2.72 × t(3.13)

where x is the drift length in cm and t is the drift time in µsec.
Data acquisition electronics
Wires are connected to 6-bit single-hit TDCs with 20 MHz clock generator, equipped bya front-end electronics board at each tube. The start signal is made from the beam spill
timing, which is commonly delivered to the near detector system. Stop signal is provided if
the wire signal surpasses the threshold voltage after amplifier. Therefore hit informationsin 3.2µs time range are recorded with the TDC count form 0 to 63 count. Maximum eightof front-end electronics boards are connected to one module-address-generator. Maximum
eight module-address-generators are connected to one main-address-generator. Finally all
the hit information is transfered to 16 memory-buffer-modules in TKO (TRISTAN-KEKONLINE) crate and accessed from the data acquisition computer. These data acquisition
electronics were also used in VENUS experiment[58]. All the electronics are tested before
construction.
More details about MRD components and the construction are described in [57].
57Front detector DAQ
online WS

Analog signal

monitor PC

Digital signal

DATA server
Ethernet

Muon Range
Detector

FIFO

ATM

FADC
(NIM)

ADC

MP

ADC

TDC

Sun Bit3

Fastbus

MemoryModuleFrontend
Board

F-I/F

TMC

MP

Input
Register

TKO

HPRT

MP

HPRT

ADC TDC

DORAE
moduleDiscri.
TGC
PMTs

IIT,CCD
SCIFI

LG
PMTs

1kt detector
PMTs

Figure 3.23: DAQ system of the near detector.

3.5.3

Fine grain detector (FGD) system

Further precise study about neutrino interaction has been performed using the events
interacted in the water target of SCIFI.
SCIFI [59] consists of 20 layers of scintillating fiber modules and 19 layers of watertargets. Hit information of fiber modules enables us to reconstruct the particle’s track
induced by the neutrino interaction. Total mass of SCIFI is 8.7 ton, including 6 ton waterand 1.4 ton of aluminum structure. At the both side of SCIFI, Trigger Scintillating Counter(TGC) planes provide the timing information of penetrating particles. At the downstreamof SCIFI/TGC, Lead Glass calorimeter (LG) is prepared to measure the energy of electromagnetic shower, and to identify electrons, positrons or gammas from muons [39]. Manyof muons penetrate LG to reach MRD, and are measured their energy.
In this thesis, FGD data are not used for the analysis.

3.5.4

Data acquisition system of near neutrino detector

The data of each detector is continuously taken on spill-by-spill basis, with the beam spill
trigger described in Section 3.4. Figure 3.23 shows the data acquisition (DAQ) system of
the near detector.
58

Near detector DAQ has three front end computers. A SUN computer collects 1kt datafrom ATMs and TRG module by the VME-TKO interface. One VME on-board computersreads the data from SCIFI, and the other on-board computer collects the data of MRD,
LG, TGC.
A event builder computer collects and sorts all of these data using the spill number
recorded in each data. The data size of the near detector is about 1 MB per spill.

59

3.6

Far neutrino detector

Super-Kamiokande detector (SK) is used as the far detector for our experiment. SK is alarge underground water Cherenkov detector. It is located in the Mozumi zinc mine at1000 m (2700 m water-equivalent) below the peak of Mt. Ikenoyama in Kamioka, which is
250 km west of the KEK [40]. Figure 3.24 is the schematic view of the SK detector andthe experiment site.

Figure 3.24: The schematic view of Super-Kamiokande detector and the experiment site.

SK have been running since 1996, for the various physical motivation, nucleon decay
search [60], atmospheric neutrino and upward muon measurement [9, 10, 18], solar neutrino
measurement [27, 26], and Supernova neutrino observation etc..
The detector is designed with similar detection schemes to Kamiokande detector. SK
and 1kt uses fairly the same hardware and software components, which are PMTs, water
purification systems, data acquisition electronics, and many online/off-line software codes.
The hardware components are described in following sections (and also described in [61]).
60

3.6.1

Detector features

Detector structure
The detector holds 50 kt of ultra pure water contained in a cylindrical stainless steel tankmeasuring 41.4 m in height and 39.3 m in diameter. The water is optically separated into
three concentric cylindrical regions.
The inner region is 36.2 m in height and 33.8 m in diameter and is viewed by 11146
20-inch PMTs, which are same PMTs used in 1kt (see Table 3.4). Each PMT is installed
every 70 cm on the wall, which is covered by black-sheet to avoid photon reflection. The
photo-coverage is about 40%.
The outer region completely surrounds the inner detector. It is 1.95 ∼ 2.2 m thick, andis viewed by 1885 outward pointing 8-inch PMTs (outer-PMTs) with 60cm square wavelength shift plates. The walls of the outer detector are lined with white Tyvek sheet. The
primary function of the outer detector is to veto cosmic ray muons and to help containment
identification.
The middle region (dead space) is 0.55 m thick between the inner and outer detectors.
In the middle region, there is a support structure made of stainless steel. Along with theouter detector the dead space acts as a shield against radioactivity from the surroundingrock.
Gain calibration of the PMTs
Gain of each PMT is adjusted and calibrated using the scintillator ball light [62]. A Xe
lamp with UV-pass filter is used as a light source. The light is guided by the optical fiber
to the scintillator ball in the tank. The scintillator ball consists of a BBOT wavelength
shifter, which emits light around 450 nm wavelength, and a MgO diffuser. Comparing theobserved charge in each PMT considering the distance and PMT acceptance, relative gain
constant is obtained, and used for the correction of the observed photo-electrons in physics
analysis. Accuracy of this correction is about 7% including the reproduceability and theimperfect isotropy of the scintillator ball. Since the number of hit PMTs are mainly morethan 1000 for neutrino events, the ambiguity in the energy measurement is estimated tobe less than 1% [61].
The gain uniformity is also confirmed by the direction dependence of the momentum
distributions of decay electrons [61]. The result shows that the gain is uniform within ±1%
level.
The absolute scale of gain is calibrated using the gamma emission from thermal neutron
capture of Nickel, with 252 Cf as a neutron source. The energy of the gamma is so low (6 ∼ 9MeV) that the expected number of hit photons for each fired PMT is one. The mean of 1
photo-electron distribution is 2.055 pC and the absolute gain is determined as ∼ 6 × 106
[61].
61

Water purification system
The source of the water filled in SK is the clean spring water flowing in the mine. In orderto reduce radioactive materials and to keep good transparency, ultra-pure water is filled in
the tank using a water purification system. It supplies about 50 ton of ultra-pure water
per hour. The water temperature is kept at 13◦ C to prevent the growth of bacteria.
The water quality is calibrated using laser light and cosmic ray muons [61].
• A dye laser provides the light with 337 to 580 nm wavelength to a diffuser ball, whichis installed into the tank. Using the CCD camera on the top of the detector, the lightintensity is measured at several distances.
• The Cherenkov photons from cosmic ray muons are always measured for the calibration. The travel length dependence of the observed number of photon is fitted withthe absolute gain G and the attenuation length Latt with following formula;`
Qcorr (`) = G × exp −Latt!

(3.14)

Where, Qcorr is the sum of the observed charge after acceptance correction, and ` isthe travel length between the emission point and the each PMT.
The measured attenuation length from these measurements agrees well and the attenuation
length is about 100 m. Obtained water parameters are put in the detector simulation.

3.6.2

Data acquisition system

The data acquisition system for inner detector is almost same as that of 1kt describedin previous Section 3.5.1. Figure 3.25 shows the system. 946 of ATM are used for thefunction of TDC/ADC and records an amount of hit timing and charge of each PMT signal.
TDC/ADC data are read separately by 8 on-line-computers through 48 SMP modules.
Trigger information recorded by TRG module are also read by another server computer.
The data are transfered to the on-line host computer by FDDI network and merged tomake complete events.
These electronics and computers are placed in one central hut and 4 electronics huts,
where room temperature are controlled to around 27◦ C and is kept within ±0.5◦ C. The
estimated inaccuracies coming from the temperature dependence is less than 0.4 ns and
0.3 pC for the timing and charge measurements, respectively [61].
Outer detector data are processed by a different electronics system. Signals of outer
PMTs are sent to QTC (Charge to Timing Converter) modules which generates rectangularpulses with a width proportional to the input charge. They are digitalized by LeCroy 1877
multi-hit TDC modules in a FASTBUS crate. The dynamic range of the TDC is set to62

Inner DAQ
×6

20-inch PMT´ 8· PMT ´ 11146

SCH
ATM

· ATM ´ 946

´ 20

´ 240

ATM
GONG

TKO

· SMP ´ 48

SUN classic· online computer
server ´ 9host ´ 1

onlinecomputer(server)interfaceSMP´ 6

SUN sparc10

trigger logic

trigger signal(to ATMs)HITSUM(from ATMs)

VME

onlinecomputer(host)VME

SUN classic

FDDI

onlinecomputer(server)interface
TRG

NIM

Figure 3.25: The data acquisition system for the inner detector.

be 16µs with the minimum time unit of 0.5 ns. The TDC data are read by VME memory
modules by a separate on-line server computer and then sent to the on-line host computer.
The rectangle HITSUM signals from ATMs are separately summed up to generate grand
HITSUM signal of inner detector. The HITSUM signals from QTC modules are also
summed up separately to make grand HITSUM of the outer detector. They are sent totrigger logic and recorded by TRG module. For normal neutrino data taking, three kindsof trigger levels are prepared. One of them is High Energy Trigger (HE trigger) which is
requiring −340 mV inner HITSUM signals corresponding to 31 hits in inner PMTs, in 200
ns time window. Another one is Low Energy Trigger (LE trigger) whose threshold level is−320 mV (29 hits), and the other is the series of Super Low Energy Trigger (SLE trigger)with lower threshold level than LE trigger. Since our neutrino beam have 1.3 GeV energy
in average, HE triggered events are used in our analysis (in Chapter 9.1).

63

3.7

Global Positioning System (GPS)The neutrino beam has a time structure of 1.1µs width in every 2.2 s. The time synchronization effectively work for the event selection from the continuous background.
Proton extraction time is recorded at KEK site, and at SK, the triggered time of neutrino
event is independently recorded. Clocks in both site should be synchronized within µs
accuracy. Global Positioning System (GPS) is used for this purpose [63].

3.7.1

Mechanism

GPS consists of 27 satellites maintained by the US Department of Defense (DOD). Eachsatellite has an atomic clock and the clock time and the position information of the satellite
are regularly calibrated by communicating each other. A GPS receiver always receives the
position and time information of the 4 ∼ 6 satellites. The receiver calculates the precise
position of the latitude, the longitude and the altitude, and also the calibrated time, named
Universal Time Coordinated (UTC) time stamp. The resolution is 40 ns in average and
150 ns in maximum fluctuation.
Figure 3.26 shows the time synchronization system. At each site, two GPS clocks run
in parallel, providing hardware backup as well as data quality check. In KEK site, thetwo receivers are placed at the beam line control room and the antennae are mounted on
the room roof. In SK site, GPS receiver is located at an external building near the mine
entrance. It is connected to a VME receiver at the central electronics hut by 2 km opticalfiber, and send the UTC time stamp signals every 1 sec. The VME receiver decodes thesignals to UTC time, and sends the calibration trigger signals to a LTC module. The LTC
module has a 50 MHz clock and it is synchronized to the calibration trigger signals. The
LTC module gets the timing signal, that is the timing signal of beam extraction in KEK, orthe event trigger in SK. An online computer records the LTC count of the event triggered
time and the calibration triggered time, and the UTC time provided by the VME module.
The UTC time of the triggered events are calculated with interpolation of the calibrated
UTC time by off-line analysis, as shown in Figure 3.26.

3.7.2

Stability check

In KEK, two independent GPS were compared for check. The results shows the agreement
to each other within 100 ns (half-width-half-maximum) [63].
In SK site, stability of the system is continuously monitored comparing UTC and LTC.
Figure 3.27 shows the difference of (Nn − Nn−1 ) from the nominal count (= 5 × 107 ), fromthe beginning of June 1999 to the end of June 2000. This ”cross check” proves the stablerunning of both UTC and LTC within the measurement accuracy of 200 ns.

64GPS receiver
VME receiver
decode to UTCTime stamp(every 1 s)Synchronization
LTC(50MHz clock)

Event trigger

LTC count

OnlineComputerevery 1 s

GPS receiver
VME receiver

UTC = Tn-1

UTC = Tn

LTC = N n-1

LTC = N n

LTC (50MHz)
LTC = N ev

SK event trig.
recorded DATA

LTC & UTC

LTC & UTCLTC

SK event time = Tn + (Nev -N n ) x UTC
LTC

Figure 3.26: Overview of the GPS in SK. Block diagram (upper) and the timing chart(lower) are shown.

400
200
0
-200
-400
-600
-800
-1000
-1200
-1400

0

50

100 150 200 250 300 350 400
1PPS-LTC

days since 1999-Jun-01

Figure 3.27: History plot of the LTC count during the each 1 sec of UTC time stamp. The
vertical axis shows the difference of the LTC count from the nominal count, expressed by
nsec unit. Horizontal axis shows the integrated days since June 1, 1999.

65

Chapter 4Monte Carlo Simulations
In order to study our detection scheme and evaluate various systematic uncertainties, Monte
Carlo simulation is used. The Monte Carlo simulation consists of following three modules;
1. Neutrino beam generation; “beamMC”.
This simulates from the proton injection on the production target, produces pions, focuses and tracks them until they decay to neutrino or dumped, and provides neutrino
flux at near and far site.
2. Neutrino interaction; “neutMC”.
This simulates interaction and provides the individual information of produced particles.
3. Detector simulation.
This simulates the passage of particles and the detector response.
In following sections they are described in this order.

4.1

Pion Production and Decay to Neutrino (beamMC)

4.1.1

Proton injection to the target

Proton profile, as a in-put of the simulation, is measured using V39-SPIC and TGTSPIC (Figure 6.7). As shown in 4.1, fitted profile width on both SPIC is extrapolated to
the width and the divergence on the target front-face, with the assumption of the ideal
emittance description as;
66

Parameters
Beam spread σx
Beam spread σySlope kx
Slope ky
Target rod
Rod diameter
HORN current

for Jun.99
1 mm
6 mm
−8 mrad/mm−0.4 mrad/mm
Al
2 cmφ
200 kAfor Nov.99 to Jun.00
3.4 mm
7.2 mm−2.5 mrad/mm−0.14 mrad/mm
Al
3 cmφ
250 kA

Table 4.1: Parameters for our standard simulation. Definitions are noted in text.

• Proton beam spreads by a 2-dimensional Gaussian with the width σx and σy . The
width is determined by the SPIC measurement as follows;
σx = σx2 + (σx2 − σx1 ) · (`/L)σy = σy2 + (σy2 − σy1 ) · (`/L)(4.1)

where, σx1,y1 and σx2,y2 are the x or y profile width measured at V39-SPIC and TGTSPIC, respectively. L = 128 cm is the distance between V39-SPIC and TGT-SPIC,
and ` = 37 cm is the distance between TGT-SPIC to the target front-face.
• In (x, dx) plane (x: distance from beam axis, dx: divergence), following linear correlation is assumed between them;dx = kx · x,anddy = ky · y(4.2)

where kx and ky are the parameters which were also determined by the measurement
as follows;
kx =
ky =

1
σx2
·L+`
σx2 −σx1

1

σy2
·L+`
σy2 −σy1(4.3)

For our standard simulation, proton beam center is at the center of the target rod. Table
4.1 summarizes the parameters which is used in beamMC. Studies of these parameter
dependences are discussed in Chapter 6.2.
67

V39 quadrupole
magnet



 V39-SPIC









































1st HORN
TGT-SPIC


















σ1
L=128cm


σ2 



σx  Target     rod 
 l =37cm

Figure 4.1: The schematic view of the proton emittance calculation.

4.1.2

Pion production in the target rod

There are some hadron interaction models to simulate pion production in the target material. This is one of the largest ambiguities of the Monte Carlo simulation. There have beenvarious pion production experiments around this energy range. However results of theseexperiments are inconsistent with each other.
We compare following two models;
1. GCALOR/FLUKA model [64, 65].
GCALOR/FLUKA is one of the hadron simulation package prepared for GEANT
simulation [66]. This model has larger p-Al cross section than other models.
2. Cho model [67].
This is a pion production model with a experimental parameterization of SanfordWang [68]. The differential yield of the secondary particle (d2 n/dθdp) is expressed asfollows;
d2 np
C3 ·pC4
C2= C1 ·p1−
exp − C5 − C6 ·θ p − C7 ·pB cosC8 θ (4.4)
dθdppB − 1
PB!

!

where, pB , p is the momentum of the primary and the secondary particle, respectively,and θ is the angle between the secondary particle and the initial beam axis.
The eight parameters C1 ∼ C8 are obtained from the global fit with their own measurement and other experimental results [69, 70]. The values of the parameters are
68listed in Table 4.2. Figure 4.2 shows the comparison of the experimental measurements and the fitting of this Cho model.
Cho model is used only for primary interaction of protons. For secondary interactionof hadrons, GCALOR/FLUKA is always used. Kaon production is calculated using
[71].

model
Cho

C1
196

C2
1.08

C3
C4
2.15 2.31

C5
C6
1.98 5.73

C7
0.137

C8
24.1

Table 4.2: Parameters of Sanford-Wang Formula 4.4, for Cho model.
As described in Chapter 6.1, the pion distribution obtained by PIMON measurement
strongly favored the simulation using Cho model. Thus we adopt the simulation with
Cho model as a standard simulation, while GCALOR/FLUKA simulation is used for acomparison.

4.1.3

Simulation of the particle tracing through the magnetic
field and the decay section.

Scattered protons and generated secondary particles are traced by Monte Carlo simulation
GEANT with GCALOR hadron simulation [66, 64], through the two HORN magnets anddecay section.
The magnetic field of 1st-HORN is given as follows;Rrr
In rod(r ≤ R) : B(r) = Bmax ·R
In air(r > R) : B(r) = Bmax ·

(4.5)
(4.6)

where R is the target radius, and Bmax is the maximum magnetic field at the surfaceof the rod, given by Formula 3.1. We ignored the skin effect inside the target rod, andassumed the static approximation for all the area. The uncertainty of the asymmetric field
is considered at the error estimation in Chapter 6.1.6.
These simulations are also used for PIMON analysis. When pions pass the PIMON
gas vessel, Cherenkov photons are emitted. The photons are ray-traced to simulate theCherenkov photon images on the focal plane. Since Cho model does not treat the production of electro-magnetic components, simulation of their contribution is always simulated
by GCALOR/FLUKA model.
69d σ/dΩdP (mb/sr/(GeV/c))

Calculated differential cross sections and measurements

2

2

10

10

Cho (12.4GeV/c) 0-12deg
Marmer (12.3GeV/c) 0,10deg
Ashbury (12.5GeV/c) 12deg

CERN compilation fit using mainly Cho et al. data

1
0

1

2

3

4

+

5

6

7

Pπ(GeV/c)

Calculated π differential cross sections in at 0-12deg

Figure 4.2: Pion yield of experimental results [67, 69, 70] and the fit by Cho model.

70pot / cm

2

Far detector site (L=250km)

Average of r<2m
12

9

Average of r<100m

8
7

4

10

8

number of neutrinos / 10

number of neutrinos / 1010 pot / cm2

Near detector site (L=300m)

GCALOR/FLUKA

6

4

Cho
2

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

6

GCALOR/FLUKA

5
4
3

Cho

2
1
0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Figure 4.3: Simulated νµ flux at near site (left) and far site (right), using the standard
250kA Monte Carlo simulation with Cho model (solid), and GCALOR/FLUKA model(dashed).

4.1.4

Simulated neutrino beam

Neutrinos are produced mainly from the pion decay,(−)

π ± → µ± νµ(4.7)

Since HORN magnets enhance π + rather than π − , the fraction of νµ dominates over that ofν¯µ . A little fraction of the neutrinos comes from muon decay in the decay volume, and fromkaon decay around the target section. According to the beamMC, about 98% of neutrinos
flying toward SK are νµ . νe is 1.3% of νµ , ν¯µ is 0.5%, and ν¯e is 0.02%.
Figure 4.3 shows the simulated νµ flux at the near neutrino detector area (300 m fromthe target) and the far site (250 km from the target). The near flux is the average of 2 m
in radius, and the far flux is the average of 100m in radius. In these figures, simulation
with GCALOR/FLUKA model and that with Cho model are compared.

4.2

Neutrino interaction simulation (neutMC)

Neutrino interaction is generated with the simulated neutrino flux as an input. The simulator of the neutrino interaction is called ”NEUT”, which is originally developed and used71

at the atmospheric neutrino analysis in Super-Kamiokande experiment [72]. NEUT mainly
consists of three parts, the part to calculate all of differential cross section, the part tosimulate individual interaction, and the part to simulate nuclear interaction for outgoinghadrons.

4.2.1

Neutrino interaction around 1 GeV

Neutrino interacts with target material by W ± exchange and Z 0 exchange. First one iscalled charged current interaction (CC) and latter one is called neutral current interaction(NC). Around 1 GeV neutrino, have following interactions;
•
•
•
•
•
•
•
•

νN → lN 0
νN → νN
νN → lN 0 + m
νN → νN 0 + m
νN → lN 0 + nπ(n ≥ 2)
νN → νN 0 + nπ(n ≥ 2)
ν 16 O → l 16 O + π ±ν 16 O → ν 16 O + π 0

CC quasi-elastic scattering
NC elastic scattering
CC single-meson production
NC single-meson production
CC multi-pion production
NC multi-pion production
CC coherent-pion production
NC coherent-pion production(∼ 30%)(∼ 13%)(∼ 29%)(∼ 10%)(∼ 13%)(∼ 4%)(∼ 2%)(∼ 1%)

where, N is a nucleon (proton or neutron), l is a charged lepton and m is a meson, mostly
a pion. The percentage of each interaction mode is shown at the end of each line. These
values are obtained with the expected flux at 1kt and the target material is water (H2 O).
Figure 4.4 shows the cross section for water target and iron target, provided by our NEUT
simulation.
The cross section of neutrino with atomic electron is roughly 1/1000 of above interactions.
Thus, it is neglected.

4.2.2

CC quasi-elastic, and NC elastic scatterings

This interaction has the largest cross section in our energy region. This interaction is twobody scattering on the nucleon. Therefore, the differential cross section is described by
the initial energy and 4-momentum transfer (Q2 = −q 2 = −(pν − pµ )2 , where pν , pµ are
injected ν and out-going lepton momentum, respectively). Since target hadron has internal
structure, vector and axial vector form factors are taken into account. The hadron current
is expressed as follows [73];h< N0|Jhad |N >= cosθc ū(N 0) γλ FV1 (Q2) +iiσλν q ν ξFV2 (Q2)+ γλ γ5 FA (Q2) u(N ),
2mN

72

(4.8)

6

σper one nucleon (× 10-38cm2)

σper one nucleon (× 10-38cm2)

6

Total cross section (H2O)
5

4

3

NC

2

CC multi-π1

CC single-meson

0

0

1

CC quasi-elastic
3
42

Total cross section (Fe)
5

4

NC

3

CC multi-π2CC single-meson

1

5

0

Energy (GeV)

CC quasi-elastic
0

1

2

3

4

5

Energy (GeV)

Figure 4.4: Neutrino cross section for water target (left) and iron target (right). The plotshows the cross section of each interaction mode. CC coherent-pion interaction is assorted
to CC single-meson interaction, in this plot. Horizontal axis is the injected neutrino energy.
Cross sections are normalized per one nucleon.
where, FV1 ,FV2 ,FA are the vector and axial vector form factors and represented as follows.


FV1 (Q2) = 1 +



i
Q2 V
Q2 −1 h V 2G(Q)+
GM (Q2) ,
E
2
2
4mN
4mN

(4.9)

i
Q2 −1 h V
2
V
2
G
(Q
)
−
G
(Q
)
,
M
E
4m2N

(4.10)

ξFV2 (Q2) = 1 +GVE (Q2 ) = 

1

2 ,
2

Q
1+ M
2

FA (Q2) = 

V

−1.23

 ,
Q2 2
1+ M
2
A

GVM (Q2) = 1 + 

ξ
2

Q
1+ M
2
V

MV = 0.84(GeV 2/c2 ),2 ,ξ ≡ µp − µn = 3.71

(4.11)

MA = 1.01(GeV 2/c2 )(4.12)

where, θc , mN , MV and MA represent the Cabbibo angle, nucleon mass, the vector mass,and the axial vector mass, respectively. The vector mass was determined by e − p scattering experiments by CVC hypothesis. The axial vector mass was determined by neutrino
experiments with about 10% uncertainty [74].
73Finally the cross section is expressed by following formula;2idσ ν
m2N G2F cos2 θc h2
2 (s − u)
2 (s − u)
A(Q
)
∓
B(Q
)
+
C(Q
)
=
dQ2
8πEν2
m2N
m4N

(4.13)

where, GF is the Fermi coupling constant, (s − u) = 4mN Eν − Q2 − m2l when ml is thelepton mass, and;Q2 
Q2  1 2
Q2
Q2 (m2l + Q2 ) h
2
2 2
4
+
|F
|
−
4
−
|F
|
+
|ξF
|
1
−
A
V
V
4m2N
m2N
m2N
m2N
4m2N
i
m2l  1
4Q2FV1 ξFV2
2 2
2,
(4.14)
−
|F
+
ξF
|
+
|F
|
+
A
V
V
m2N
m2N


Q2
2
1
2
(4.15)
B(Q ) =
F
+
ξF
F
A
V
V
m2N
1
Q2 ξF 2 C(Q2) =
|FA |2 + |FV1 |2 + 2 | V |2
(4.16)
4
mN 2

A(Q2) =

Figure 4.5 shows the quasi-elastic cross section as a function of initial neutrino energy
calculated using our simulation. It gives a consistent result to various bubble chamber
measurements round 1 GeV [75, 76, 77, 78]. Uncertainty of the axial vector mass MAchanges the overall scale of the cross section, as shown in Figure 4.5. However, it hardly
change the differential distribution, like Q2 dependence.
For the NC elastic scattering, following relations are used according to [79].
σ(νp → νp) = 0.153 × σ(νn → e− p)σ(νn → νn) = 1.5 × σ(νp → νp)(4.17)(4.18)

When target nucleons are bounded in the nuclei, Fermi motion and Pauli blocking effectmust be taken into account. Fermi gas model is adopted to simulate Pauli blocking, by
requiring the final nucleon momentum to be over Fermi surface momentum. This calculation uses a nucleon-nucleus potential distribution which is derived from the e−12 C (e− Ni)scattering experiment [80] for oxygen (iron) nuclei. The measured value of Fermi surface
momentum is 217MeV/c for oxygen and 237MeV/c for iron nuclei. Figure 4.5 exhibits thecomparison by changing the Fermi surface momentum to 237, 217, 250MeV/c.

4.2.3

Single-meson production

Single-meson production is the next dominant interaction mode to the quasi-elastic scattering. This interaction consists of following reactions;
74

2

1.2

-38

Our simulation
2 2
MA=1.11GeV /c2 2
MA=0.91GeV /cPFermi=217MeV/c

1.4

PFermi=237MeV/c

1.2

1

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

1

2

3

0

4
5
Energy (GeV)

PFermi=250MeV/c

1

0.8

0

CC quasi-elastic, with Pauli blocking

1.6

σper one neutron (×10σfor free neutron (10-38ANL-12ft, 1977
BNL-7ft, 1981
CPS-GGM, 1977
Serpukhov, 1985

1.6
1.4

cm )

1.8

CC quasi-elastic

2

cm )

1.8

0

1

2

3

4
5
Energy (GeV)

Figure 4.5: (Left figure) Cross section of CC quasi-elastic scattering to one free neutron in
our simulation. The standard one with MA = 1.01GeV2 /c2 is shown by solid line, whereas
the dashed(dotted) line shows the simulation with MA = 1.11(0.91)GeV2 /c2 . Horizontal
axis is the injected neutrino energy in Lab. frame. Measurements from various experiments(ANL:[75], BNL:[76], GGM:[77], and Serpukhov:[78]) are overlaid. Error bars on the marks
mean the error quoted in their papers. (Right figure) CC quasi-elastic cross section with
Pauli blocking effect. The unit is cm2 per one neutron.

75

• Charged Current (CC)νn → l − pm0
νn → l − nπ +
νp → l − pπ +(4.19)(4.20)(4.21)

νnm0
νpm0
νpπ −
νnπ +

(4.22)(4.23)(4.24)(4.25)• Neutral Current (NC)
νn
νp
νn
νp

→
→
→
→

where, m0 is the neutral meson (mainly π 0 , and a little fraction of η, and K 0). These
interactions are simulated using the method by Rein and Sehgal[81]. In their method, thesingle-meson production is mediated by a certain baryon resonance states as;
resonance production
resonance decayνN → lN ∗N ∗ → mN 0

where, N ∗ is one of the baryon resonances. When this interaction occurred through one
resonance state, the differential cross section is expressed by following formula;
d2 σ
1 X
1
· ·
=
|T (νN → lN ∗ )| · χEν · δ(W 2 − M 2 )22
dQ dEν
32πmN Eν 2 spins(4.26)

where, Eν is the neutrino energy, mN is the nucleon mass, W is the invariant mass ofhadronic system, and χEν is the decay probability of resonance. The last δ-function is
calculated for each resonance with given mass M and width Γ, using following Breit-Wigner
formula:δ(W 2 − M 2 ) →Γ
1·
2π (W − M)2 + Γ2 /4(4.27)

In our case, dominant resonance is ∆(1232) and other 17 higher resonance states are also
considered, until W is less than 2 GeV. Figure 4.6 compares our calculated cross sections
with the experimental data [82, 83, 84].
Angular distribution of mesons from ∆(1232) is calculated using this Rein-Sehgal’s
method. For the decay of other resonance states, the meson direction is assumed to be
isotropic in the resonance rest frame.
76

Our simulation±30% scaled

2
-38

1

0.6
0.4

BNL-7ft, 1986

0.2

CPS-GGM, 1979

0

0

n→µ
ν
pπ

0

2

+

0.8

ANL-12ft, 1982

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

p→µ
ν
pπ

σ(10

mass cut M(pπ)<1.4GeV

cm )

1.2

CC-singleπ

4Energy (GeV)

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

0

2

4
Energy (GeV)

24Energy (GeV)

+

n→µ
ν
nπ

0

Figure 4.6: Cross section of CC single-pion production (solid), with experimental data
(ANL:[82], BNL:[83], GGM:[84]). ±30% scaled ones (dashed) are also shown as a reference.

774.2.4Multi-pion production

In higher energy region, deep in-elastic scattering dominates to the elastic or resonanceinteraction. The cross section of CC deep in-elastic scattering is calculated based on Bjorken
scaling, and expressed as;i
d2 σ ν
G2F mN Eν h1
1=
· (1 − y + y 2 + C1)F2 (x) + y(1 − y + C2 )[xF3(x)] (4.28)
dxdy
π
2
2
2
2
m
ml (y − 2) mN xy
−
− l2
C1 =
4mN Eν x
2Eν
4Eν
2
ml
C2 = −
4mN Eν x

where, x = Q2/(2mN (Eν − El ) + m2N ) is Bjorken scaling variable, in low energy, y =(Eν − El )/Eν is the fractional energy transfer to the hadron system, mN (ml ) is nucleon(lepton) mass and Eν (El ) is initial neutrino (final lepton) energy. The nucleon structure
functions F2 and xF3, as a function of x and Q2 , are given by GRV-94[85].
In our simulation, the events are generated from W > 1.4 GeV according to this formula.
In 1.4 < W < 2 GeV range, pion multiplicity is calculated using the measurement at
Fermilab bubble chamber experiment [86]. It is found to be (0.06±0.06)+(1.22±0.03)lnW 2 .
Assuming hnπ+ i = hnπ− i = hnπ0 i and < nπ+ >= 1/2 < nc >, mean multiplicity including
neutral pion is estimated as follows;hnπ i = 0.09 + 1.83lnW 2(4.29)

When the pion multiplicity is determined to one, the event is ignored, in order to avoid
double counting with resonance (single-meson) contribution. For an individual Monte Carloevent, pion multiplicity is finally determined KNO(Koba-Nielsen-Olesen) scaling [87], which
well reproduce the previous experimental data. The charge of each hadron is randomly
chosen keeping the charge conservation. Forward-backward asymmetry of the produced
pions is also taken into account in the hadronic center of mass system as [88];“forward00
0.35 + 0.41lnW 2=“backward00
0.50 + 0.09lnW 2(4.30)For the events with W > 2 GeV, kinematics are determined by JETSET/PYTHIA [89].
For the NC multi-pion production, ratio of NC/CC is estimated in [90] for less than 3
GeV neutrinos, and in [91] for greater than 3 GeV neutrinos. Then following relations are
used;



(Eν <3 GeV) 0.26σ(νN → νX)
0.26+
0.04(E/3−1)(3 GeV<Eν <6 GeV)=νσ(νN → l − X) 

0.30
(6 GeV<Eν )78(4.31)

4.2.5

Coherent pion production

Coherent interaction occurs as whole nucleus, instead of the individual nucleon. Theyinteract without any change of charge or isospin for recoil nucleus. Since the transferredmomentum is very small, angular distribution of recoil leptons and produced pions have
sharp peaks in the forward direction.
The cross section for oxygen nucleus is calculated employing the Rein-Sehgal model [92],which is expressed by following formula;
G2F mN Eν 2 2
1 h πN i2
MA2 2 −b|t|
d3 σ
2
=
f
A
(1
−
y)
(1
+
r
)
σ
e
Fabs (4.32)
πdxdyd|t|
2π 2
16π tot
MA2 + Q2
RefπN (0)r =ImfπN (0)where, fπ = 0.93mπ is the decay constant, A is atomic number (oxygen:A = 16), b =1(R0A1/3 )2 is of the order of traverse dimensions of the nucleus (∼ 80(GeV)−2 for oxygen),3
and t is the square of 4-momentum transfered to the nucleus. Fabs is the considerable
term for pion absorption in the nucleus. For iron nucleus, coherent cross section is scaled
proportional to A1/3 from the cross section of oxygen nucleus.

4.2.6

Experimental constraint of the CC total cross section

CC-total cross section is also compared with the measurement of bubble chamber experiment [93, 94, 95]. In Figure 4.7, left figure shows the CC-total cross section, and rightfigure shows σ(νn) over σ(νp). In these figures, cross section is corrected to the watertarget by the ratio of proton and neutron. Coherent interaction is neglected in this comparison. Ambiguity of ±30% of in-elastic / elastic cross section ratio covers most of theexperimental data.

4.2.7

Nuclear effect for hadrons

Since neutrino interaction occurs inside of the nucleus, produced hadrons often interact
before leaving the nucleus. This “nuclear effect” has been studied for oxygen nuclei. For
iron nuclei, the nuclear effect is known to be larger than that for oxygen nuclei, because
the density of iron nuclei is large. However, our standard simulation of iron interaction
assumed same nuclear effect and the uncertainty of the effect is assigned to the systematic
error.
Following interactions are considered;• For pions, an in-elastic scattering, a charge exchange, and an absorption are considered. The cross section of each interaction is calculated by the model of Oset et. al.
79

-38

σ/ E per one nucleon (101.4

Our simulation (H2O)
in-elastic ±30% scaled

ANL-12ft, 1979
BNL-7ft, 1982
CPS-GGM, 1979

1.2

R=σ
(ν
n)/σ
(ν
p)

CC-total2

cm /GeV)6

1.6

Cross section ratio
Our simulation (isoscalar target)
in-elastic ±30% scaled5

ANL-12ft, 1979
BNL-7ft, 1982

4

1
3

0.8
0.6

2

0.4
1

0.2
0

0

1

2

3

4
5
Energy (GeV)

0

0

1

2

3

4
5
Energy (GeV)

Figure 4.7: σ(CC-total)/Eν (left) and σ(νn)/σ(νp) (right) as a function of the neutrinoenergy. The absolute values are normalized to the water target case. Dotted lines show thecases with scaled single-meson and multi-pion cross section by ±30%. Other experiments(ANL: [93], BNL: [94], GGM: [95]) are overlaid.
[96]. In the cross section calculation, nuclear density in oxygen nucleus is assumed
to be the Wood-Saxon form, which is typically expressed for protons;ρp (r) =Z1
ρ0
A 1 + exp( r−c)a(4.33)

where r is the distance from the center of the oxygen. In our simulation, ρ0 = 0.48m3π ,a = 0.41fm, and c = 2.69fm for 16 O.
Figure 4.8 shows the cross section of each interaction for π + , and the interaction
probability for π 0, as a function of the pion momentum. Measurements of otherexperiments are also shown there.
• The absorption of resonance baryon (∆) is considered. 20% of produced ∆ is absorbed[97].
Protons and neutrons contribute a little for our event in 1kt, MRD, and SK. Therefore,
nuclear effect of protons and neutrons are neglected.

4.2.8

Uncertainty of the neutrino interaction

Considering the ratio of the near and far observation, absolute scale of the cross section iscanceled. Remaining uncertainties are arranged into following two items.
80

1
probability

cross section for π + + 16 O (mb)

600

500

400

charge exchange
0.8

inelastic scattering

0.6

absorption(i)+(ii)+(iii)

300

0.4
200

(i) inelastic

00.2(ii) absorption

100

no interaction(iii) charge exchange
0

100

200

300
+

(A) momentum of π

400

500

600

(MeV/c)

0
100

200

300

400

500

600

(B) initial momentum of π 0 (MeV/c)

Figure 4.8: Cross section for pi+ (left) and π 0 (right) on oxygen nuclei.
• Cross section ratio between Charged current (CC) and Neutral current (NC). We
change the NC cross section by ±30%, and estimate the effect for the analysis.
• Cross section ratio of in-elastic cross section relative to CC quasi-elastic and NC
elastic scattering. We change the cross sections of single-meson production, multimeson production, and coherent-pion production mode of both CC and NC by ±30%,
simultaneously, and estimate the effect.
These assigned uncertainties are suitable to cover the experimental data (as shown in Figure
4.6 and 4.7).
For iron nuclei, following two uncertainties are also taken into account.
• Uncertainty of the Pauli blocking threshold.
We simulate with different Fermi surface momentum of 217, 237, and 250MeV/c.
• Uncertainty of the nuclear effect.
We prepare two simulations. One is assumed to have same nuclear effect as theoxygen nuclei. The other is the simulation with 100% absorption of hadrons.

4.3

Detector simulation

After neutrino interaction occurs, passage of generated particles is simulated using GEANT
simulation [66]. GCALOR package is used for the hadron interaction simulation Validityof the simulation is experimentally checked by the measurement of proton range in iron[98]. The results show the simulation with GCALOR well reproduces the measurements.
81Simulated events are saved with the same data format as real data. This enables us to
use the same analysis codes which is used for real data.

4.3.1

Simulation of MRD

Full structure of irons, drift-tube modules, and gas in MRD are taken into account. Whencharged particles pass the each cell, hit information is saved after conversion to TDC
count. For each hit, 97.5% hit efficiency is applied. Noise hits are generated according to
the estimation from the real data, although our noise rate is small enough not to affect forour track identification.

4.3.2

Simulation of water Cherenkov detector (1kt, SK)

Same water Cherenkov detector simulation is used at 1kt and SK. The water volume works
as a neutrino target and also a radiator of the Cherenkov photon. The simulator emits
photons according to Formula 3.11 and 3.12.
Emitted photons are tracked with considering the absorption and scattering in the water.
At the black sheet on the wall and at the surface of PMTs, reflection is considered as afunction of the incident angle [61].
For simulating PMT response in photon detection, measured quantum efficiency is used.
Obtained photo-electron signals are smeared according to measured 1 photo-electron distribution and timing resolution. Finally detected photo-electrons are converted to TDC
and ADC information.

82

Chapter 5
Analysis Strategy
5.1

Overview of the Analysis

In the following chapters, study of the νµ disappearance is discussed. As described in
Chapter 2.2 and Formula 2.2, the study was performed by comparing the observed neuSK
SK
trino events in SK (Nobs) to the expected number (Nexp) derived from the near detector
measurement.
The discussion is described in following order.
1. Proton intensity measurement.
Neutrino beam intensity can be normalized by proton intensity measured by CTs, inparticular, TGT-CT. The accumulation of protons on the target (p.o.t.) is used forthe normalization of rate, to correct the live spill difference between each detector
measurement.
2. Pion distribution measurement using PIMON.
PIMON measurement provides the pions’ (pπ , θπ ) distribution before decaying toneutrinos, by measuring the Cherenkov photon distribution. This confirms beamMC,
which predicts the neutrino energy spectrum and the flux ratio Φf ar /Φnear . The
results and the systematic errors are described.
3. Proton beam and secondary muon measurement.
Proton beam profile and its stability is continuously measured using SPICs. Secondary muons are measured using MUMON after the beam dump. They work as thespill-by-spill monitors of the beam. The results of these stability measurements andthe effect for our analysis are discussed.
4. Neutrino beam measurement using MRD.
Neutrino beam is continuously measured with the iron interacted events in MRD. The
83

neutrino beam direction and profile width are measured during the whole running
period. Stability of the event rate and the muon distributions confirms the neutrino
beam stability. The event selection and the results are described.
5. Neutrino event rate measurement using 1kt.
Number of near events is extracted from the events measured in 1kt. The event
selection, results and the related systematic errors are described.
6. Neutrino event measurement at SK.
Neutrino event selection and the results at SK are presented.
7. Comparison of near and far event rate.
The comparison between the observed number of events at SK and the expected
number is discussed. The quantitative discussion of probability of the neutrino event
reduction is discussed.

5.2

Operation of the ExperimentDuring the experiment, the proton beam had been controlled to get best targeting efficiency
and best pointing to SK. The muon profile center at MUMON had been kept to the designed
direction to SK. And we continuously monitored the intensity ratio of MUMON and CT,
which is the indicator of pion production efficiency.

5.3

Good Beam Spill Selection

Proton intensity was measured by CTs. We used the measurement of TGT-CT as thenormalization of accumulated protons on target. Figure 5.1 shows the accumulated numberof protons on the target (p.o.t.) measured by TARGET-CT. The averaged number ofprotons per one beam spill (ppp) was typically 4 ∼ 6 × 1012 as also shown in Figure 5.1.
In total, 2.6 × 1019 p.o.t. was injected to the target since May 1999.
This accumulated p.o.t. includes some fraction of the unusable periods, for example,
beam tuning, fail of the data acquisition. ”Good beam spill” is defined to be used for ouranalysis, with following criteria.
• We use the data from June 1999 to June 2000.
• Exclude the machine study, beam tuning, or PIMON measurement.
• Exclude the period of beam line component trouble.
• Proton intensity is greater than 1 × 1012 ppp (proton per pulse).
84

Accumulated POT (10^18)

25

20

15

10

5

Protons/Pulse (10^12)

0
6
4
2
0
Apr99

Jul99

Oct99

Jan00

Apr00

Jun00

Date

Figure 5.1: Accumulated number of proton on the target (upper) and the averaged proton
intensity (lower), measured by TARGET-CT.

• Horn current is greater than 240(190) kA where nominal current is 250(200) kA from
Nov. 1999 to June 2000 (in June 1999).
• SK is alive.
In short, we used the period as long as SK is alive and beam line is properly running, asshown in Table 5.1. Table 5.2 summarizes the used p.o.t.s for each near detector analysis
in each month. We have about 2.29 × 1019 p.o.t. for SK analysis, whereas 2.10 × 1019 p.o.t.
and 1.97 × 1019 for MRD and 1kt, respectively.

85

SK alive
SK deadSK alive
SK dead

1kt aliveused(19.7 × 1018 p.o.t.)
not used

1kt dead
used, need correction(3.2 × 1018 p.o.t.)
not used

MRD aliveused,(21.0 × 1018 p.o.t.)
not used

MRD dead
used, need correction(1.9 × 1018 p.o.t.)
not used

Table 5.1: Chart of the used spill definition. Values are the accumulation from June 1999
to June 2000.

PeriodFrom
To
Target diameter
HORN current
P OTSK (×1018 )P OT1kt (×1018 )P OTM RD (×1018 )Jun.99Jun.4
Jun.26
20mmφ
200kA
3.10
2.60
2.93

Nov.99 Jan.00
Oct.29 Jan.14
Nov.24 Jan.29

3.57
2.62
2.72

2.22
1.81
2.04

Feb.00 Mar.00 May.00
Feb.2 Mar.1 May 11
Feb.26 Mar.23 May 28
30mmφ
250kA
4.04
3.71
2.56
3.74
3.35
2.42
3.81
3.49
2.51

Jun.00May.31
Jun.21

3.75
3.16
3.54

Table 5.2: Summary of the used p.o.t. (protons on the target) for each detector analysis.

86

Chapter 6
Proton and Secondary Particle
Measurement
6.1

Pion Distribution Measurement using PIMON

6.1.1

PIMON measurement

PIMON measurements have been done in the special run in June 1999 (Ihorn = 200 kA)
and Nov. 1999 (Ihorn = 250 kA). Special beam time is occupied by PIMON measurement
because materials of PIMON structure affect to the secondary beam, and because the low
intensity beam is needed to avoid PMT saturation. Low intensity operation is achieved by
the adjustment of the Booster injection. In June run, data are taken with typically 7× 1010
ppp of 1 bunch operation. After studying the lower gain operation of PMTs, data is takenwith typically 7 × 1011 ppp of full (= 9) bunch operation in Nov. run. The operation
parameters are summarized in Table 6.1.
This chapter presents mainly the results in Nov. run. Results of June run is presented
in Appendix E.1 and other documents [46].

6.1.2

Cherenkov photon distribution

Figure 6.1 shows the typical signal distribution of the observed ADC counts in each PMT,
after pedestal subtraction. Pedestal value of each PMTs are provided from the off-spill
data. The observed signals contain the “background” Cherenkov photons and the beam
associated radiation noises, as much as the “signal” Cherenkov photons emitted at thefiducial area in the beam line. In order to subtract these “background” signals and noises,
the MIRROR-OFF run is taken, where mirror is set to the wrong direction. Figure 6.1
shows the typical result of MIRROR-ON data, and MIRROR-OFF data, and the subtracted
result. In order to obtain fine photon distribution, PMTs are slid by half channel and data
87

Parameter
Target diameter
HORN current
Proton intensity (during PIMON run)Proton beam bunch
Number of refractive indices
PMT gain
PMT saturation

June 1999
20mmφ
200 kA
7 × 1010 ppp
1
9
300
exist

Nov. 1999
30mmφ
250 kA
7 × 1011 ppp
99
20 or 50
none

Table 6.1: Summary of the beam condition and PIMON operations in June and Nov. run.

are taken. Accordingly, 40 data points of the Cherenkov photon distribution are taken foreach refractive index. In these subtraction and combination process, data are normalized
by the proton intensity, measured by TGT-CT.
Figure 6.2 shows the Cherenkov photon distribution after MIRROR-OFF subtraction,with various refractive indices. Following systematic errors are considered in these distributions.
(r.m.s.)• The error due to spill-by-spill fluctuation, which is estimated by √.
nspill• Uncertainty of the gain adjustment for each PMTs. 5% error is quoted for each PMT(see Chapter 3.2.6).
• Uncertainty of lower gain operation estimated by the difference between two datawith different gain (gain= 20 and gain= 50) at same refractive index of n = 1.00129.

6.1.3

Subtraction of electro-magnetic shower contribution

There is non-negligible contribution from the electro-magnetic shower. Electro-magnetic
shower is caused by the converted γ from π 0. Subtraction of this background is performed
using beamMC, which is normalized in lowest index measurement of n = 1.00024. Absolutenormalization is determined by the lowest index case. As shown in Figure 3.6, high momentum pions above 6.4 GeV/c are negligible compared to electro-magnetic components.
Electro-magnetic components make broad distribution.
Figure 6.2 proves that the electro-magnetic component (shaded area) estimated bybeamMC with one normalization factor well reproduces the broad background distribution at all refractive indices.
The obtained Cherenkov photon distributions are compared to beamMC. Figure 6.3
shows the comparison to the distribution predicted by beamMC, based on Cho model (left)88CT corrected ADC count mean

600
500
400
300
200
100
0

2

4

6

8

10

12

14

16

18

20

CT corrected ADC count mean

PMT number
300
250
200
150
100
50
0

2

4

6

8

10

12

14

16

18

20

PMT number

Figure 6.1: Typical example of the MIRROR-OFF subtraction at n = 1.000243, in June
1999. Signal of MIRROR-ON and MIRROR-OFF (top) and subtracted result (bottom)
are shown. Horizontal axis shows the PMT number, which are vertically aligned at the
focal plane with 3.5 cm repetition. PMT-1 is at the top, and PMT-20 is at the bottom.

89

Pion Monitor Meas. and MC (e+-)

Pion Monitor Meas. and MC (e+-)

120

0.15
0.1
0.05
0

100
80

10

20

10

20

n=1.00048

60
40

0.2
0.15
0.1
0.05
0

20
0

30

0.2
0.15
0.1
0.05
0

5

10

15

20

25

30

35

0.2
0.1
10

20

n=1.00024

30

0

10

20

n=1.00074
0.3

140

0.05

0.1

100

0

30

n=1.00095

0.1

0.2

120

30

n=1.00058

10

20

30

0

10

20

n=1.00129

80

30

n=1.00129

60
0.15

40

0.1

20

0.05

0

5

10

15

20

25

30

0

35

n=1.00041

0.1
0.05
10

20

30

n=1.00176

0

10

20

30

n=1.00242

Figure 6.2: Measured cherenkov photon distribution in various refractive indices in Nov.
1999 run (Ihorn = 250 kA), shown with the systematic error bars. Horizontal axis means
the PMT position number (1 unit corresponds to 1.75 cm) with respect to the y-axis at
focal plane. Large number in the horizontal axis means the bottom PMT, which measuresrelatively large divergence angle with respect to the beam axis. Vertical axis shows the
ADC count. Pedestal and MIRROR-OFF distribution (see text) are already subtracted.
PMT gain correction is applied. Shaded area is the estimated Cherenkov photons from theelectro-magnetic shower components, normalized to the lowest pressure data (see text).

90

10

20

40
20
0

30

20

ADC counts

10

20

30

PMT number (n=1.00176 meas.)

50
10

20

200
100
0

10

20

30

20

40
20
0

30

10

20

30

150
100
50
0

10

20

100
75
50
25
0

100
0

PMT number (n=1.00242 meas.)

10

20

30

PMT number (n=1.00176 meas.)

30

10

20

30

200
100
0

30

200

20

PMT number (n=1.00074 meas.)

PMT number (n=1.00095 meas.)

300

10

PMT number (n=1.00048 meas.)

PMT number (n=1.00058 meas.)

30

300

ADC counts

80
60
40
20
0

PMT number (n=1.00129 meas.)
ADC counts

ADC counts

0

30

100

0

30

100

20

150

PMT number (n=1.00095 meas.)

200

10

10

60

PMT number (n=1.00041 meas.)

PMT number (n=1.00074 meas.)
ADC counts

10

30

60

PMT number (n=1.00058 meas.)
100
75
50
25
0

20

ADC counts

ADC counts

ADC counts

40
30
20
10
0

10

PMT number (n=1.00048 meas.)

ADC counts

30

PMT number (n=1.00041 meas.)

ADC counts

0

40
30
20
10
0

10

20

30

PMT number (n=1.00129 meas.)
ADC counts

10

ADC counts

20

20

ADC counts

10

data vs. MC (FLUKA/GCALOR)ADC counts

ADC counts

ADC counts

data vs. MC
20
15
10
5
0

400
300
200
100
0

10

20

30

PMT number (n=1.00242 meas.)

Figure 6.3: Cherenkov photon distribution measured in Nov. (dots) and two sets of beamMC (histograms). The simulation in left figures is based on Cho model and the simulationin right figures is based on GCALOR/FLUKA model. Error bars are quoted in previous
Section6.1.2.
or GCALOR/FLUKA model (right). These figures clearly show that the simulations using
Cho model have good agreement to the data, while the simulation using GCALOR/FLUKA
model has some difference.

6.1.4

Extraction of the pion energy and angular distribution

Obtained Cherenkov photon distributions are fit with the pion distribution on (pπ , θπ )plane, as described in Chapter 3.2.4. Figure 6.4 shows the fitted answer and its error on(pπ , θπ ) plane.

6.1.5

Prediction of the neutrino energy spectrum

Basically the neutrino flux from pions with (pπ , θπ ) is calculated by the Formula 3.3. Eachneutrino flux at the near or the far site is made from corresponding (pπ , θπ ) bin, withfollowing two assumptions;• Flat population inside the each (pπ , θπ ) bin.
• The same spatial distribution of the pion as the one from beamMC.
91

Pion angle (*10mrad)

Pion angle (*10mrad)

5

4

3

5

4

3

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3

-4

-4

-5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

-5

Pion momentum (GeV/c)

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Pion momentum (GeV/c)

Figure 6.4: Fitted results of pion kinematic distribution, the center value (left figure) andtheir error (right figure) in Nov. run. These values are arbitrary numbers.
Systematic errors from these assumptions are discussed in next Section 6.1.6. Then, all thecontributions from (pπ , θπ ) are summed up to predict the neutrino spectrum at near andfar site, and lead to the flux ratio.
The neutrino flux contribution from the decay before PIMON, are added. This is estimated by beamMC. Amount of this is about 7% and 10% of the total flux in the near site
and the far site, respectively. The uncertainty is also discussed in next Section 6.1.6.
Left figure of Figure 6.5 shows the predicted neutrino energy spectrum in Nov. run. The
simulated spectrum based on beamMC with Cho model (see Chapter 4.1.2) is overlaid.
Although absolute scale is arbitrary, beamMC well reproduced the predictions based on
PIMON reconstruction above 1 GeV.
Right figure of Figure 6.5 shows the ratio of far and near flux (Φf ar /Φnear ) as a functionof the neutrino energy. This energy dependence is explained by following reasons.
• Low energy neutrinos are produced from low energy pions, which decay at relatively
upstream of the decay section. On the contrary, high energy pions decay at relatively
downstream. It gives the larger acceptance of neutrinos for near detector.
• High energy pions have small decay angle. It gives the larger acceptance of neutrinos
for far site.
Energy integration of these ratio gives the total flux ratio (Φf ar /Φnear ) used in Formula
2.2.
92

x 10 8KEK flux

6000

MC

Integrated
Pion monitor above 2.5GeV

5000
4000

far/near

x 10

-5

0.3
Pion monitor

0.25

3000

MC

2000
0.2

1000
0
x 10 2
4500
4000
3500
3000
2500
2000
1500
1000
500

0.5

1

1.5

2

2.5

3
0.15

SK flux

MC
Integrated
Pion monitor above 2.5GeV

0.1
Integrated
above 2.5
GeV

0.05

0

0.5

1

1.5

2

2.5

0

3

E(GeV)
ν

0

0.5

1

1.5

2

2.5

3

E(GeV)
ν

Figure 6.5: Left: Prediction of the neutrino energy spectrum at near and far site in Nov.
(Ihorn = 250 kA). Neutrino flux above 2.5 GeV is integrated. Standard beamMC based on
Cho model is overlaid. Normalization is done by the entry above 1 GeV, which are arranged
to the expected number of ”neutrinos/cm2 /1020 p.o.t.” Right: Prediction of the flux ratioof far and near (Φf ar /Φnear ) as a function of energy, in Nov. run. Standard beamMC basedon Cho model is overlaid. In both figure, error bars include all the systematic errors, which
are described later.
These figures again show the agreement between PIMON prediction and the beamMC. Hereafter we use the flux ratio and the energy spectrum shape estimated with thissimulation, for the analysis in following chapters.
Figure 6.6 shows the neutrino spectrum and ratio compared with the simulation basedon GCALOR/FLUKA model. This model gives fairly different spectrum and flux ratio
from Cho model. PIMON measurement strongly suggests the Cho model.
We also emphasize that the difference of the flux ratio below 1 GeV is small because it
is mainly determined by the geometry of the decay section. Therefore, the uncertainty of
the flux ratio in this range is assigned from the difference of these expectations from thebeamMC.

6.1.6

Systematic error of the energy spectrum and Far/Nearratio

Various systematic errors were estimated on these PIMON analysis. They are summarizedin Table 6.2 and 6.3 for Nov. run. They are explained in following section.
93

Nov. 1999
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Energy bin (GeV)
Fitting error
Mirror reflectivity
Refractive index uncertainty
Low and high beam intensity
Beam stability (PIMON run)φ asymmetry of the HORN field
PIMON alignment
Proton injection point
MIRROR-OFF subtraction
Electro-magnetic subtraction
Fitting method
Pion decay before PIMON
Radial distribution of pions
Kinematic bin of pions
Total

Nov. 1999
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Energy bin (GeV)
Fitting error
Mirror reflectivity
Refractive index uncertainty
Low and high beam intensity
Beam stability (PIMON run)φ asymmetry of the HORN field
PIMON alignment
Proton injection point
MIRROR-OFF subtraction
Electro-magnetic subtraction
Fitting method
Pion decay before PIMON
Radial distribution of pions
Kinematic bin of pions
Total

Errors on spectrum at near1 − 1.5 1.5 − 2 2. − 2.5
±6.2%
±4.8%
±7.7%
−2.0%
+2.9%
+3.4%
−5.1%
+7.3%
+4.6%
−1.2%
+0.6%
+4.0%
—
—
—
−3.6%
+5.2%
+0.7%
—
—
—
—
−2.0%
—
—
—
—
—
—
—
+6.8%
−7.7% −15.3%
—
±0.8%
±0.5%
±0.5%
±1.0%
±4.3%
+2.7%
−2.4%
−7.0%
+9.1% +10.7% +11.3%−9.5%−9.7% −17.7%

Errors on spectrum at far
1 − 1.5 1.5 − 2 2. − 2.5
±8.1%
±4.9%
±7.6%
−3.1%
+1.8%
+4.0%
−8.6%
+5.4%
+1.1%
−2.1%
−1.5%
+3.1%
—
—
—
−5.7%
+2.5%
+0.7%
—
—
—
—
—
—
—
—
—
—
—
—
+11.0% −10.2% −12.3%
±0.5%
±1.5%
±1.1%
±0.5%
±0.5%
±3.1%
+0.5%
−2.4%
−5.4%
+13.7%+8.1%+9.8%−13.6% −11.8% −15.7%

> 2.5
±12%
+0.6%
+37%
+5.0%
±5.5%
+10.6%
—
−4.8%
—
—
+12%
−21%

—
±20%
−10.0%+47.3%−33.8%
> 2.5
±12%
—
+33%
+7.8%
±4.8%
+9.8%
—
−4.9%
—
—
+1.6%
−32%

—
±10%
−15.4%+38.9%−39.5%

Table 6.2: Systematic errors of neutrino spectrum at near and far detector in Nov. run.

94

Errors on flux ratio (Nov. 1999, HORN current 250 kA)
Energy bin (GeV)
0 − 0.5 0.5 − 1
1
Fitting error
2Mirror reflectivity
3
Refractive index uncertainty
4
Low and high beam intensity
5
Beam stability (PIMON run)
6 φ asymmetry of the HORN field
7
PIMON alignment
8
Proton injection point
9
MIRROR-OFF subtraction
10
Electro-magnetic subtraction
11
Fitting method
12
Pion decay before PIMON
13
Radial distribution of pions
14
Kinematic bin of pions
+5.1
+7.3
15
Hadron model (MC)−9.5 %−2.5 %+5.1% +7.3%−9.5% −2.5%
Total

1 − 1.5

1.5 − 2

2. − 2.5

> 2.5

+3.2%
−2.9%

+1.0%
−0.9%

−1.2%
−3.7%
−1.9%
—
−2.6%
—
—
—
—
+4.0%
±0.7%
—
±2.1%

−1.1%
−1.8%
−3.7%
—
−2.4%
—
+1.2%
—
—

+0.5%
−3.3%
−1.9%
—
−2.4%
—
—
—
—

+1.4%
−3.0%

+3.2%
−4.6%

±0.7%
±0.5%
—

±1.7%
±1.3%
+1.7%

—
−2.6%
+2.9%
±0.5%
−1.0%
—
—
—
—
−14.5%
±0.5%
±8.5%
−7.1%

+4.6%
−6.2%

+2.9%
−6.2%

+5.3%
−7.4%

+2.2%
−2.9%

+2.2%
−2.1%

+9.1%
−16.2%

Table 6.3: Systematic errors of neutrino flux ratio (Φf ar /Φnear ) in Nov. run.

95

x 10 8
8000
7000

MC

KEK flux

6000

Pion monitor

5000

Integrated
above 2.5GeV

far/near

x 10

-5

0.3
Pion monitor

0.25

MC (GCALOR)

4000
3000
2000

0.2

1000
0
x 10

0.5

1

1.5

2

2.5

3
0.15

2

MC
Pion monitor

5000

SK flux4000

0.1
Integrated
above 2.5GeV

Integrated
above 2.5
GeV

3000
0.05

2000
1000
0

0.5

1

1.5

2

2.5

0

3

0

0.5

1

1.5

2

2.5

3

E(GeV)
νE(GeV)
ν

Figure 6.6: Comparison with the simulated neutrino spectrum and Far/Near ratio using
GCALOR/FLUKA model, in Nov. run (Ihorn = 250kA). Notations are same as Figure 6.5.
1. Fitting error.
The error listed in Section 6.1.2 are assigned for each data point of the Cherenkov
distributions. The fit of Cherenkov distributions gives the fitting errors on the (pπ ,θπ ) distribution (shown in Figure 6.4). For the error estimation, we randomly change
the (pπ , θπ ) distribution within the fitting errors, and predict the neutrino spectrum
and the flux ratio from various (pπ , θπ ) distribution. The differences of the results
are quoted as the systematic errors of the fitting error.
2. Mirror reflectivity.
The laser system confirms the mirror reflectivity suffered no damage within ±6%
during both 1999 run. The systematic error is assigned based on the difference of theresults considering a few percent deterioration around the beam center.
3. Refractive index uncertainty.
The major uncertainty of the refractive index comes from the wavelength dependence
as shown in Figure 3.12. Two simulations are compared. One includes this wavelength
dependence down to 160 nm, and the other is the standard one with particular index
calibrated by the primary proton threshold (Figure 3.14). The difference is quoted
as the systematic error.
4. Difference between the low and high beam intensity.
In Nov. run, both of the horizontal and vertical profile of proton beam were about96

20 ∼ 30% narrower from the normal run. Systematic errors are assigned based on
the comparison between these simulations with two profiles.
5. Beam stability during the PIMON measurement.
Proton beam was monitored using two SPICs (V39-SPIC and TARGET-SPIC). The
fluctuation of the proton beam center is about 0.1 ∼ 0.2 mm during the PIMON run.
Secondary muon yield was also monitored by SPDs. They show the rate stability
was 1.4% and the profile center was stable within ±1 cm. Various simulations are
performed with the various proton injection according to these fluctuation. They
provide the systematic error.
6. Azimuthal angular symmetry (φ symmetry) of the magnetic field inside
the HORN magnet.
Since the spherical mirror samples small (12 degree) azimuthal region, PIMON analysis is affected by the azimuthal asymmetry of the pion distributions.
Systematic errors are assigned based on the comparison between the beamMC with
15% of 4-fold asymmetric field and the original one.
7. Alignment of the PIMON with respect to the beam line center.
PIMON is well aligned to the beam line. An optical survey ensures that, the heightof the mirror is aligned within 1 mm, and the horizontal position is precisely adjusted
within a few hundred µm from the designed beam axis. Systematic errors from thisare negligible.
8. Proton injection point to the target.
Secondary beam axis in normal neutrino run is monitored by the proton profile center
measured by SPICs and the muon profile center at MUMON. For PIMON run, theprofile center of the proton is same within 1 mm compare to the normal run. Muon
profiles measured by SPD have less than 10 cm shift compared to the normal run,which confirms that the proton injection point is within 1 mm in Nov. The systematic
error is estimated by the beamMC study in both case.
9. Systematic error of MIRROR-OFF subtraction.
We took the data with the mirror rotation up to 14.5 degree off from the nominal direction. It proves that the background components are uniform. Estimatedsystematic errors are negligibly small.
10. Electro-magnetic component subtraction.
BeamMC well reproduces the shape of contributions from electro-magnetic components. Therefore the systematic error is estimated by changing the normalization
factor by +1σ of χ2 from the best fit. This error mainly affects to the distribution of97

high momentum pions, which corresponds to high energy neutrino flux. The error is
negligibly small in Nov.
11. Fitting method.
Monte Carlo test is performed to confirm the analysis method. Simulated Cherenkov
photon distributions are analyzed to extract the (pπ , θπ ) distribution, and to predict
the neutrino spectrum and the flux ratio. These “results” are compared with fullysimulated distributions by same beamMC as Cherenkov photon simulation.
For this Monte Carlo test, three beamMC is used. One is the standard beamMC
with Cho model, with the HORN current of 250 kA. Another is the beamMC with
GCALOR/FLUKA hadron model, with 250 kA. The other is the beamMC with Chomodel, with the HORN configuration of Jun.99 run (200 kA). The largest differenceis quoted as the error due to the fitting method.
12. Decayed pions before PIMON.
Uncertainty of the contribution of pion decay before PIMON, is estimated by comparison between the beamMC with Cho and GCALOR/FLUKA model.
Neutrinos from kaons are order of 10−2 of these from pions. Thus the error from thekaon contributions is neglected.
13. Radial distribution of pions.
Radial distribution of the pions affects to the decay probability due to the finite
decay volume. The difference of neutrino prediction from the beamMC with Cho and
GCALOR/FLUKA models is assigned as the systematic error.
14. Kinematic bin size in (pπ , θπ ).
Inside of the (pπ , θπ ) bin, flat population is assumed. Systematic bias from thisassumption is estimated by comparing the spectrums of full simulation with thespectrums which are predicted from the (pπ , θπ ) distribution given by same beamMC.
15. Uncertainly of the neutrino flux below 1 GeV.
BeamMC is used for the neutrino flux and flux ratio below 1GeV. Error of the neutrino
spectrum is quoted as ±100% which is well within 1kt measurement (see Chapter
8.3.1). Error of the flux ratio is estimated by the beamMC by changing the parametersat the formula 4.4 within 90% C.L. of pion production experiments.

98

6.2

Stability of the Proton Beam

6.2.1

Proton beam profile measurement

Proton targeting are continuously monitored by two SPICs; V39-SPIC and TARGETSPIC, which are located in front of the target (Figure 3.1 and Figure 4.1). Typical proton
profile measured by these SPICs are shown in Figure 6.7. Transported proton beam has
Gaussian like distribution in x and y projection, with certain offset caused by pedestal level
fluctuation.

2250

2120.
16.74
3.257

2000
1750

ADC count

ADC counttypical profile
Constant
Mean
Sigma

1390.
18.54
1.636

1200

1500

1000

1250

800

1000

Constant
Mean
Sigma

1400

600

750
400

500

200

250
0

10

20

0

30

10

20

Constant
Mean
Sigma

1400

1416.
19.78
5.495

1200

30

ch
ADC count

ADC countchConstant
Mean
Sigma

1600

1495.
11.86
4.880

1400
1200

1000

1000
800

800

600

600

400

400

200

200

0

10

20

0

30

10

20

ch

30

ch

Figure 6.7: Typical proton profile measured at V39out-SPIC (upper) and TARGET-SPIC(lower) in Nov. 1999 run. Gaussian fit is also shown. 1 channel corresponds to 5 mm
for V39out-SPIC and 1.27 mm for TARGET-SPIC. For these SPIC, small channel number
corresponds to the Southern or bottom side.
Stability of these proton profiles is studied by following two steps.
1. Spill-by-spill fluctuation.
Analysis procedure is explained in Figure 6.8. Simple mean position and r.m.s. of the99

proton profile are studied on spill-by-spill basis. When the proton beam is shifted,
the mean value changed. The mean and r.m.s. of V39-SPIC and TGT-SPIC are
analyzed on each 100 spills (which correspond to one sub-run of beam line DAQ).
Figure 6.8 exhibits the spill-by-spill fluctuation is small enough to deal with summed
profile of one sub-run.
2. Periodical fluctuation.
The profile summed over each sub-run (100 spills) are fitted with Gaussian function
plus linear offset. The fluctuation of these profile center (width) is less than ±5 mm(±25%) at V39-SPIC and less than ±3 mm (±20%) at TGT-SPIC during the wholerun.
Stability of the proton targeting is obtained from the extrapolation of these proton
beam profiles. Proton beam width and the divergence at the target are calculatedwith Formula 4.1 and 4.3, as described in Chapter 4.1.1, in each period. And thefluctuation of the beam center δx and the injection angle ∆θx are calculated withfollowing formula;center shift : δx = ∆x2 + (∆x2 − ∆x1) · (`/L)
angle shift : ∆θx = (∆x2 − ∆x1)/L

(6.1)
(6.2)

where, ∆x1 and ∆x2 are the center shift from the nominal point, for V39-SPIC and
TGT-SPIC, respectively. With same formula, δy and ∆θy are also calculated.
Figure 6.9 shows the time variation of these proton beam properties, and their projection.
The effect to the analysis, that is the event ratio of each detectors, from these targeting
uncertainty is studied using beamMC in following sub-sections.

6.2.2

Injection angle dependence

Neutrino flux is simulated with pencil-like proton beam (no profile spread, and no divergence) with injection angle of 0, 2, 4, and 6 mrad with respect to the nominal beam axis.
Table 6.4-A shows the relative numbers of observed events in 1kt, MRD, and SK, and theirratio. The fluctuation of the injection angle is ±1.8 mrad and ±0.8 mrad by r.m.s. of x andy, shown in Figure 6.9. And the typical emittance spread which is neglected in Chapter
4.1.1 is also several mrad. The study proves that the injection angle of several mrad makes
negligible effect for the event ratio of Far/Near.
100

Typical profile(spill-by-spill)

TGT-SPIC(horizontal)

50

mean of the
profile35

r.m.s. of the
profileTypical plot of

30

40

25

30

20
15

20

10
10

5

0
17.4

17.6

17.8

18

18.2

18.4

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5.4

TGT-X center

4500
4000
3500
3000
2500
2000
1500
1000
500
0

4000
3500
3000
2500
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1500
1000
500
0
0.1 0.2 0.3 0.4 0.5
0RMS of each sub-run
3500
TGT-X width fluct.
3000

TGT-X center fluct.

0

6000
5000

5.8

6

6.2

TGT-Y center fluct.

r.m.s. of above"fluctuation dist."

0.1 0.2 0.3 0.4 0.5
RMS of each sub-run
TGT-Y width fluct.

2500

4000

are filledin these plots
for Nov.99 run(9070 sub-run)

2000

3000

1500

2000

1000

1000

500

0

5.6

TGT-X width"fluctuation ineach sub-run(100 spill)"0

0.1 0.2 0.3 0.4 0.5
RMS of each sub-run

00

0.1 0.2 0.3 0.4 0.5
RMS of each sub-run

Figure 6.8: Spill-by-spill stability of the profile center and width of TGT-SPIC. Top figureis the typical proton profile measured by TGT-SPIC (horizontal). The mean and standard
deviation (r.m.s.) of this plot is filled to the second histograms of “fluctuation distribution”
in each sub-run. Then, r.m.s. of these “fluctuation distribution” means the spill-by-spill
stability of profile center and profile width, analyzed for each sub-run. This values in
Nov.99 run are filled to the lower four histograms. They are x-profile center (left-top),width (left-bottom), y-profile center (right-top), and width (right-bottom) of TGT-SPIC
data. Unit of horizontal axis is channel, which is 1.27 mm spacing. These results show the
proton profile is quite stable in each sub-run (100 spills).

101

(A) Injection angle dependence
Injection angle (mrad) 02
1kt
1. 1.01
MRD
1. 1.01SK
1. 1.00
MRD/1kt
1. 1.00
SK/1kt1. 1.00
SK/MRD
1. 1.00

4
1.01
1.01
1.00
1.00
0.99
0.99

(B) Injection point dependenceCenter shift (mm) 02
4
1kt
1. 0.99 0.96
MRD
1. 0.99 0.96
SK
1. 0.98 0.95
MRD/1kt
1. 1.00 1.00
SK/1kt
1. 0.99 0.99
SK/MRD
1. 0.99 0.99

6
0.99
0.99
1.00
1.00
1.01
1.00

6
0.94
0.94
0.94
1.00
1.00
1.00

(C) Profile width, divergence dependence
config-1 config-2
Width σx (mm)3.4
2.3
Width σy (mm)7.2
5.0Slope kx (mrad/mm)
−2.5
−4.0
Slope ky (mrad/mm) −0.14
−0.36
1kt
1.
1.04
MRD
1.
1.07
SK
1.
1.06
MRD/1kt
1.
1.02
SK/1kt1.
1.02
SK/MRD
1.
1.00
Table 6.4: Proton targeting dependence of the observed events.
Proton targeting dependence of the observed events, estimated by beamMC. These
numbers are the relative number of observed events in each detector and their ratio. For
injection angle dependence study (A), monochromatic pencil proton beam was injected tothe target, whereas, for other studies, standard beamMC was used. In Table-C, config-1
means the default beamMC, and config-2 is the configuration which is based on anotherprofile estimation (see text).
102

0

10000
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1
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-0.03

10000
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Jun

Mar

-0.006May-0.004

-0.03

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-0.02

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-0.002

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0

-0.01

Nov

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5000
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Jun

0.5

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0.5

May

1

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1

center-y

10000

20000

-1

-0.5

0

angle-y10000

0-0.06 -0.05 -0.04 -0.03-0.08 -0.07 -0.06 -0.05 -0.04
20000
sigma-x
sigma-y
15000
15000
10000
10000
5000
5000
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divergence-x
divergence-y
20000
10000
10000
5000
Feb

-0.08
1.5

Jun

1.5

Nov

-0.06

center-x000.01 -0.006-0.004-0.002

0

0.002

Figure 6.9: Stability of the proton profile in front face of the target from 1999 to 2000.
Left figures are the history plot. One data point means the average of half day. In Jun.99,
relative geometry of TGT-SPIC was a little different from the other period. Right figures
are their projection from Nov.99 to Jun.00. Every fitted result is filled in the histograms.

6.2.3

Injection point dependenceThis is studied with beamMC with standard profile (Table 4.1) and the several injection
point of 0, 2, 4, and 6 mm shift from the nominal center of the target. Table 6.4-B shows
the result of the relative number of events. The fluctuation of the injection center is 0.8mm and 0.9 mm by r.m.s. of x and y shown in Figure 6.9. This causes negligible effectwithin 1% for the event ratio of Far/Near.

6.2.4

Profile width and divergence dependence

As described before, profile width and the divergence are calculated from the observed
proton profile width at V39-SPIC and TGT-SPIC, typically shown in Figure 6.7. Twoanalyses are performed to fit the proton profile.
1. configuration-1
One is the fit with Gaussian function. Fitted profiles give us the parameter set of
proton width and the divergence at the target, which are shown as ”config-1” in Table
6.4-C. These parameters are used for standard beamMC (Table 4.1).
2. configuration-2
The other is the fit with Gaussian plus linear offset as noted above. This fitting
103

function is attempted to eliminate the flat background due to the electrical noise.
The obtained parameters are called ”config-2” as shown in Table 6.4-C.
Two simulations are performed with these two parameter sets. The results are also
shown in Table 6.4 (lower table). They shows the difference of the event ratio Far/Near is±1 ∼ 2% level, which is quoted as the systematic error due to the fitting method.
The periodical fluctuation of the profile width and the divergence shown in Figure 6.9 issmaller than this discrepancy from the fitting method difference. Therefore, fitting method
error is adopted as the systematic error of the profile width and the divergence.

6.2.5

Systematic errors due to the proton targeting

Proton is transported along the designed trajectory. Therefore, the injection angle is given
with the accuracy of comparable to the time fluctuation. When proton injection point is 1
mm shifted, the muon profile at MUMON is about 10 cm shifted, due to the magnetic fieldin side of the HORN [50]. Proton beam is controlled being monitored the muon profile(described in next subsection), in addition to the proton profiles at SPICs. Therefore, theinjection point is confirmed with the accuracy of comparable to the time fluctuation. In
addition, neutrino profile center is continuously measured by MRD in Chapter 7.3, and thesystematic error of the neutrino beam direction is estimated there. Hence, systematic errors
due to the injection angle and the injection point are assigned from their time fluctuation
estimated in this section.
In summary, estimated systematic errors from the proton targeting are shown as follows;
systematic errors for MRD/1kt
Injection angle±0.0%
Injection center±0.0%
width, divergence
+2.1%
+2.1%
Quad.-sum
−0.0%

104

for SK/1kt for SK/MRD
−0.3%
−0.3%
−0.8%
−0.8%
+1.6%
−1.0%
+1.6%
−1.3%

+0.9%
−1.4%
+0.9%
−1.6%

6.3

Stability of the Muon Profile Center

Muon profile information measured by MUMON is used for beam steering during the wholerun. Stability of the muon profile center gives the spill-by-spill stability of the neutrino
beam direction, which supports the neutrino beam measurement at MRD. Figure 6.10
shows the typical profiles measured by MUMON-SPD and MUMON-ICH, after pedestal
subtraction and gain correction.
The time variation of this fitted center is analyzed in following two steps like proton
profile case in previous section.
1. First, spill-by-spill fluctuation of the mean of the profile in every 100 spill (one subrun) is analyzed. Although this simple mean has less than half sensitivity of fitted
center motion, it follows the actual shift. Figure 6.11 shows no obvious fine fluctuation. This fact confirms the next step of Gaussian fit after the integration of 100
spills.
2. After taking 100 spill average of the profile, ICH profile is fitted with Gaussian function, while SPD is fitted with asymmetric Gaussian function, in order to obtain profile
center. Figure 6.12 shows time variation of the fitted center from Jun.99 to Jun.00.
They show profile center is always distributed around the designed direction within
1 mrad. Fitted center of SPD profile is also directed to the expected direction within
1 mrad in all the time period, while SPD pad information may be different from thex,y projections of profile in ICH.
These results confirm that neutrino is continuously pointed to the intended direction to
Super-Kamiokande.

105

1000

North

ICH-X

South

1200

800

ICH-Y

Top

800

600

600

400

400

200

200

0

Bottom

1000

-50

0

0

50

-50

0

50

cm
900
800
700
600
500
400
300
200
100
0

North SPD-X

South

-50

50

0

cm
900
800
700
600
500
400
300
200
100
0

BottomSPD-Y

-50

0

Top

50

cm

cm

Figure 6.10: Typical muon profile of MUMON-ICH (top) and MUMON-SPD (bottom) in
Jan. 2000 run. Left two show the horizontal direction and right two show the verticaldirection. Vertical axis is the corrected ADC count, which is already applied pedestal
subtraction and gain correction. This profile is averaged over 100 spill. Both profiles are
fitted with Gaussian function, in order to obtain profile center.

ICH-X center fluct.

5000
4000

4000

3000

3000

2000

2000

1000

1000

0

0

ICH-Y center fluct.

5000

0.1 0.2 0.3 0.4 0.5
RMS of each sub-run

00

0.1 0.2 0.3 0.4 0.5
RMS of each sub-run

Figure 6.11: Spill-by-spill fluctuation of the mean of MUMON-ICH profile in Nov.99 run.

106

fitted center (ch)fitted center (ch)  














 











   North Downward




 














  
designed









  

direction+1mrad+1mrad










  








  














  












  







 Jun. Nov.Jan. -1mrad





   Jun. Nov. -1mrad






 99 99 00





   99 99










   South Jan. Feb.Mar.May Jun. Upward Feb.Mar.May Jun.












00 00 00 00
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    




 
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(1
data
point
/
100
spill)







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 
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 (1
 
 data   point   / 100   spill)   







35

35

30

30

25

25

20

20

15

15

10

10

5

5

0

10000

20000

30000

40000

50000

0

time (1point = 100 spill)

10000

20000

30000

40000

50000

time (1point = 100 spill)

Figure 6.12: Time variation of the muon profile center measured by MUMON-ICH. Left
figure shows the center of horizontal (x) direction. Right figure shows the center of vertical(y) direction. Middle solid line is the designed center toward Super-Kamiokande. Two
dotted line means ±20 cm (1 mrad from the target) shift. One data point corresponds tothe every 100 spill integration.

107

Chapter 7
Neutrino Beam Measurement
7.1

Neutrino Event Selection at MRD

7.1.1

Overview of the MRD analysis

Neutrino events in Muon Range Detector (MRD) is analyzed to confirm the neutrino beam
direction and the stability of the neutrino flux. For these purposes, vertex profile, event
rate and the produced muon distribution are analyzed throughout the whole run.
Figure 7.1 shows the typical neutrino event interacted in the iron plate in MRD. Such aneutrino induced muon track is reconstructed by a track finder.

7.1.2

Overview of the track finder

The track finder consists of the four part, ”Cell fit”, ”Fragment fit”, ”2-D fit”, and ”3-Dfit”, working in this order. They are summarized as follows, and detailed algorithm is
described in Appendix A.
1. First, noise hits are rejected which is mainly caused by the electronics. This removes
typically 20 of noise hits per each one spill data.
2. Cell fit connects all the combination of two hits in X-view (top view) or Y-view(side-view) independently, and makes evaluation of the track to select reliable ones.
3. Fragment fit divides the “cell-fit track” into “fragments” which have more than 3 hitsin 4 drift-tube planes1 Each fragment is fitted with a linear line, considering the drift
time from the reconstructed time of particle arrival (called “Time-zero”: T0).
1

The word ”plane” means the transversely aligned cells in the given z-position. That is, there are two
X-planes and two Y-planes between the neighboring iron plates.

108







        


























        


















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











               









X-view


Fiducial-A(419ton)
Fiducial-B(329ton)
Fiducial-C(73ton)

FGD







 








 Y-view  


MRD
6m

3m

ν

6m

ν

Figure 7.1: The typical MRD event. Hit channels are expressed by closed circles. Noise
hits are already removed. Three fiducial volumes are also indicated.

109

4. 2-D fit connects these fitted fragments from the most upstream fragment to thedownstream fragments, with adopting the best combination based on the distanceand angle between each fragments.
5. 3-D fit combines a 2-D track in X-view and another 2-D tracks in Y-view. It selectsfrom the longest overlap length along the beam axis. Finally these 3-D tracks areused to various analysis as the muon track candidate in MRD. Start point, end point,
path length and track directions are also calculated. Muon energy is calculated fromthe path length in the iron.
Fitted tracks are good agreement with the eye scan. As a result, typically 0.2 tracks arefound in one spill. Tracking efficiency is discussed in latter section.

7.1.3

Neutrino event selection

The fitted tracks are mainly neutrino-induced muons. For quantitative study of the event
rate and the muon distribution, we have to select muon tracks contained in the MRD, andwhose vertices are in the fiducial volume.
Three fiducial volumes of the iron target are defined inside of MRD. Figure 7.1 showstheir geometry.
• Fiducial-A.
The largest cubic volume is used for neutrino profile measurement. This has 6m × 6
m transverse area and from 1 to 9-th iron plate longitudinally (1.4 m total thickness).
Total amount of iron mass is 419 ton.
• Fiducial-B.
This large volume is used for the neutrino beam stability monitor. This is the cylinderof 6 m diameter and 1 to 9-th plate longitudinally. Total amount of iron mass is 329
ton.
• Fiducial-C.
Quantitative analysis of the number of events and the muon distribution are performed using this upstream fiducial, in order to attain better efficiency. The 6 m
diameter is same as Fiducial-B and the longitudinal length is limited from 1 to 3-rdiron plate (10cm thickness × 3 plate). Total amount of iron mass is 73 ton.
Figure 7.2 is the flow chart of the selection. Selection efficiencies of observed data andthe Monte Carlo simulation (neutMC) are summarized in Table 7.1
1. Consistency between X-view and Y-view.
First, some badly fitted tracks are rejected by considering the between a 2-D trackin X-view and another 2-D track in Y-view. We require;110

Reconstructed track

MRD event selection algorithm

Consistency between X-view and Y-view( difference <10count )T0( -45<(difference)<30cm )z of start-point( -45<(difference)<80cm )z of end-point

and.
and.

Longest track selection
cut 2nd(3rd,4th,..) tracks unless( VTXdist and ENDdist >=1m ).or. ( |TIMEdist|>=10count )Time window( 0<T0<35count )Containment ( start & end contained )( start contained )N-layer require ( penetrated iron>=2 )vertex in Fiducial-A ( = 6m x 6m x 1-9th layer )Fiducial-A

Energy range ( 0.5<E<2.5GeV )SAMPLE-A(Fully-Contained)

SAMPLE-Adash(Vertex-Contained)

vertex in Fiducial-B ( = 6m φ x 1-9th layer )SAMPLE-B (for stability meas.)vertex in Fiducial-C ( = 6m φ x 1-3rd layer )SAMPLE-C (for event rate meas.)
Figure 7.2: Flow chart of the event selection scheme. The selection of SAMPLE-A,
SAMPLE-B, and SAMPLE-C are described in this section, while the SAMPLE-A-dashis explained in Appendix B.
111

• Difference of T0 in X-view and in Y-view to be within 10 count (= 500 ns, Figure
7.3-A ).
• Difference of the z-coordinate of the start point to be within −45 and 30 cm(Figure 7.3-B ).
• Difference of the z-coordinate of the end point to be within −45 and 80 cm(Figure 7.3-C ).
The effects of these cuts are about 10% and can be reproduced by neutMC.
2. Longest track selection.
When data are selected at least one track in one spill, about 14% of these spills have
two or more tracks in same spill. Some of them are due to the multiple neutrino
interactions. Others are considered to have associated short tracks near the longtrack. This is considered mainly due to the hadron activity around the vertex. In
order not to count as the double neutrino interactions, such associated tracks are
removed.
When two or more tracks remain in one spill, following three parameters are checked
for all the two track combinations.
• Distance from start point of the second track to the first track (V T Xdist).
• Distance from end point of the second track to the first track (ENDdist).
• Difference of T0 (T IM Edist).

When(V T Xdist < 1 m or ENDdist < 1 m ) and |T IM Edist| < 10 count,the shorter track2 is removed. Figure 7.4 shows the typical distribution of the threeparameters for data and neutMC which have two tracks in one spill. The simulation
does not include multiple event in one spill. Therefore, in the simulation, more than
99% of the second tracks are removed. On the other hand, data can have somefraction of multiple events in one spill. Hence, 66% of the second tracks remain. The
miss-rejection rate of the multi-event is estimated to be 13% by the study of random
matching test of the selected tracks.
This cut acts as the conversion from number of tracks to number of neutrino interactions.
2

In correct definition, the track with shorter overlap length between X-view and Y-view is removed.
This track has mostly the shorter total length than the other track.

112

x 10
10000

30000

7500

20000

5000
10000

2500
0
-20

-10
0
10
20
count
T0 difference

7

10
6
10
5
10
4
10
3
10
2
10
-200

-10
0
10
20
count
T0 difference

6

10
5
10
4
10
3
10
2
10
-100
0
100 200
start-Z difference cm

7

10
6
10
5
10
4
10
3
10
2
10
-200

0
-20

-200

-100
0
100 200
start-Z difference cm

6

10
5
10
4
10
3
10
2
10
-100
0
100 200
end-Z difference cm

-200

-100
0
100 200
end-Z difference cm

Figure 7.3: A: Difference of T0 in X-view and in Y-view. B: Difference of z-coordinate of
the start point in X-view and in Y-view. C: Difference of z-coordinate of the end pointin X-view and in Y-view. In each plot, data (left) and neutMC (right) are compared. In
these distributions, the events are already selected with requiring the vertex containment.

113

TIMEdist (count)

40

40

20

20

0

0

-20

-20

-40

-40
0

100

200

300

400

0

100

TIMEdst (count)

VTXdist (cm)
40

20

20

0

0

-20

-20

-40

-40
100

200

300

300

400

VTXdist (cm)

40

0

200

400

ENDdist (cm)

0

100

200

300

400

ENDdist (cm)Figure 7.4: 2-dimensional distribution of V T Xdist or ENDpoint and T IM Edist for two
track sample. Data and neutMC are compared.

114

70000

16000

60000

14000

50000

12000
10000

40000

8000

30000

6000

20000

4000

10000

2000

0

0

20

T0

40

60

count

0

0

20

T0

40

60

count

Figure 7.5: Reconstructed T0 distribution.

3. Time window
Because the data acquisition is synchronized with beam extraction timing, time window is adopted as 0 < T0 < 35 count (1.75µs width) to reject cosmic ray backgrounds
and late timing activities supposed to be the sky-shine neutron activities. Figure 7.5
shows the T0 distribution.
4. Containment requirement.
Muon energy can be reconstructed only when its start and end points contain in the
MRD, which is called “fully-contained” track. Therefore, fully-contained tracks areused for the analysis. When an associated hit exists at the first or last drift-tube
layer, the track is discarded. To check entering or exiting from the side of MRD,
start and end points are extrapolated one layer further in front side and back side.
When the extracted point is more than 5 cm away from the any wire position, thistrack is judged as entering or exiting, and is excluded from the analysis.
iron
≥ 2.
5. Number of penetration layer Nlayer
iron
Nlayer is defined as the number of penetrated iron plates. In some portion of the shortiron
tracks contains the hit of hadron (p and π) activity. Then, tracks with Nlayer≥ 2 areused to keep safety side.

6. SAMPLE-A, for profile study.
Large coverage is effective to analyze the profile center and the width. Therefore,
Fiducial-A is adopted as the fiducial volume for profile study. The events whose
vertices are in Fiducial-A are selected. This cubic Fiducial-A has relatively uniform
115

0
1
1
2
3
4
5
6
6
7
8

selection
number of track
Consistency of T0
Consistency of start/end-point
Longest track selection
Time window
Containment requirement
Nlayer ≥ 2
Vertex in Fiducial-A
0.5 < Eµ < 2.5 GeV
Sample-A
Vertex in Fiducial-B
Sample-B
Vertex in Fiducial-C
Sample-C

DATA
687599664244600575561321552853274713
192664165125(0.97)(0.90)(0.93)(0.98)(0.50)(0.70)(0.86)

neutMC
141778138471130137123416123383
83450
55700
47903

(0.98)(0.94)(0.95)(1.00)(0.68)(0.67)(0.86)

164935(1.00)

47876(1.00)

144091(0.87)

42056(0.88)

53294(0.37)

15274(0.36)

Table 7.1: Summary of the event selection process. DATA is the observed event from
Nov.1999 until Jun.2000 run. MC event is only generated inside the iron plate, although
DATA contains many beam-induced events from outside.

series of iron-drift-tube structure and enables us to avoid an inefficient area near theside of the detector. Tracks with less than 0.5 GeV energy or more than 2.5 GeV are
not used, because their selection efficiency is low. For low energy muons, they do notpass more than 2 iron plates. For high energy muons, they do not contain inside ofthe detector.
7. SAMPLE-B, for the stability study of event rate and muon distributions.
Since the neutrino flux has a radial dependence, cylindrical Fiducial-B and Fiducial-C
are used for the event rate study and the muon distribution study. For the stability
study, larger Fiducial-B is used, in order to gain the event statistics. The events
whose vertices are in Fiducial-B are called ”SAMPLE-B”.
8. SAMPLE-C, for the event rate and muon distribution study.
In order to obtain lower threshold energy and better acceptance, upstream Fiducial-C
is used for quantitative study of the event rate, the muon energy spectrum, and themuon angular distribution. SAMPLE-C is required as whose vertex is in the first
three iron plates with 10 cm thickness.

116efficiency

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

SAMPLE-A
A-dashSAMPLE-B
SAMPLE-C

0

2

4

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

1

Eν(GeV)

2

3

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

Eµ(GeV)50θµ(deg.)

Figure 7.6: Selection efficiency of the function of Eν , Eµ , and θµ . Solid line shows theefficiency for SAMPLE-C, dashed line is for SAMPLE-B, and dotted line is for SAMPLE-A.
Dot-dashed line means the efficiency for SAMPLE-A-dash, which is described in Appendix
B.

7.1.4

Selection efficiency

Event selection efficiency is estimated using neutMC. For SAMPLE-C, overall efficiency,
which is number of selected events divide by number of generated neutrino events in thefiducial, is 0.36. The efficiency of each interaction type is summarized in Table 7.2. Figure
7.6 shows the neutrino energy dependence, and muon distribution dependence.

type
CC
CC
CC
NC

quasi-elastic
single-meson
multi-πallallgenerated
14309
11277
6149
11208
42943

selected efficiency
7942
0.56
4815
0.43
2305
0.37
212
0.019
15274
0.36

Table 7.2: Summary of the selection efficiency for each interaction type, in Fiducial-C. they
are estimated by Monte Carlo simulation.

117

7.2

Check of MRD Performance and its Stability

The performance of MRD is experimentally checked, and its stability is monitored during
the running period. Following items are discussed in this Section.
• Hit efficiency of the drift-tubes.
• Tracking efficiency.
• Reconstruction resolution.
Finally, the distribution of cosmic ray muons is analyzed for overall confirmation of thedetector stability.

7.2.1

Hit efficiency

Each drift-tube has a little inefficiency for detecting charged particles inside the cells.
In addition, the gaps between the tubes and the masked noisy channels contribute to
the inefficiency of the detector. Effective hit efficiency have been monitored by counting
number of hits on the long tracks during the whole run. Number of included hits divided
by passed drift-tube planes defines the effective hit efficiency.
The analysis use muon tracks which passed longer than 10 planes (passed 4 iron plates),
whose tan θx and tan θy were less than 0.5, and requiring the time window of 5 < T0 <35count.
The results of the effective efficiency from June 1999 to June 2000 are shown in Figure7.7. Average efficiency is 93.9% for x-tube and 93.2% for y-tube. Monte Carlo simulation is
performed with various intrinsic cell hit efficiency from 97% to 100%, which are also shownin Figure 7.7. The result indicates 97.5% to 98.5% efficiency MC has the best agreementwith data. Intrinsic cell hit efficiency of 97.5% is adopted for standard neutMC. The inefficiency of 2.5% includes the geometrical effect coming from a possible miss-alignment of thedrift-tube modules, as well as the real hit efficiency. According to the Monte Carlo study,
1% uncertainty of the hit efficiency yields about 1% difference of the selection efficiencyof SAMPLE-C. Although, this uncertainty also affects the tracking efficiency estimated innext sub-section. Hence, this uncertainty of the hit efficiency is taken into account as thedifference of the tracking efficiency, and provides the systematic error for the event rate at
MRD.
Uniformity of the hit efficiency is analyzed in this way applying to tracks in various area.
The result says the non-uniformity of the hit efficiency is estimated to be less than 1%.
Therefore, effects on the neutrino profile determination are negligible.
118

94

93

93

92

92

91

91

Jun00

94

May00

95

Mar00

95

Feb00

96

Jan00

96

Nov99

97

Jun99

effective hit efficiency (%)

97

96
98
100
cell hit efficiency (%)

Figure 7.7: Left: The effective hit efficiency for each month. closed circles show the hit
efficiency of X-tubes, while closed triangles show that of Y-tubes. Right: The effective hit
efficiency by neutMC, with various hit efficiencies of each cell itself (horizontal axis).

7.2.2

Tracking efficiency

Tracking efficiency is analyzed with performing a re-tracking test. The test is schematicallyexplained in Figure 7.8. The test checks whether the track is reconstructed with restricted
hits in “test area”, from the already “known” long muon tracks. It corresponds to the testiron
= 2 ∼ 4. The method and theof SAMPLE-C tracks with penetrating iron layers of Nlayer
results are described as follows.
1. Data sample.
Following two data samples are used for this re-tracking test.
• Neutrino induced long tracks.
(typically shown in Figure 7.8) Their vertex is contained in 1st or 2rd iron plates.
They passes the Fiducial-C. And they reaches at least one layer downstream of
the test area. The test area is set with 3, 4, or 5 drift-tube layers (whichiron
corresponds to Nlayer= 2,3, or 4) from the 3rd or 4th drift-tube layer.
• Cosmic ray muon tracks.
(typically show in Figure 7.9) They passes the Fiducial-C, and which leave hits
at least one layer downstream of the test area. The test area starts from 2nd,
3rd or 4th drift-tube layer, and have length of 3, 4, or 5 drift-tube layers. These
tracks are taken with a coincidence trigger of upstream- and downstream-TGC
hits in both side of SCIFI.
119

K2K Fine-Grained Detector (Side View) 












 

2) Mask hits  

except test area










 



 


Test area

 


Run 2225 Spill 26396 TRGID 1
100 1 14 2 12 57 0
Nvtx 0100 cm

100 1 14 2 12 57 0
Nvtx 0100 cm1) Long track sample
start-point < test area
end-point > test area





















































































































K2K Fine-Grained Detector (Side View)

Run 2225 Spill 26396 TRGID 1

3) Track finding efficiency
Consistency between
re-fitted track and original one.

Figure 7.8: Method of the re-tracking test.

Due to the geometry of the experimental site, the tracks are distributed as twogroups, as shown in Figure 7.9. One is due to the muons which enter at thelower part of the MRD 1st plane and go downward. The other is due to themuons which enter at the top of MRD detector and exit from the upper part of
the MRD 1st plane.
2. Hit mask.
All the hit informations are masked except the test area.
3. Re-tracking
The track finding routine is applied to the remaining hits. The re-fitted tracks are counted when they match to the original tracks within (start and end point
difference)< 20 cm, and (T0difference) < 4 count.
iron
Figure 7.10 shows the results of the tracking efficiency, as a function of Nlayer, using
neutrino induced tracks or cosmic ray muons. Monte Carlo simulations of neutrino events(neutMC) and the cosmic ray muons are generated and analyzed with same procedure.
The results are overlaid with dashed line in Figure 7.10. The efficiency is more than 90%,iron
= 2 in analysis ofand consistent with simulation a few %. A difference is found at Nlayer

120

Side view

Backward

K2K Fine-Grained Detector (Side View)

Forward

Run701137 Spill

225

y-position at 1st layer

200

81 TRGID2000

175

100 6 11 21 32 44 0
Nvtx 0150

Backward

125

µ

100
75
50
25
0
-400

400

Forward

µ

-200

0

200
400
start point y (cm)Vertical angle

350
300
250

100 cm

200
150
100

Triggercounters

50
0

-50

0

50
θ
y (degree)

Figure 7.9: Typical event display of the cosmic ray muon (left). Distributions of thevertical position at 1st drift-tube layer (right-top) and the vertical angle (right-bottom) of
the cosmic ray sample.

121

tracking efficiency

tracking efficiency

1
0.95
0.9
0.85

1
0.95
0.9
0.85

0.8

0.8

0.75

0.75

0.7

DATA(99Jun-00Jun)

0.7

DATA(cosmic ray)

0.65

MC

0.65

MC

0.6

0.6

Vertex=2nd,3rd iron

0.55
0.5

2

3

4
number of penetrating iron

Vertex=1,2,3rd iron

0.55
0.5

2

3

4
number of penetrating ironFigure 7.10: Tracking efficiency obtained from the re-tracking test. The left figure is theresult using the neutrino induced tracks. The right figure is the one using the cosmic rayironmuons. Horizontal axis means the number of penetrating iron plates (Nlayer). The resultsfrom Monte Carlo simulation are overlaid (box).
cosmic ray muons, in particular, for tracks with large angle. This difference is taken into
account for the systematic error, and the effect for the total number of event is estimatedto be less than 1%, as described in Section 7.5.3.

7.2.3

Reconstruction resolution

Reconstruction resolution is experimentally checked by following two methods.
• Residual of the fit.
Residual of the 2-D fit is investigated. Figure 7.11 shows the results. Width (sigma)of the residual distribution is 8 mm for data, and 7 mm for neutMC. These residuals
mainly come from the multiple scattering of muons in the iron.
• Difference between the re-fitted track and the original one.
In the re-tracking test in previous sub-section, the reconstruction difference of themis investigated. Figure 7.12 shows a typical result. These distributions suggest us theintrinsic vertex and end point determination of typically 5 cm and 1 count (50 ns),
Re-tracking test of neutMC gives the consistent results.
These agreement of the data and neutMC allows us to estimate the resolution using
neutMC.
122

4500
4000
3500
3000
2500
2000
1500
1000
500
0
-10

4702.
Constant
Mean
Sigma

/ 80
2412.
-0.20540.78851400

1314.
Constant
Mean
Sigma

1200

/ 65
699.6
-0.2069
0.6916

1000
800
600
400
200
-5
0
5
10
residual distance (cm)

0
-10

-5
0
5
10
residual distance (cm)Figure 7.11: Residual distribution of the 2-D tracks for data (left) and for neutMC (right).

1500
1000

3000

1500

2000

1000

500

1000

500

0

0

0

0
20
40
start point diff. (cm)020
40
end point diff. (cm)

-4 -2 0 2 4
T0 diff. (count)

Figure 7.12: Distributions of the difference of the start point (left), end point (center), andT0 (right), between the re-fitted track and the original one. Start (end) point differencemeans a 2-dimensional distance between the re-fitted start (end) point and the interpolated
penetrating point at same z-position from the original track information.

123

1400

3500

1000

1200

3000
800

1000

2500
600

800
600

2000
1500

400

400

1000
200

200
0
-50

0

50

500

0
-0.5

0

X (cm)∆

Eµ(GeV)
∆

0.5

0

-20

0

20

θ
∆
µ(deg.)

Figure 7.13: Reconstruction resolutions of the vertex, energy and angle for SAMPLE-C,
which are estimated with neutMC.

• Comparison between reconstruction and the MC true information.
Difference from the MC true value of the muon energy and the polar angle of thereconstructed tracks are estimated for SAMPLE-C. Figure 7.13 shows the result.
Their r.m.s. are 127 MeV and 5.3 degree for the energy and the angle, respectively.
The x-vertex reconstruction of the neutrino events is also estimated. The reconstructed start point is, by our definition, on the drift-tube plane, although the ”true”
vertex position is inside the iron. Including this systematic smearing, the vertex canbe determined within 7cm by r.m.s. as shown in Figure 7.13.
Extend to the case of SAMPLE-A and SAMPLE-B, these resolutions are almost the
same.

7.2.4

Cosmic ray measurement

Cosmic ray muons are measured for the demonstration of the stable operation of the detector. The data are taken by the off-spill trigger, which is 1 sec after the on-spill trigger. Only
the cosmic ray muons contribute to the off-spill data as tracks. The same track finder isapplied to find the muon tracks. Figure 7.14 shows the time variation of the reconstructed
3-D track rate. The average number of tracks is about 11 per 1000 triggers and has beeniron
distribution and angular distributions arestable within the statistical error. The Nlayer
also analyzed on a monthly basis. The results show no time variation is observed over the124

99 10 30 15 56 48 0
Nvtx 010 cm

Ntrack / 1000 triggers

K2K Fine-Grained Detector (Side View)
Run 2026 Spill 13616 TRGID 20

18
16
14
12
10
8
6
4
2
0

0

25

50 
75
100 125 150 175

200




Ntrack/1000triggerIntegrated
days

Figure 7.14: Number of reconstructed 3-D tracks from the off-spill data as a function oftime. The horizontal axis shows the integrated days. The vertical axis shows the numberof tracks per 1000 triggers.

statistical fluctuation [57]. The stability of these distribution show the detector has beenworking in these period.

125

7.3

Neutrino Profile at MRD

Neutrino beam profile is obtained by measuring the vertex distribution in MRD. In ourstandard analysis in this section, fully-contained (FC) events are analyzed. In addition,
another profile analysis is performed using vertex-contained (VC) events, for the crosscheck. This is described in Appendix B.

7.3.1

Vertex profile of fully-contained (FC) events

SAMPLE-A is used for this analysis. It is defined as the event whose start point is in
Fiducial-A, (6m × 6 m) and whose end point is contained inside of the MRD. The distributions are corrected with the geometrical acceptance as follows.
1. SAMPLE-A is arranged to be a distribution of X-vertex, Y-vertex, and the reconstructed energy. In this analysis, there are 12 bins (50cm × 50 cm bin) in X-vertex
and Y-vertex, and 4 bins (0.5 GeV bin, from 0.5 GeV to 2.5 GeV) in energy.
2. Acceptance for the muon track has a dependence on the vertex position and theenergy. Thus, the acceptance of each bin is estimated by Monte Carlo simulation foreach X, Y, and energy region. Only for this estimation, neutrino event is uniformly
generated with flat spectrum, in order to avoid the position dependent bias and toacquire enough statistics for high energy muons.
3. The corrected distributions in all the energy bins are summed up. Obtained 2dimensional distribution is taken to the projection of x and y direction.
Three profile distributions are obtained with different muon energy range.
• FC-All-Energy (0.5 < Eµ < 2.5 GeV).
All the energy bins are summed.
• FC-Low-Energy (0.5 < Eµ < 1.0 GeV).
Lower energy muons mainly come from lower energy neutrinos. Typical neutrinoenergy is 1.4 GeV in average.
• FC-High-Energy (1.0 < Eµ < 2.5 GeV)High energy muons mainly come from high energy neutrinos. Typical neutrino energyis 1.7 GeV in average.
Figure 7.15 shows the corrected profile of FC-Low-Energy (top) and FC-High-Energy(bottom), for Nov.99 to Jun.00 run. (The obtained profile for Jun.99 run is presented inAppendix E.2.) They prove that neutrino is well pointed to the designed direction to theSuper-Kamiokande. The neutMC with same reconstruction procedure are overlaid. Theirwidth of distribution agrees well with the observation.
126

35000

DATA

35000

30000

MC

30000

25000

25000

20000

20000

15000

15000

10000

10000

5000

5000

0

-200

0

Low Energy
22500
20000
17500
15000
12500
10000
7500
5000
2500
0

-200

0

High Energy

0

200

-200

x (cm)

Low Energy
22500
20000
17500
15000
12500
10000
7500
5000
2500
0

200

0

x (cm)-200

0High Energy

200y (cm)200

y (cm)

Figure 7.15: Corrected vertex profile of fully-contained (FC) events in MRD, for Nov.99 toJun.00 run. Number of contained events is corrected with acceptance. DATA (cross) andneutMC (box) are overlaid, with normalization by the area under the histograms. Error
bars are due to data statistics and also MC statistics of the applied efficiency correction.
In these profiles, 30 cm shift corresponds to 1 mrad off from the nominal direction.

127

profile sigma x (cm)profile center y (cm)

80
60
40
20
0
-20
-40
-60
-80
-100

500
450
400
350
300
250
200
150
100
50
0

profile sigma y (cm)profile center x (cm)

100
80
60
40
20
0
-20
-40
-60
-80
-100

500
450
400
350
300
250
200
150
100
50
0

integrated day (1 data point / 5 days)

integrated day (1 data point / 5 days)

Figure 7.16: Stability of the neutrino profile center (left figure) and width (Gaussian sigma,
in right figure) from June 1999 to June 2000, obtained from FC-all analysis. DATA isanalyzed every five days integration. The error bars mean the Gaussian fitted error. They
mainly come from the statistics of DATA and Monte Carlo event used for acceptancecorrection. Designed beam direction is x = 0 cm and y = −15.8 cm (solid line in left
figure). Dashed line in left figure means the ±1 mrad (= ±30 cm) boundary. Dashed line
in right figure means the width estimated by neutMC.

7.3.2

Stability of the neutrino profile

Long-term stability of the profiles is studied as follows. Vertex profiles are integrated every
five days, to obtain enough statistics for reconstruction. Short time stability within fivedays are monitored and confirmed to be stable, by the proton measurement (SPIC) andthe secondary muon measurement (MUMON) as discussed in Chapter 6.2 and 6.3.
Each profile is fitted with Gaussian function to obtain the profile center and the width.
Gaussian function is proper because reduced chi-square is always equal to or less than 1.
Figure 7.16 shows the results of fitted center and its width (Gaussian sigma) in whole run.
Since MRD is located at about 300 m away from the target, 30 cm shift corresponds to 1
mrad-off direction. The result show the profile center of both X and Y have been always
distributed around the nominal direction (solid line) within 1mrad (dashed line).
Stability of FC-Low-Energy profile and FC-High-Energy profile are also analyzed. Profile
center of FC-High-Energy analysis is always pointed to nominal direction to SK within 1
mrad. While the center of FC-Low-Energy analysis is confirmed with 2 mrad accuracy.
This is because low energy events have broad profile as shown in Figure 7.15. Although,128

center x
0.
+18
+5
+24
+13
+20
+11
+17
+14

nominal center
Jun.99Nov.99
Jan.00
Feb.00Mar.00
May.00
Jun.00Nov.99 to Jun.00

(cm)
±8
±6
±7
±6
±6
±6
±6
±5

center y
−16
−45
−30
−28
−29
−25
−28
−34
−29

(cm)

width x(cm)

width y

(cm)

±10
±6
±8
±6
±6
±7
±7
±5

340
308
311
307
305
312
322
311

±17
±12
±13
±11
±11
±13
±13
±9

354
301
325
308
313
322
320
314

±19
±11
±15
±11
±12
±14
±13
±10

Table 7.3: Summary of the fitted center and width of the neutrino profile by FC-all analysis,
on monthly basis from June 1999 to June 2000. Fitting errors are also shown.

this broad profile means the direction determination of low energy event is less important
than that of high energy event. Profile width of both analyses is agreed with that ofneutMC.
Fluctuation of the neutrino beam direction is discussed.
1. The fitted center distribution is made by projection of the each point in Figure 7.16left, with weighted by its number of observed events in this period. R.M.S. of this
distribution shows the degree of fluctuation of the neutrino beam direction.
2. On the other hand, the average of the fitted error in each data point of Figure 7.16-left
is calculated.
The results are as follows.
12xy
R.M.S. of the profile center 11 cm 13 cm
average of the fitted error 11 cm 12 cm

The agreement of these two values proves that the distribution is explained by the statisticalfluctuation, no other unexpected instability is observed.
The stability allows us to fit an integrated profile by each month. The fitted center andthe width for each month are summarized in Table 7.3. The neutrino beam direction isstable within the fitting error, again.

7.3.3

Profile reconstruction test by Monte Carlo simulation

The profile reconstruction is tested by neutMC with shifted beam axis. Same analysis
routine is applied for x + 50 cm shifted and y ± 50 cm shifted MC sample. The fitted129

beam shift
CenterX +50cm
Y +50cm
Y −50cm

method(nominal)
FC-all(nominal)
FC-all(nominal)
FC-all(nominal)
FC-allcenter
(0)
+1
(+50)
+54
(0)
+1
(0)
+5

x (cm)±5±9±7±9center
(−16)
−16
(−16)
−17
(+34)
+57
(−66)
−62

y (cm)width

x (cm)width

y (cm)

±5

292

±9

300

±10

±9

275

±14

293

±16

±11

266

±12

291

±16

±11

296

±17

294

±17

Table 7.4: Reconstruction test of FC profile, with neutMC with shifted beam axis.

results are summarized in Table 7.4. The results almost agree with the nominal input axis.
But, in some case, the reconstructed center is outside of the true position. Therefore, thesystematic errors of these methods are quoted from the largest discrepancy among thistest, as follows;
for FC-all analysis :−23cm × (center shift)/50cm

This error is adopted instead of the fitting error, only for the near side to the nominal
center.

7.3.4

Conclusion of the neutrino beam direction

Finally, the neutrino beam direction is concluded as following precision;
periodJun.99Nov.99 to Jun.00

directionx√ 2y 2x +y
x√ 2y 2x +yprofile center at MRD+18+8−8 cm (South)+13−29−10 cm (Down)
35+12−15 cm+15+5−7 cm (South)−13+6−5 cm (Down)
20+7
−9 cm

angle
0.6 mrad1.0 mrad1.1 mrad0.5 mrad0.4 mrad0.7 mradIn addition, the analysis results with vertex-contained (VC) events are presented in Appendix B. They show consistent results with above results. We conclude that the neutrino
beam is stably directed to SK within 1 mrad accuracy.
When the neutrino beam is shifted from the designed direction, neutrino flux is decreased
at both near site and far site simultaneously. Monte Carlo simulation is performed with 1.7
130Off-direction
1kt
MRD
SK

0
1.
1.
1.

x + 1.7 mrad
0.99
0.98
0.99

Off-direction
MRD/1kt
SK/1kt
SK/MRD(Jun.99)
1.1 mrad
1.00
1.01
1.01

y − 1.7 mrad
0.98
0.98
0.99

x + 1.7, y − 1.7 mrad
0.97
0.96
0.99

(Nov.99 to Jun.00)
0.7 mrad
1.00
1.01
1.01

Table 7.5: Relative rate at 1kt, MRD and SK when beam is off-direction, which are estimated by the Monte Carlo simulation. Normalization is done by the number of injected
proton.

mrad off-centered flux and obtained the observed event rate at Near detector (1kt, MRD)
and Far detector (SK). The results are summarized in Table 7.5. The change of the event
rate ratio due to the 1 mrad miss-direction is expected to be about 1%. This is negligibly
small comparing to other systematic errors.
In this thesis, center value of the event rate is kept to the case of perfect direction,and the difference due to the off-direction is assigned as the systematic error. This error
amounts to 0.6% (1.1%) for SK/1kt event ratio, in Nov.99 to Jun.00 run (Jun.99 run).

131

7.4

Muon Distribution at MRD

7.4.1

Observed muon spectrum and angular distribution

When a νµ interacts to a nucleon by CC quasi-elastic scattering, the neutrino energy canbe reconstructed by measuring the out-going muon energy Eµ and the polar angle θµ withrespect to the neutrino direction, as follows3 ;Eν =mN · Eµ − m2µ /2
mN − Eµ + pµ cos θµ(7.1)

where, mN (∼ 0.94 GeV) and mµ (∼ 0.106 GeV) are nucleon and muon mass. Therefore,
distributions of the muon energy and polar angle are the confirmation of the neutrinoenergy spectrum. In this sub-section, observed distributions are compared with those ofneutMC. SAMPLE-C is used for this study.
Figure 7.17 is the Eµ spectrum and the θµ distribution in Nov.99 to Jun.00 run. Observed
data is plotted by solid cross. The dashed line shows the distribution of neutMC, whichassumes the same hadron interaction inside the iron nucleus (nuclear effect) as in the oxygen
nuclei, as noted in Chapter 4.2.7. The dotted line shows the “muon-only” simulation, in
which only muons are put to the detector simulation. This corresponds to 100% nuclear
absorption of hadrons. Figure 7.17 shows that the observed distributions are between
these two simulations. Therefore, the difference of these two simulations is assigned as thesystematic error for comparison of ν − Fe and ν − H2 O interaction. The results of Jun.99
run are presented in Appendix E.3.

7.4.2

Stability of the muon distribution

The time variation of the muon energy spectrum and angle distribution are studied. Stability of the muon distribution is the evidence of the stable neutrino spectrum. It is alreadyshown that MRD responses; they are efficiency and noise, have been stable during thewhole period.
SAMPLE-B is used for this stability analysis. Due to the large mass of MRD irontarget, contained events of every five days have enough statistics to be compared eachother. Figure 7.18 clearly proves the monthly stability from Nov.99 to Jun.00. Figure 7.19
shows the reduced chi-square of the shape of the muon energy and angle distribution fromthe averaged ones, in every five days. Comparison is done after the normalization with its
number of observed event. The variation is consistent with the statistical fluctuations.
These muon distribution stabilities imply the neutrino energy spectrum is stable throughout this experimental period.
3

Fermi motion of the target nucleon is neglected in this formula.

132

10000

16000

DATA

14000

MC, standard

DATA
MC, standard
8000

MC, µ
-only

12000
10000

MC, µ
-only
6000

8000
4000

6000
4000

2000
2000
0

0

0.5

1

1.5
Muon energy

2

2.5
3
Eµ(GeV)

0

0

10

20

30

40

50

Muon angle

60

70

80
90
θ
µ(degree)Figure 7.17: Eµ spectrum and θµ distributions observed in MRD, for Nov.99 to Jun.00 run.
Observed data (solid) and standard neutMC (dashed) are overlaid, with normalization by
their entry. Dotted line shows the muon-only Monte Carlo, in which produced hadrons
are killed (see text). Normalization of the dotted histogram is done by its generated event
relative to the standard neutMC (dashed). Difference of the selected event is 5.6% whichis correspond to the difference of their area.

133

0

1

2

Jan.00
Average0

1Mar.00
Average0120Eµ(GeV)2

Feb.00
Average0

1

May.00
Average120Eµ(GeV)

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

2

Jun.00
Average1

arbitrary unit

arbitrary unit

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Nov.99Average

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

arbitrary unit

arbitrary unit

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

2
Eµ(GeV)

Nov.99Average0050

Jan.00
Average050

Feb.00
Average050Mar.00
Average

May.00
Average

Jun.00
Average500θµ(degree)500θµ(degree)50θµ(degree)reduced χ for Eµ

Figure 7.18: Monthly plot of Eµ and θµ distributions (solid), overlaid with the average ofNov.99 to Jun.00 (dashed). Normalization is done by its number of observed event. Error
bars mean statistical errors only.
3

2

2.5
2

1.5
1
0.5
0

reduced χ for µθ

3

2

2.5
2

1.5
1
0.5
0
integrated day (1 data point / 5 days)

Figure 7.19: Reduced chi-square of the Eµ spectrum and θµ distortion from the averaged
ones. The data are analyzed in every 5 days. Vertical axis are already divided by the
degree of freedom, which is typically 9 and 14, for Eµ and θµ , respectively.

134

Period
Target diameter
HORN
Number of spill
P.O.T. (×1018 )Observed SAMPLE-C
Ncorr
Event rate (/1015pot)

Jun.9920mmφ
200kA
615896
2.93
7417
21516
7.4

Nov.99

Jan.00552335
2.72
8140
22886
8.4

390715
2.04
5997
16861
8.3

Feb.00 Mar.00
30mmφ
250kA
724648 627875
3.81
3.49
11228
10306
31568
28975
8.3
8.3

May.00

Jun.00467142
2.51
7464
20985
8.3

649740
3.54
10159
28562
8.1

Table 7.6: Summary of the number of observed event (SAMPLE-C) in MRD. Efficiency
corrected number of interactions Ncorr and the event rate are also shown.

7.5

Neutrino Event Rate at MRD

7.5.1

Event rate stability

Table 7.6 summarizes the number of observed events. The number is normalized by accumulated number of targeting protons measured by TGT-CT, and summarized by every halfdays and two days. Figure 7.20 shows the time variation of the event rate of SAMPLE-B(upper solid) and SAMPLE-C (lower solid). Each point corresponds to the two days average rate. In Jun.99, experiment was running with different HORN system. Thus, theevent rate is different from other period by factor of 0.86 for SAMPLE-B and 0.89 for
SAMPLE-C.
No fluctuation is observed except for statistical ones either in half days integration plot
or in two days plot. Right figures of Figure 7.20 show the difference distribution from theaveraged rate for SAMPLE-B and SAMPLE-C. Standard deviation (r.m.s.) of each plotis 5.5% and 6.8% for SAMPLE-B and SAMPLE-C, respectively. These are completely
explained by the statistical fluctuation. For another verification, chi-square is calculated
from the average rate. Total chi-square of the period is summarized at the bottom tablein Figure 7.20. They show the chi-square value is almost equal to the degree of freedom.
It is concluded that the MRD events is stable within the statistical error.

7.5.2

Calculation of the neutrino interaction rate at MRD

Neutrino interaction rate presents the product of the neutrino flux and the cross section.
Number of observed SAMPLE-C events is corrected by the event selection efficiency (M RD )of 0.356 (0.345) for Nov.99 to Jun.00 (Jun.99), estimated by neutMC. And it is normalized
M RD
by p.o.t. to obtain the interaction rate rcorr. The results are shown in Table 7.6.
135

x 10 4Fe event / 5×10 ppp

0.07

2000

12

1750

0.06

1500
1250
1000

0.05

750

SAMPLE-B

500
250

0.04

0
0.7

0.8

0.9

1

1.1

1.2
1.3
relative rate

1.1

1.2
1.3
relative rate

SAMPLE-B

x 10 4

0.03

2000
1750

SAMPLE-C

0.02

1500
1250
1000
750

0.01

500

Jun.99 Nov.99 Jan.00 Feb.00 Mar.00 May.00 Jun.00

250

0

0
0.7

0.8

0.9

1
SAMPLE-C

integrated day (1 data point / 2 days)

SAMPLE-B
SAMPLE-C

periodaverage rate
χ2
average rateχ2

Jun.990.034
57 (39 d.o.f.)
0.013
43 (39 d.o.f.)

Nov.99 to Jun.00
0.040
234 (220 d.o.f.)
0.015
260 (220 d.o.f.)

Figure 7.20: Left figure shows stability of the MRD event SAMPLE-B (upper solid) andSAMPLE-C (lower solid), from Jun.99 to Jun.00. One data point corresponds to theaveraged rate of each two days. The event rate is normalized to 5 × 1012 protons on target,
which is the typical proton intensity per one spill. Error bars are statistical error only.
Right two figures are their projection. Right-upper figure is the event rate distributionof SAMPLE-B, which is divided by the average rate of corresponding horn configuration.
In this figure, the event rate is calculated on every half days. Right-bottom figure is thecorresponding distribution of SAMPLE-C. Bottom table summarizes the average event rate
and the chi-square from the average.

136

Item
Fiducial volume
Selection criteria
Tracking efficiency
Background contamination

Systematic error+1.2 −2.1 %+1.0 −4.5 %+1.0 −1.0 %−0.3 %

Table 7.7: Systematic errors from MRD event detection scheme. This is used for theobserved MRD event rate per unit proton intensity, that is, the normalization factor of theneutrino flux determination.

7.5.3

Systematic errors at MRD

Table 7.7 shows the systematic errors from MRD detection scheme, except the physics
uncertainty.
1. Fiducial volume error.
Fiducial volume is defined by the x, y and z coordinate of the tracks start point.
The tracking residual shows no systematic bias for the miss-vertex reconstruction
produced by the tracking algorithm.
We compare the event rate with different fiducial definition as shown in Table 7.8.
+0.8%
+0.9%
Radial dependence is within −2.1%
and z-dependence is within −0%. Quadrature sum+1.2%
is taken to be concluded the systematic error of the fiducial volume definition is −2.1%.
2. Selection criteria error.
Estimation of the event selection errors is summarized in Table 7.9.
Errors from ”consistency between X-view and Y-view” and ”time window” are estimated by changing the cut value. Maximum difference between data and simulation appears when start point difference limits to 0 < (dif f.) < 30 cm instead of−45 < (dif f.) < 30 cm. This tight cut prohibits the situation that: two y-tubes
have no hits and more than one of the x-tubes has a hit. One reason is that neutrino
interaction in the chamber of x-tube makes hits only at x-tube. In the neutMC, thechamber mass is considered, but the events were generated in the iron.
Uncertainty of the ”longest track selection” is considered from the rejection probability of a coincidental two events. This “over-killing” probability is 13%, which is
described in Section 7.1.3. The probability of the multi-events occurs in one spill isabout 0.05. Then, 0.7% of the neutrino events are rejected by this cut. This number
is quoted as the systematic error of this cut.
137

Fiducial volume
Number of events
radiusiron plate DATA MC difference< 3m
1 to 3rd
1.
1.
default< 2m
1 to 3rd
0.53 0.54
−2.1%
< 4m
1 to 3rd
1.33 1.32+0.5%
all the iron 1 to 3rd
1.39 1.38
+0.8%
< 3m
4 to 9rd
1.70 1.69
+0.9%
< 3m
1 to 9rd2.70 2.69
+0.6%
+1.2%
Quadrature sum−2.1%
Table 7.8: Event rate comparison with different fiducial volume definition. DATA and MCmeans the relative number of events in their own fiducial volume, for Nov.99 to Jun.00
data and the neutMC, respectively.

Selection
cut value change
Difference of T0±1 count
Difference of start/end-point various combination
Time windowloosen 10 countLongest track selection (see text)
Quadrature sum

maximum difference+0.2 −0.0%+0.7 −4.5%+0.1 −0.0%+0.7 −0.0%+1.0 −4.5%

Table 7.9: Error estimation of the MRD event selection.

+1.0%
To summarize, quadrature sum of these errors is −4.5%, as the systematic error due
to MRD event selection.

3. Systematic error from tracking efficiency.
Tracking efficiency is estimated by the re-tracking test for long track sample describedin Section 7.2.2. This re-tracking test is the overall test including physics process(energy deposit, multiple scattering), detector simulation (hit efficiency) and tracking.
iron
Figure 7.10 shows the tracking efficiency as a function of Nlayer
and track slope foreach vertex iron plate. We apply the efficiency correction to observed neutrino eventwith the estimated efficiency from data or neutMC as follows;

Ncorr =

θµ nlayer
Vz XX
X Nobs (Vz , θµ, nlayer)(Vz , θµ , nlayer)

138

(7.2)

All
1st layer
2nd layer
3rd layer

Nobs
53295
19144
18622
15529

DAT A
Ncorr
55985
19947
19715
16323

MC
Ncorr
56021
19912
19771
16338

difference
−0.1%
+0.2%
−0.3%
−0.1%

Table 7.10: Comparison corrected number of track with estimated tracking efficiency fromdata and simulation. Nobs is the observed number of track from 1999 June to 2000 June.

where Vz means the vertex iron plate number, Nobs is observed number of events, and is the estimated efficiency. The results are summarized in Table 7.10. Considering
the statistical error of the tracking efficiency study and the discrepancy of the hit
efficiency estimation (Section 7.2.1), the systematic error of the tracking efficiency isquoted ±1%.
4. Background contamination.
Three probabilities of the background event are considered.
• One probability is due to the cosmic ray tracks, miss-reconstructed as the contained events. Another probability is due to drift-tube noise. These probability
is estimated by analyzing the off-spill-timing data (same data as used for thecosmic ray measurement in Section 7.2.4). The data are analyzed with sameprocedure as neutrino data. The result is; 18 events are satisfied the criteria of
SAMPLE-C, per 2, 067, 886 trigger. They are mainly made by cosmic ray muons
with large scattering inside of MRD. This selection rate is about 0.06% of thetypical neutrino event rate.
• The other probability is due to beam-induced muons. They enter from upstream,
but the track finder fails to identify the entering points. This probability is estimated by analyzing the cosmic ray muons entering or exiting from the upstream.
The cosmic ray data are triggered by TGC hits, same as Section 7.2.2 (see Figure7.9). The entering point to MRD is calculated by extrapolation of both TGC
hits. Total 5904 events are analyzed. The track finder identifies most of themto “incoming muons”. Only 10 events (0.2%) are miss-reconstructed to be thecontained tracks.
Using this miss-reconstruction probability, the contamination rate of the upstream muon is estimated. In the neutrino data of Nov.99 run, 9128 eventsare coming from the upstream, when 8140 events are in SAMPLE-C. Thus, thecontamination rate is less than 0.2% for SAMPLE-C.
139

Consequently, probability of the background contamination is estimated to be negligibly small (< 0.3%).

140

Chapter 8
Measurement of the Neutrino Event
Rate at 1kt Detector
8.1

Neutrino Event Selection

8.1.1

Overview of the 1kt analysis

Neutrino events in 1kt water Cherenkov detector (1kt) are analyzed in order to measure the
1kt
event rate Nobs
in the near site. Comparison of the neutrino event rate in 1kt and SK is thebetter than the comparison of MRD and SK, because of same interaction target (water),and same detection techniques. The systematic errors on the comparison of the event rate
are almost canceled by adopting the similar selection criteria to SK. For this reason, theactivities are counted, when total Cherenkov photons exceed the detection threshold, andthe interaction vertex are in the fiducial volume.
Figure 8.1 shows the typical neutrino event. Event selection is explained in the following
sub-section. Table 8.1 shows the typical number of selected events in each step in Jan.00
run, and Table 8.2 summarizes the numbers of all the period.

8.1.2

Event selection

1. Good beam selection.
The commonly-defined good beam spills are used, as described in Chapter 5.3.
2. Triggered on-spill data.
Events occurred in beam time of 1.2µs are recorded by HITSUM trigger described in
Chapter 3.5.1
3. Without pre-activity.
The events with pre-activity within 1.2µs before beam timing are rejected with TDC
141

Figure 8.1: A typical neutrino event in 1kt detector.

1

2
5
6
6

number of used spills
P.O.T. (×1018 )(MC) generated in Fiducial-C
triggered spills
total
total peak in FADC (Npeak)
1
1 peak in FADC (Npeak )Vertex in Fiducial-B
Vertex in Fiducial-C

DATA
346158
1.81

MC125616
91864
85238
67641
6513
3505

17535290300

Table 8.1: Summary of the number of events at each selection stage, in Jan.00 run. Presented number of spills are after pre-activity cut (3).

142

Nov.99

Jan.00

Feb.00

May.00

Jun.00Solid - DATA
Dashed - MC

Mar.00Figure 8.2: Efficiency curve of the total photo-electron selection around the thresholdheight. The efficiency estimated from data (solid line) and from MC simulation (dashedline) are overlaid. In Nov.99, the efficiency curve was distorted by the disconnection of oneof PMTSUM cables (see text).

information recorded in TMC module. The source of the pre-activities are mainlycosmic ray muons, which could cause fake in-time events by reflection signal on thecables. The fraction of the spills with the pre-activity event is about 1.9% (3% in1999 run, before the buffer-amplifiers were installed). Those spills are not counted in
the accumulated number of spills and p.o.t.
4. Total photo-electron threshold.
Analyzed events are required to have more than about 1000 photo-electron of PMTSUM (sum of all the inner PMTs) in Flash-ADC (FADC). This threshold is equivalent
to visible energy deposit of about 100 MeV. Figure 8.2 shows the efficiency curve as afunction of total photo-electron for data and Monte Carlo simulation. This thresholdis set to avoid electron signals from muon decay in the vessel.
5. Single event selection.
In 1kt detector, the rate of the neutrino-induced activity is about 0.2 ∼ 0.3 events
per spill. Therefore, more than two neutrino events sometimes occur in the same
spill. In these “multiple-events,” it is hard to reconstruct the real vertex position.
143

10

6

10

5

10

4

10

3

12000

10000

8000

6000

4000
10

2

2000

10
1

2

3

4

FADC npeak (2000/Jan-Mar)

0
-200

5

peaks/spill

0

200

400

600

800

1000

FADC allpeak time (2000/Jan-Mar)

1200

1400

nsec

Figure 8.3: Left: Number of peaks in one spill. Right: Timing distribution of selectedpeaks.
In addition, several quantities are distorted by overlapping of the events. Therefore,
only the events with single interaction are used for this analysis.
The number of the events in one spill is measured by counting the number of peaksin PMTSUM signals in FADC, within 1.1µs of beam time window. Figure 8.3 shows
the distribution of number of peaks in one bunch, and the timing distribution of ofthe selected peaks.
The effect of multiple-events is taken
to the number of events. The into accounttotal
1
correction factor of multiple-events Npeak /Npeak is simultaneously calculated. Thistotal
) divided by theis the ratio of the number of total peaks at FADC signal (Npeak
1
number of events that have only one peak in each spill (Npeak ).
6. Fiducial volume cut.
In order to distinguish neutrino interactions from incoming background events fromoutside, the following three fiducial volumes are defined inside of the detector. The
fiducial volumes are shown in Figure 8.4.
• Fiducial-A, for neutrino profile analysis.
Perpendicular cylinder with 3 m radius, and 6 m length.
• Fiducial-B, for the event rate stability.
Horizontal cylinder with 2 m radius, and 4 m length. Total mass is 50 ton.
144

yFiducial volume C(for event rate, 25t)
Fiducial volume B(for stability, 50t)
6m

4m

ν
z

Fiducial volume A(for profile, 170t)

2m
4m
6m

Figure 8.4: Definition of the fiducial volume in 1kt.

1kt
• Fiducial-C, for the measurement of the number of event Nobs.
Horizontal cylinder with 2 m radius, and −2 < z < 0 m length, where the tankcenter is z = 0. Total mass is 25 ton.

The vertex point is reconstructed by the ”TDC fit”, which is explained in Appendix
C, using the TDC information of PMTs. When the fitted vertex point is in thisfiducial volume, the event is selected as a neutrino event candidate.
In Nov.99 run, one of four PMTSUM cables was disconnected by mistake. The missing of
one cable decreased the event selection efficiency by 1%, and distorted the efficiency curveas shown in Figure 8.2. The effect is included in the detector simulation of this period.
In May.00 and Jun.00 run, the stop-timing signal to FADC were sometimes drifted andthe 8-th and 9-th bunches sometimes went outside of 1.1µs gate time window. To avoid
this gate timing uncertainty, we analyzed the neutrino data in 1 to 7-th bunches. Then,the correction factor of (7-bunch)/(9-bunch) ≡ k7→9bunch is applied to measure the neutrino
event rate. The k7→9bunch was calculated based on the real data in which the stop signal
was not drifted in this period. The k7→9bunch has been quite stable during the running
period. The instability of k7→9bunch are assigned as a systematic error of ±1.2%.

8.1.3

Selection efficiency

Figure 8.5 shows the selection efficiency for the Fiducial-C as a function of neutrino energy
and vertex position. The efficiency is 88% for CC events and is 56% for NC in-elastic
145

efficiency

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

200
Vertex-r (cm)

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

-250 0 250
Vertex-z (cm)

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

2
4
Eν(GeV)

Figure 8.5: Selection efficiency for events in fiducial-C, as a function of its vertex position(A,B) and neutrino energy (C). For figure (A), horizontal axis is the radius from the z-axis(beam direction). For figure (B), horizontal axis is the z-position.

events. The expected ratio of CC to NC gives an overall efficiency of 72%. The main
source of inefficiency is the 1000 photo-electron threshold.

8.1.4

Background estimation

The fiducial cut rejects most of the cosmic ray muons and neutrino induced incoming muons
from outside. The contamination rate of the remaining background events is estimated asfollows.
• Cosmic ray muons.
The rate of cosmic ray muons is estimated by the random-triggered data. The data
are analyzed with the same selection. As the result, the cosmic ray contamination is
1.0% of the neutrino candidates in the Fiducial-C. In Jun.99 and Nov.99 run before
the installation of the buffer-amplifiers, the reflection pulse in a signal cable sometimes
caused fake events miss-identified as the Fiducial-C events. During this period, thecontamination was estimated to be 2.6%.
• Neutrino induced incoming muons.
The random-triggered data do not include in-coming muons from the neutrino interaction in surrounded materials. Most of them are injected from the upstream of146

Period
Target diameter
HORN
P.O.T. (×1018 )total
total peak in FADC Npeak
1
1 peak in FADC
Npeak
Observed events
Nobs
Efficiency
1kt
BackgroundRBKG
7-bunch correction
k7→9
Total interactions
Ncorr
Event rate (/1015 pot)

Jun.99
20mmφ
200kA
2.60
109119
89782
4282
0.706
0.031
−
7150
2.76

Nov.99

Jan.002.62118321
96304
4923
0.708
0.031
−
8286
3.17

1.81
85238
67641
3505
0.719
0.015
−
6052
3.34

Feb.00 Mar.00
30mmφ
250kA
3.74
3.35
177437 155778
140740 122651
6986
6080
0.724
0.719
0.015
0.015
−
−
11985
10581
3.21
3.17

May.00

Jun.00

2.42
88558
74135
3574
0.718
0.015
1.282
7510
3.10

3.16
114739
95652
4745
0.718
0.015
1.283
10021
3.17

Table 8.2: 1kt event summary.

the tank and they penetrate the front side of outer-detector. Some of the selected
neutrino candidates in Fiducial-C, with outer-detector hit were visually scanned byphysicists. It was found about 1/4 of them are identified to the incoming muons fromthe upstream, which amounts to 0.5% of the total neutrino candidates.
Therefore, RBKG = 1.5% (3.1% for 1999 run) of the neutrino candidates are considered as
the incoming muons. The number of neutrino events are corrected with this factor RBKG .

8.2

Neutrino Event Rate

8.2.1

Event rate calculation

In order to obtain the number of events in 1kt, the events in Fiducial-C (Figure 8.4) areselected. The results are summarized in Table 8.2.
The total number of neutrino interactions are calculated as;
Ncorr =

1
Nobs
·

total
Npeak
1
Npeak

! 

·

1
1kt

Where,
147

 

·

1
(·k7→9bunch )1 + RBKG


(8.1)

ppp
Event / 5 x 10

12

0.05

0.04

0.03

0.02

0.01

0.

2

4

6

8

10

12

14

16

18

Integrated POT (x 10

20
18

)

Figure 8.6: Stability of the 1kt event in Fiducial-B, from Jun.99 to Jun.00. Number of
events are efficiency corrected by Formula 8.1. Data point is summarized by every 2 days,
and plotted by integrated proton on target in horizontal axis. Vertical axis is the event
rate per 5 × 1012 protons. Error bars are only the statistical error.
Ncorr
1
Nobs


total
Npeak
1
Npeak



1kt
RBKG
k7→9bunch: The number of neutrino interactions in Fiducial-C.
: Number of observed events in Fiducial-C.
Correction factor of multiple-event (Section 8.1.2).
:
Typically 1.2 ∼ 1.3.
Event selection efficiency (Section 8.1.3).
:
Typically 0.71 ∼ 0.72.
: Background contamination rate (Section 8.1.4).
Correction factor for 7-bunch analysis,:
only in May.00 and Jun.00 run (Section 8.1.2).

In total, 34095 events are observed during the corresponding period of 1.97 × 1019 p.o.t.
This number is corrected to be Ncorr = 61585 ± 335(stat.) events.

8.2.2

Event rate stability

Stability of the 1kt event rate is studied. Fiducial-B are used to increase the statistics.
Figure 8.6 shows the observed rate of every two days. There are no obvious time variations
148

1
2
3
4
5
6

PeriodFiducial volume
Multi-event treatment
FADC threshold
Energy scale
Background rate
7-bunch/9-bunch
Total

Jun.99Nov.99

±1.0%

±1.4%

±1.0%
±5.3%

±5.4%

Jan.00−±5.2%

Feb.00 Mar.00
±4.0%
±3.0%
±1.0%
±1.0%
±0.5%
±5.2%

±5.2%

May 00

Jun.00±1.2%±5.4% ±5.4%

Table 8.3: Systematic errors of 1kt measurement.

except for the statistical fluctuation.

8.2.3

Systematic errors at 1kt

Systematic errors of the event rate are summarized in Table 8.3 and described as follows;
1. Fiducial volume error.
The vertex reconstruction of TDC fit is experimentally studied using cosmic ray, as
described in Appendix D and [52]. The result proves that the vertex reconstruction ismuch better for transverse direction with respect to the particle direction than thatfor longitudinal direction. The neutrino events are dominantly directed to z-axis.
therefore, z-vertex distribution is compared.
Vertex profile is analyzed with the selected event in the Fiducial-A. Due to the cylindrical shape of the volume, target mass correction is applied to the horizontal profile.
Figure 8.7 shows the reconstructed vertex distribution of horizontal (X), vertical (Y)and longitudinal (Z) direction. Monte Carlo simulations (neutMC) are overlaid in
the figures.
In principle, the z-vertex distribution should be flat. However, the observed distribution is systematically uneven structure, due to the effect of the vertex reconstruction.
Therefore, the event rate of data and neutMC are compared with various fiducial
volume definition of z-vertex. Table 8.4 shows the results. The largest discrepancy
between the data and the neutMC is 3%. The X and Y profiles show good agreement
between data and neutMC. The difference of the event rate of data and neutMC
along the X and Y direction is within 1%. In consequence, ±4% error is assigned forfiducial volume related uncertainty.
149

DATA
MC

18
16

20

events/ton/day

events/ton/day

events/ton/day

20

DATA
MC

18
16

20

16

14

14

14

12

12

12

10

10

10

8

8

8

6

6

Horizontal

4
2
0
-300

North
-200

-100

0

100

X profile (2000/Jan-Mar)

6

Vertical

4

South
200

2

300

cm

0
-300

DATA
MC

18

Lower
-200

-100

Upper
0

Longitudinal

4100

Y profile (2000/Jan-Mar)

200

2

300

cm

0
-300

Back
-200

Forward
-100

0

100

Z profile (2000/Jan-Mar)

200

300

cm

Figure 8.7: Vertex profile of horizontal, vertical, and longitudinal direction in 1kt detector,
after target mass correction.

z-vertex−2 < z < 0 m (Fiducial-C)−3 < z < 0 m−2 < z < +2 m (Fiducial-B)−2 < z < +3 m
−2 < z < +4.5 m

DATA neutMC
16571
13223
24990
19418
31290
25720
39330
32139
49449
38425

relative DATA/MC
1.
1.03
0.97
0.98
1.03

Table 8.4: Event rate comparison (DATA/MC) with various fiducial volume definition ofz-vertex. DATA means the observation from Jan.00 to Mar.00.

150

FADC threshold change
Default
−10%
−5%
+5%
+10%

number of events relative rate
90300
1.
91081
1.01
90723
1.01
89838
0.99
89320
0.99

Table 8.5: Effects for the event rate caused by the FADC threshold change. ”Event” means
the selected events in Fiducial-C. This is estimated by neutMC.

2. Multiple-event treatment error.
The FADC peak search algorithm cannot distinguish multiple-events occurred at one
bunch in the spill from a single neutrino interaction. The probability of the multipleevents in one bunch is estimated to be 3%. This 3% is assigned as the systematic
error due to the multiple-event treatment.
3. FADC threshold error.
The threshold of FADC is set at about 1000 photo-electron as shown in Figure 8.2.
The threshold is stable within 10% for full period. The 10% change on the thresholdcauses 1% change on the event rate, as shown in Table 8.5.
In Nov.99 run, the analog-summed cable is disconnected as described in Section 8.1.2.
An additional error 1% was estimated the difference between the obtained efficiency
curve from the data and the simulation with multiple-event consideration. The error
was assigned to be 1.4% by the quadrature sum of these errors.
4. Energy scale error.
The absolute energy scale of 1kt detector is calibrated within 5% accuracy, as described in Chapter 3.5.1. If the energy scale is 5% shifted, FADC threshold is effectively changed. Table 8.5 shows that 5% change causes less than 1% changes for the
event rate. The energy scale error is conservatively assigned to be 1%.
5. Background rate uncertainty.
Estimation of the background rate (RBKG ) is described in Section 8.1.4. The uncertainty of the estimation is ±1% in 1999 and 0.5% to the other period.
6. Correction factor for 7-bunch analysis.
Correction factor of 7-bunch/9-bunch (k7→9−bunch ) is described in the previous Section
8.1.2 and its error is quoted to be ±1.2%.
151

8.2.4

Summary of the neutrino event rate at 1kt

In summary, the total number of neutrino interactions from Jun.99 to Jun.00 (1.97 × 1019
p.o.t.) are;Ncorr = 61585 ± 335(stat.) ± 3261(syst.)

8.3

Constraint of the Low Energy Neutrino Spectrum

Neutrino energy spectrum is well predicted only above 1 GeV by PIMON analysis as
described in Section 6.1. However, beamMC says about 16% of the observed events at
SK are expected to come from the neutrinos below 1GeV in case there is no neutrino
oscillation. Then, the neutrino flux below 1 GeV should be confirmed. For this purpose,
total photo-electron distribution of 1kt is studied.

8.3.1

Total photo-electron distribution

Total photo-electron basically corresponds to the total energy deposit of the muons in
the 1kt water. Charged pions and gamma conversion from π 0 emit additional photons if
in-elastic interaction occurs. Proton has small contribution due to the high Cherenkov
threshold.
Figure 8.8 is the comparison of the total photo-electron distributions between observed
data and the neutMC in Fiducial-C. There is a discrepancy between the observation andthe neutMC, which may be explained by the detector systematics (absolute energy scale,scattering parameters, or other systematic differences), or physics reason (cross section, or
neutrino spectrum shape). It is hard to solve this discrepancy, but we can conservatively
exclude some extreme cases to take the constraint to the neutrino flux below 1 GeV.
Figure 8.8-right shows the comparison of the observed total photo-electron distribution
with MC with changing the flux below 1GeV by ±100%. The histograms are normalized
by the total entry in 7000 < (total p.e.) < 20000, because they definitely come from theneutrinos with more than 1GeV energy. From this figure, ±100% is the rather conservative estimation of the flux uncertainty below 1 GeV, and used for the number of event
comparison.

152

arbitrary unit
            




DATA
(Nov99- Jun00)
5000









































2000










































DATA (Nov99 - Jun00)  MC,  energy    scale  +-  5%




















MC simulation














4000








MC, flux +-100%
1000


































3000

















                       
0















            
4000







DATA(Nov99Jun00)
            
2000







MC,
int.
uncertainty
3000







+30%













2000




1000

















1000









0 







0 10000
20000

































































0


































































01000020000
 Total
photo-electronTotal
p.e.




2250

DATA (Nov99 - Jun00)

5000

2000

MC simulation

1750

Energy scale +5%
Energy scale -5%

1500

1250

4000

1000

750

500

3000

250

arbitrary unit

0

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

total p.e.

4000

DATA (Nov99 - Jun00)

3500

2000

MC simulation
Int. uncertainty +-30%

3000

2500

2000

1000

1500

1000

500

0

0

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

20000

Total p.e.

Total photo-electron

Figure 8.8: Comparison of observed total photo-electron distribution (bold cross) overlaid
with the neutMC (histogram). In left-top figure, the MC with ±5% shifted energy scale arealso overlaid. Left-bottom figure shows the various MC with changing both the NC crosssection by ±30% and the in-elastic cross section by ±30%. For both figure, normalization
is done by the entry of each histogram over 2000 p.e. In right figure, the MCs which
are changed the neutrino flux below 1GeV by ±100%, are overlaid. These histograms arenormalized by the area of 7000 < (total p.e.) < 20000.

153

Chapter 9
Neutrino Event Measurement at
Super-Kamiokande
9.1

Neutrino Event Selection”K2K candidate” is selected from a large amount of cosmic ray background, radioactive
background and natural neutrino activities in Super-Kamiokande (SK). Figure 9.1 showsa typical neutrino event observed in SK.
The best mark of our neutrino event is the time matching to the beam spill time, basedon GPS. The dime difference ∆(T ) is defined as follows;∆(T ) ≡ TSK − TKEK − T OF

(9.1)

where, TSK is the observed time in SK, TKEK is the start time of the beam spill in KEK,
and T OF (= 833µs) is the time-of-flight from KEK to SK. After then, contained neutrino
events are selected with similar selection algorithm to the atmospheric neutrino observationin SK [61].
The selection criteria are briefly described as follows, and the number of selected events
are summarized in Table 9.1.
1. Good beam spill definition.
The good beam spills are defined in Chapter 5.3.
2. Rough GPS time cut.
From all of the triggered events in SK, we select the events with the criteria of|∆(T )| < 500µs matching to each of the good beam spill.
3. High energy (HE) trigger.
HE-triggered events are used for K2K candidate search. Threshold of the HE trigger
154

Super-Kamiokande
Run 8356 Event 11385639
100-02-19:18:35:49
Inner: 2296 hits, 10885 pE
Outer: 1 hits, 0 pE (in-time)
Trigger ID: 0x07
D wall: 512.3 cm
FC mu-like, p = 1298.2 MeV/c

Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2

460

KEK Beam
direction marked
by diamond

368
276
184
92
0
0

500

1000

1500

2000

Times (ns)Figure 9.1: Typical neutrino event in Super-Kamiokande, observed on Feb. 19, 2000.
Observed charge (photo-electron) in each PMT is indicated by color scale. The large
map shows the inner PMTs and upper-right figure shows the hit map of the outer PMTs.
Lower-right figure shows the corrected timing distribution. This event passes the following
selection criteria and fitted as a contained event with 1 µ-like ring.

155

Selection
1
Analyzed number of spill(MC) generated in the tank(MC) generated in fiducial
2|∆(T )| < 500µs
3HE-trigger
4
Decay electron cut
5
Total photo-electron cut
6
Flasher cut
7
Outer detector cut
8
Fitting goodness cut
9Visible energy cut
10
Fiducial volume cut
11−0.2 < ∆(T ) < 1.3µs

DATA4404180MC
30495(13938)

17102
8944
8797
51
50
46
29
28

↓
18739
18190
15917
15907
15448
10937
↓

Table 9.1: Summary of the number of selected events in each step.

is given by requiring more than about 31 hits in inner PMTs (described in Chapter
3.6.2). This is equivalent about to 50 ∼ 100 photo-electrons.
4. Decay electron cut.
If muons stop inside the tank, decay electrons make Cherenkov rings, which often
miss-identified to the neutrino events. Therefore, events which have activities before
30µs are removed. Dead time factor caused by this selection is less than 1/1000, since
the total trigger rate (except SLE trigger) is typically ∼ 10 Hz.
5. Total photo electron cut.
Since the HE trigger threshold is smeared by PMT relative gain fluctuation, moreconservative cut is applied after gain correction. Number of total photo-electrons(p.e.) in 300 ns time window is calculated from the reformatted data. The thresholdis set at 200 p.e. This threshold is equivalent to 20 MeV deposited energy. Figure
9.2 shows this cut for data and neutMC. Rejected events in the first peak around 100
p.e. is mainly the events interacted by NC elastic scattering.
6. Flasher cut.
It is already known that there are some ”flasher PMTs” in SK. They are causedby sparks inside of the PMTs. They sometimes make similar ring hit patterns like
Cherenkov light. To inhibit such fake events, ”flasher cut” is applied. First, (maximum photo-electron)/(total photo-electron)≤ 0.2 is required as Figure 9.3. Next,156

number of events

10

3

10

2

10

1
1

1.5

2

2.5

3

3.5

4

4.5

5
5.5
6
log10(total p.e.)

Figure 9.2: Distribution of total photo-electron (p.e.) in 300 ns time window. The horizontal axis is log10 p.e., and the vertical axis is entry. The hatched area is neutrino eventof neutMC, normalized by its expected number of event by equivalent POT. Greater thanor equal as 200 p.e. is required.

two identical flasher cut is applied for the fake event cut. One of this cut eliminates
continuous flashing events after 1200 to 1700 ns. The other cut uses ring pattern
identification after low energy ring fitting.
7. Outer detector cut.
The events which have more than 10 PMT hits in the largest hit cluster in outer detector arrays are rejected as shown at Figure 9.4. This cut effectively selects
fully-contained events from the large background of cosmic ray activities. Also theevents which have more than 50 hits within 800 ns time window in outer detector are
eliminated.
8. Fitting goodness cut.
In order to define vertex point of the interaction, TDC fit (described in Appendix C)
is applied to the remaining events. Little fraction of badly fitted events are reduced
when the fitting goodness shows less than 0.
9. Visible energy cut.
In order to avoid the threshold uncertainty of the total photo-electron cut, moreconservative energy cut is applied. Electron-equivalent energy Evis is calculated fromthe sum of the observed signal belonging to the Cherenkov ring, considering theattenuation correction. Evis ≥ 30 MeV is required.
157

number of events

10

4

10

3

10

2

10

1
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 0.8 0.9
1(max. p.e.)/(total p.e.)number of events

Figure 9.3: Ratio of maximum photo-electron in one PMT over total photo-electron. The
hatched area is neutrino events of neutMC.

10

4

10

3

10

2

10

1
0

2.5

5

7.5

10

12.5

15
17.5
20
OD hit in cluster

Figure 9.4: Number of outer PMTs in largest hit cluster. The highest bin contains theevents with number of PMTs ≥ .20.

158

number of events

14
12

14
12

10

10

8

8

6
4

6
4

2

2

0

0

1
2
3
log10(visible energy)

0

0

1
2
3
log10(visible energy)

Figure 9.5: Visible energy distribution for observed data (left) and neutMC (right). Threshold is set at 30 MeV of electron equivalent energy.

10. Fiducial volume cut.
The event is required to have its reconstructed vertex point 2 m from the tank wall.
This requirement avoids the event reconstruction uncertainty near the PMTs. As aconsequence, a fiducial volume of 22.5 kt water is defined in the SK tank.
11. Fine GPS timing cut.
Tighter timing cut is applied using GPS time stamp. The resolution and the uncertainty of the time stamp is about 0.2µs. Therefore, time window of −0.2 < ∆(T ) <1.3µs is the suitable cut for timing requirement. Figure 9.7 shows the precise timing
distribution. The events are clearly identified in the expected time window.
Figure 9.8 shows the selection efficiency of the neutrino events interacted in the fiducial
volume, as a function of the neutrino energy, estimated by neutMC. The efficiency for CC
interactions is 93%, and for NC in-elastic interactions it is 68%. The efficiency for all theinteractions is 78%.

9.2

Observed events

After these event selection, 28 fully-contained events are observed during the whole running
period from June 1999 to June 2000. Figure 9.7 clearly shows that observed events wereaccumulated at the expected arrival time. The figure also exhibits that the background
events due to the atmospheric neutrinos are very rare, as expected.
159

number of events

8
7
6
5
4
3
2
1
0

0

500 1000 1500
distance from wall

8
7
6
5
4
3
2
1
0

0

500 1000 1500
distance from wall

Figure 9.6: Reconstructed vertex distance from the tank wall. The events with (distance)≥ 2 m away are selected. Left figure is for observed events, and right figure is for neutMC.
Figure 9.9 shows the reconstructed vertex distributions. This figure shows that neutrino events are uniformly distributed and no obvious bias is observed with this statistics.
Reconstructed direction and momentum for each Cherenkov ring are expressed by the line
direction and their size. They are obtained after the ring-counting routine which is used forthe atmospheric neutrino analysis in SK [9, 61]. The momentum and angular distributions
are shown in Appendix G, without any quantitative discussion.
An expected background is atmospheric neutrino interactions. Typical rate of the fullycontained events in SK is 8 events per day [9]. Considering the 1.5µs time window, theaccidental contamination of atmospheric neutrino events are estimated to be order of 10−3
events during the whole period.

160

number of events

10

2

HE trigger ratecontained event
events in fiducial

10

1

number of events

-400
18
16
14
12
10
8
6
4
2
0

-5

-4

-200

-3

-2

0

-1

0

200
400
GPS time (µ
sec)

1

2

3
4
5
GPS time (µsec)

Figure 9.7: Time difference distribution of HE triggered events(solid line), fully contained events after visible energy cut(hatched), and selected events in fiducial volume(darkhatched). Upper figure is ±500 ns and lower figure os ±5 µs. We can see clear peak at justwithin 1.1 µs of beam spill width and ±0.2 µs of GPS precision.

161

efficiency

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.5

1

1.5

2

2.5

3

3.5

efficiency

4

4.5
5
Eν(GeV)

Figure 9.8: The selection efficiency at Super-Kamiokande, as a function of neutrino energy.
This is estimated using neutMC.

vertex position

vertex position

beam direction

beam direction

0

0

2 GeV

y

2 GeV

z

x

x

Figure 9.9: Reconstructed vertex distribution in SK. Left figure shows the top view andthe right figure is the side view with respect to the beam direction. Outer circle and box
represent the inner detector wall, and the inner circle and the box represents the boundaryof the fiducial volume. Each circle point shows the reconstructed vertex position and theline represents the reconstructed particle momentum along the Cherenkov ring. Closed
circles correspond to the events whose vertices are in the fiducial volume. Open circles are
the events whose vertices are out of the fiducial volume.
162

Chapter 10
Comparison of Near and Far Event
Rate
In this chapter, a comparison of the number of events between the near and the far site is
discussed.

10.1

Key Issues of the Near Site Measurement

Following neutrino beam properties are measured and confirmed;• PIMON measures the distributions of Cherenkov photons emitted by pions. They
correspond to the momentum and angular distribution of pions. The result is well
reproduced by the Monte Carlo simulation (beamMC) with hadron interaction parameterized by Cho experiment. Therefore, the neutrino energy spectrum and theflux ratio Φf ar /Φnear are obtained from beamMC and their systematic errors are
estimated using PIMON results.
• Neutrino profile is measured by MRD. It confirms that neutrino beam is continuously pointed to Super-Kamiokande within 1 mrad accuracy. The profile width isreproduced by the Monte Carlo simulation (neutMC) with the neutrino beam prediction from beamMC. Muons from pion decay are measured using MUMON. It also
supports the neutrino beam direction on spill-by-spill basis.
• Neutrino beam stability is continuously monitored by MRD. The distributions of the
profile width, the muon spectrum, and the event rate are analyzed. These distributions are quite stable through the whole run, which confirms the neutrino beamstability. The event rate at 1kt is also stable during the whole run.
163

These facts allow us to compare the event rate at the near site with that at the farsite. The number of expected neutrino events in SK is estimated based on the numberof observed events in the near detector. The 1kt measurement is used for the estimation,
because the target nuclei is same and the detection technique is similar to SK.

10.2

Estimation of the Expected Number of Events

10.2.1

Extrapolation formula

SK
The number of expected neutrino events Nexp
at SK is derived by extrapolation the number
1kt
of observed events Nobs at 1kt by following formula;
SK
1kt
Nexp
= Ncorr· RSK/1kt ·P OTSK· SK
P OT1kt(10.1)

1kt
where, Ncorr
is the number of neutrino interaction defined by Formula 8.1, SK is the event
selection efficiency, P OT1kt and P OTSK is the number of proton on target (p.o.t.), andRSK/1kt is the ratio of the number of neutrino interaction at SK and 1kt. The values are
explained as follows;

1kt
Number of neutrino interaction at 1kt: Ncorr
1kt
Ncorr
is the total number of neutrino interactions in 1kt, which is obtained with Formula 8.1.
1kt
In the formula, Nobs
is the observed events in the Fiducial-C of 1kt. Table 8.2 summarizes
the result of the observation and the correction.

Ratio of the number of neutrino interaction: RSK/1kt
RSK/1kt is given as follows;
RSK/1kt =k · ΦSK · σH2 O · MSKk · Φ1kt · σH2 O · M1kt

(10.2)

where, ΦSK and Φ1kt are the neutrino flux per unit P.O.T, per unit area, averaged over theirfiducial area, σH2 O is the cross section, MSK and M1kt are the fiducial mass, and k is a normalization factor corresponding to Avogadro constant NA . After cancellation, RSK/1kt represents the flux ratio ΦSK /Φ1kt multiplied by the fiducial mass difference MSK /M1kt ∼ 900.
Since the beamMC well reproduces the PIMON measurement (Chapter 6.1), the energy
integrated ratio RSK/1kt is provided by the beamMC. That is 6.81 × 10−4 for Jun.99 run,and 6.71 × 10−4 for other periods.
164

SK
Live time correction: PP OT
OT1kt

As shown in Table 5.1, 1kt data was not taken (or not used) in 14% of SK live time.
Neutrino events in these periods are extrapolated with p.o.t. normalization.
Selection efficiency at Super-Kamiokande: SK
Selection efficiency of SK is estimated using Monte Carlo simulation. Efficiency curve as afunction of neutrino energy is shown in Figure 9.8. The integrated efficiency is 0.781 for
Jun.99 run, and 0.785 for other periods.

10.2.2

ResultSK
Table 10.1 summarizes the results of Nexp
. In total,
SK
+3.8
Nexp
= 37.8 ± 0.2(stat.) −4.0
(syst.)+3.8= 37.8−4.0(stat. + syst.)

events are expected when a neutrino oscillation does not occurred, for 2.29 × 1019 p.o.t.
Statistical error (stat.) comes from the number of observed events in 1kt. The systematic
error (syst.) is described in the next section.

10.2.3SK
Systematic error for Nexp

SK
Systematic errors on Nexp
are estimated in Table 10.2. The largest systematic error isdue to the uncertainty of RSK/1kt (6(b)), which is derived from the PIMON analysis. The
second dominant error is related to the 1kt measurement (1), described in Chapter 8.2.3.
The third dominant error comes from the uncertainty of the neutrino energy spectrum(6(a)). This is due to the difference of the energy threshold of SK and 1kt.
The systematic errors are explained as follows.

1. 1kt measurement.
The error on the event rate at 1kt is already discussed in Chapter 8.2.3.
2. P.O.T. normalization.
The analysis extrapolates the event rate to the 1kt dead time, normalized by accumulated P.O.T. The uncertainty of the number of events in this period comes fromthe stability of the event rate with P.O.T. normalization. The error is expressed by;(r.m.s. of event rate stability in 1kt) × (percentage of the 1kt dead time) (10.3)
Using this formula, the error is calculated on monthly basis.
165

Period
Target diameter
HORN
1kt
Nobs
1kt
Ncorr
P OT1kt (×1018 )P OTSK (×1018 )RF ar/N ear (×10−4 )
SK
SK
Nexp
Stat. error
Syst. error

Jun.99
20mmφ
200kA
4282
7150
2.60
3.10
6.81
0.781
4.54
±0.07
+0.75
−0.64

Nov.99 Jan.00

4923
8286
2.62
3.57

3505
6052
1.81
2.22

5.95
±0.09
+0.55
−0.61

3.90
±0.07
+0.35
−0.39

Feb.00 Mar.00 May.00 Jun.00
30mmφ
250kA
6986
6080
3574
4745
11985 10581
7510
10021
3.74
3.35
2.42
3.16
4.04
3.71
2.56
3.75
6.71
0.785
6.83
6.17
4.17
6.27
±0.09 ±0.08±0.07 ±0.10+0.62 +0.56+0.38 +0.58−0.68 −0.61−0.42 −0.63+3.8
SK
Total: Nexp
= 37.8 ± 0.2(stat.) −4.0
(syst.)

Table 10.1: Calculated number of expected event at SK from 1kt measurement.

1
2
3
4
5(a)
5(b)
6(a)
6(b)
7

Item
1kt measurement (Table 8.3)
P.O.T. normalization
Neutrino profile (direction)
Proton targeting stability
NC/CC uncertainty
in-elastic cross section
Neutrino energy spectrum
RSK/1kt ratio
SK selection efficiency

Jun.99
±5.3
±1.0
+1.0

Total

+16.5
−14.1

Nov.99±5.4±1.9

Jan.00±5.2±1.1

Feb.00 Mar.00
±5.2
±5.2
±0.4
±0.7
+0.6
+1.6
−1.3
+0.6
−0.7
+0.3
−0.5

+6.7
−7.9
+13.6
−9.8
+9.3
−10.2

+9.0
−9.9

±3.0
+9.0
−9.9

May.00±5.4±0.3

Jun.00
±5.4
±1.0

+9.1
−10.0

+9.2
−10.0

+3.9
−3.6
+5.1
−6.8
+9.0
−9.9

SK
Table 10.2: List of systematic error for Nexp
from 1kt measurement. Unit is %.

166

3. Neutrino profile error.
Uncertainty of the neutrino beam direction is discussed in Chapter 7.3. There, Table
7.5 presents the change of the number of events, due to the off-pointing.
4. Errors from proton targeting stability.
The uncertainty of the monitor of proton targeting is discussed in Chapter 6.2. Mostof the systematic error comes from the uncertainty of the proton profile measurement.
5. Uncertainty of the neutrino interaction.
Neutrino interaction is described and its uncertainty is discussed in Chapter 4.2.8.
Since the target material is water in both detectors, uncertainty of the absolute crosssection is canceled. However, the selection efficiency for each interaction mode in SK
is different from that in 1kt. Therefore, the uncertainty of the neutrino interaction
model causes the uncertainty of the ratio of the event rate at SK and 1kt. They arefollowing two issues;(a) The ratio between the Neutral Current (NC) and the Charged current (CC)cross section.
This uncertainty is estimated by changing the NC cross section by ±30% comparing to CC interaction in neutMC. Table 10.3 shows the change of the selection efficiency. The difference of SK /1kt from the default one is quoted as thesystematic error due to ”NC/CC uncertainty”.
(b) The cross section of the in-elastic interaction compare to (quasi-)elastic scattering.
This uncertainty is estimated by changing the in-elastic (single-meson production, multi-pion production, and coherent-pion production of both CC and NC)
cross section by ±30% comparing to (quasi-)elastic scattering cross sections, inneutMC. The results are also shown in Table 10.3. The difference of SK /1kt
from the default one is quoted as the systematic error due to “in-elastic crosssection uncertainty”.
6. Errors from neutrino energy spectrum and RSK/1kt uncertainty.
The selection efficiency of 1kt and SK have energy dependence as shown in Figure 8.5
and 9.8). The flux ratio ΦSK /Φ1kt also have energy dependence as shown in Figure6.5. In Formula 10.1, and Formula 10.2, the selection efficiency 1kt, SK , and theratio of number of interaction RSK/1kt are calculated as a integration of these plots
over the all energy range. Therefore, the uncertainty of the neutrino energy spectrum
affects to these values; 1kt, SK , and RSK/1kt . Then, it provides the systematic errorSK. This systematic error is estimated.
of Nexp
167

σN C

1.
1.
1.
1.
1.
1.
1.
1.

σinelastic
1kt
M RD
SK
M RD /1kt
SK /1kt
SK /M RD

1.3
1.
0.96
0.93
0.96
0.97
1.01
1.03

0.7
1.
1.05
1.08
1.04
1.03
0.99
0.96

1.
1.3
1.01
0.98
1.02
0.97
1.00
1.03

1.
0.7
0.98
1.02
0.98
1.03
1.00
0.95

Table 10.3: The event selection efficiency =(selected)/(generated) change for each detector,
when the NC cross section and in-elastic cross section change by ±30% relative to CC quasielastic scattering. “In-elastic” includes single-meson production, multi-pion production,and coherent-pion production, of both CC and NC.

The values 1kt , SK , and RSK/1kt are provided by neutMC, as follows;1kt =

1kt
Nobs
1kt
Ngen

!

SK =
MC

SK
Nobs
SK
Ngen

!

RSK/1kt =
MC

SK
Ngen
1kt
Ngen

!

MC

where, Ngen is the number of generated events, and Nobs is the number of observedSK
events in neutMC. Then, Nexp
is expressed as;
SK
Nexp

=

1kt
NobsDAT
A ·

SK
Nobs
1kt
Nobs

!

(10.4)MC

In this formula, other corrections are neglected.
When the neutrino flux of each energy bin i at 1kt changes by ∆φi, change of thethe neutrino flux at SK is expressed by the sum of the correlated change and theSKchanges to N0exp as follows;
un-correlated change as (∆φi + ∆ri). Then, Nexp
N0exp ='

1kt
NobsDAT
A ·
SK
Nexp
·

"

1+

SK
Nobs
+ i (∆φi + ∆ri ) · nSK
i
P
1kt
Nobs
+ i (∆φi ) · n1kt
i

P

X
i

∆φi

n1kt
nSK
i
i
−
SK
1kt
Nobs
Nobs

!!

+

!

MC

nSK
∆ri iSK
Nobs
i

X

!#

(10.5)
MC

where, ni is the number of observed events from the neutrinos in i-th energy bin
P1kt( i ni = Nobs ), in neutMC. The second expression is valid when ( ∆φi · (n1kt
i /Nobs ) SK1 ), and ((∆φi + ∆ri) · (nSK
i /Nobs )  1). The second term and the third term
168

express the “(a) error from the near spectrum” and “(b) error from the flux ratio”,
respectively.
Changeable rangeof ∆φ i and ∆ri is given bytheuncertainties of the energy spectrum
and the flux ratio ∆R, which are estimated by PIMON
at the near site ∆ΦΦ i
R i
analysis in Chapter 6.1. These uncertainties are shown in Table 6.2, and Table 6.3.
We estimate the systematic error with considering following correlation,• Errors are estimated in 6 energy bins (0 − 0.5, 0.5 − 1, ..., 2.5− GeV). Errors
between different energy bin have large correlation each other. Thus, linear sumof the errors in each energy bin is taken.
• The error from “(a) near spectrum” does not correlated to “(b) error from theflux ratio”. Thus, quadrature sum of these two errors is quoted as the total
systematic error of these uncertainties.
SK
Then, the systematic error of Nexp
is estimated as follows,
SK
∆Nexp

=

SK
Nexp
·

q

(A)2 + (B)2

(10.6)6 X∆ΦSum of errors from)=the near spectrum
Φ
i=1



6
X
∆R
Sum of errors fromB ≡ ()=
the flux ratio
R
i=1





A ≡ (

i

·

nSK
n1kt
i
− i1kt
SK
Nobs
Nobs

nSK
i
·
SK
Nobs
i

!

!

(10.7)
MC(10.8)MC

The validity of this error estimation is checked as follows. We prepare various beamMCs with various pion distributions within the quoted error. Each of these beamMC
gives the energy spectrum at near site, and the flux ratio in each energy bin. The
differences of these values from the standard beamMC are summed-up according to
the Formula 10.6 to 10.8, to obtain the “predicted” uncertainty of (N SK /N 1kt ). On
the other hand, the beamMC gives the actual difference of (N SK /N 1kt ) from thestandard one. As the result, the “predicted” error range conservatively covers mostof the actual difference. Then, this error estimation is proper for our experiment.
Table 10.4 summarizes the estimation
with this formula. The limit of the neutrino flux∆Φ
below 1GeV is obtained as Φ
= ±100% by 1kt analysis described in Chapter
1,2
8.3.1.
7. Errors from SK selection efficiency.
Following systematic errors are considered in the selection efficiency at SK;• Event selection described in Chapter 9.1 is obvious and there are negligible
systematic uncertainties except for the vertex reconstruction.
169

Eν bin (GeV)
0.0 − 0.5 0.5 − 1.0
Nov.99 to Jun.00 (250 kA) run
ni /Nobs (1kt, MC)
0.00
0.15
ni /Nobs (SK,
MC)
0.01
0.15

∆Φ
±100%
±100%
Φ


i

∆R
R i

(a) Error from(b) Error from



∆Φ



 Φ i

∆R
R i

+5.1%
−9.5%

+7.3%
−2.5%

±0.9%

∓0.2%

±0.1%

+1.1%
−0.4%

1.0 − 1.5 1.5 − 2.0 2.0 − 2.5

2.5−

0.36
0.29

0.29
0.29

0.13
0.16

0.06
0.09

+9.1%
−9.5%
+4.6%
−6.2%
−0.6%
+0.7%
+1.4%
−1.8%

+10.7%
−9.7%
+2.9%
−6.2%

+11.3%−17.7%
+5.3%
−7.4%
+0.4%
−0.6%
+0.9%
−1.2%

+47.3%−33.8%+9.1%−16.2%
+1.6%
−1.2%
+0.9%
−1.5%

(a) Sum of errors from near spectrum(b)
Sum of errors from flux ratio
Jun.99 (200kA) run(a) Sum of errors from near spectrum(b)
Sum of errors from flux ratio

∓0.1%
+0.8%
−1.8%

= +3.9%= +5.1%

−3.6%
−6.8%

=
=

−7.9%
−9.8%

+6.7%
+13.6%SK
from (a) the near spectrum and (b) the flux ratio uncertainty.
Table 10.4: Errors on Nexp

170

GPS timing cut is applied with 1.5 µs time window. As shown in Figure 9.7, thesystematic error from the uncertainty of the timing information is negligible.
• The observed events in SK are required to originate in the 22.5 kt fiducial volume.
The vertex position is reconstructed using ”TDC-fit”. For the confirmation,
another vertex reconstruction method so called ”MS-fit” is applied to fullycontained single ring events, after ring counting and particle identification. MSfit is the vertex fitter with particle type (muon-type or electron-type) dependent
fitting parameters, which is recently used for atmospheric-neutrino analysis inSuper-Kamiokande experiment [61]. In the Monte Carlo simulation, the two
results show ±2% difference.

• Statistical error of Monte Carlo event sample is about ±1%.

Therefore, total systematic error of SK selection efficiency is assigned to be ±3%.

10.3

Cross-check of the Expected Number of Events
From MRD.

SKThe number of expected neutrino events at SK Nexp
is also estimated based on the MRD
SKmeasurement, a cross-check. Nexp is estimated using same Formula 10.1, from the number
M RDof observed event in MRD Nobs
. The results are summarized in table 10.5. In total,SK
Nexp= 41.0 ± 0.2(stat.) ± 6.3(syst.)

Estimated systematic error is summarized in 10.6.
Since the target nuclei is Fe, the uncertainty of the cross sections difference is additionallyestimated as follows;
8. Uncertainty of the Fe cross section, comparing to the H2 O target.
They are already described in Chapter 4.2.8.
(a) In quasi-elastic and elastic scattering, we compared different iron interacted
neutMC with Fermi surface momentum (correspond to Pauli blocking threshold) PF ermi = 217 MeV/c and 250 MeV/c instead of 237MeV/c in default. Thechange in the observed number of events in MRD is +3.4% and −1.7%, respectively.
(b) Hadron interaction uncertainty inside of the iron nuclei. Since the hadron interaction in iron nuclei is assumed to be larger than that in oxygen nuclei, thedefault neutMC, which has the same interaction as oxygen, gives the minimum
estimation of the hadron interaction effect inside of the iron nuclei. On the other171

Period
Target diameter
HORN
M RD
Nobs
M RD
Ncorr
P OTM RD (×1018 )P OTSK (×1018 )RF ar/N ear (×10−4 )
SK
SK
Nexp
Stat. error
Syst. error

Jun.99
20mmφ
200kA
7417
21516
2.93
3.10
2.81
0.781
5.00
±0.06
+1.00
−0.91

Nov.99 Jan.00

8140
22886
2.72
3.57

5997
16861
2.04
2.22

6.59
±0.07
+0.97
−1.00

4.03
±0.05
+0.59
−0.61

Feb.00 Mar.00 May.00 Jun.00
30mmφ
250kA
11228 10306
7464
10159
31568 28975
20985 28562
3.81
3.49
2.51
3.54
4.04
3.71
2.56
3.75
2.80
0.785
7.34
6.76
4.68
6.64
±0.07 ±0.07±0.05 ±0.07+1.08 +0.99+0.69 +0.98−1.11 −1.02−0.71 −1.00

SKTotal: Nexp
= 41.0 ± 0.2(stat.) ± 6.3(syst.)

Table 10.5: Calculated number of expected events at SK from MRD measurement. ThisSK
estimation is for the cross-check of the Nexp
from 1kt measurement in Table 10.1.

1
2
3
4
8
5(a)
5(b)
6(a)
6(b)
7

Item
MRD measurement (Table 7.7)
P.O.T. normalization
Neutrino profile (direction)
Proton targeting stability
σF e /σH2 O
including p and π int. in nuclei
NC/CC uncertainty
in-elastic cross section
Neutrino energy spectrum
RSK/M RD ratio
SK selection efficiency
Total

Jun.99 Nov.99 to Jun.00
+1.9
−5.1

+1.4

< ±0.1
+0.8
+0.9
−1.6
+7.3
−3.4

+11.1
−12.0
+13.6
−9.8
+20.0
−18.1

+3.3
−3.7
+3.3
−4.8

+9.8
−9.5
+5.6
−7.1

±3.0

+14.7
−15.1

SK
from MRD measurement. Unit is %.
Table 10.6: List of systematic errors for Nexp

172

hand, we also analyze with “muon-only” simulation, which gives the 100% nuclear absorption of hadrons. Figure 7.17 shows the difference The 5.7% differenceis quoted as the systematic error.
Linear sum of these two errors is assumed as the systematic error of the cross section
difference between Fe and H2O.
SK
SKObtained Nexp
from MRD is consistent with the Nexp
from 1kt measurement, within thesystematic errors.

10.4

Observed Number of Events at SK

Neutrino events in 22.5 kt fiducial volume in Super-Kamiokande is analyzed as describedin Chapter 9.1. As the result of the whole running period of 2.29 × 1019 P.O.T., numberSKof observed fully-contained events Nobs
is;
SK
Nobs
= 28

10.5

Discussion

10.5.1

Statistical significanceTwenty-eight of fully-contained events are observed, when 37.8+3.8−4.0 events are expected.
In order to obtain statistical judgment, following purely statistical “Monte Carlo test” isperformed.
Poisson distributions are generated repeatedly which have the average around 37.8 smeared by a Gaussian function with the attached error ±4.0 (small difference between 3.8
and 4.0 is neglected). The probability of this observation is calculated as the integrationof the probability of less than or equal to 28 events. This definition is expressed as follows;

P (x ≤ n; µ0 ± ∆µ) =e−µ µx·e
x=0√x!

R ∞ Pn0−(µ−µ0 )2
2∆µ

2π∆µ

dµ

(10.9)

where n, µ0 , and ∆µ are the number of observed events, a center value of the number of
expected events, and its error. In our case, n = 28, µ0 = 37.8, and ∆µ = 4.0.
This test is performed 106 times. The obtained probability is 9.6% for this observation of
28 event. The null oscillation hypothesis is excluded with more than 90% C.L. (confidence
level) by one side (lower side) test.
173

Gaussian distribution

Poisson distribution
60000

50000
50000
40000
40000
30000
30000

20000

20000

10000

0

10000

15

20

25

30

35

40

45

50

55

60

0

0

10

20

30

40

50

60

Figure 10.1: Results of the statistical test. The left figure shows the Gaussian distribution
with mean 37.8 and sigma 4.0. This gives the probability of the mean of the Poisson
distribution in the right figure. The area less than or equal to 28 event occupies 9.6%of the total right histogram. These are the results with 106 trials of the random number
generation.

10.5.2

Physics Conclusion

An evidence of the neutrino disappearance is obtained. The most likely explanation is
the neutrino oscillation. Assuming the neutrino oscillation between 2 flavors, νµ and νx ,the oscillation probability is expressed as Formula 1.10. Though one measurement of the“number of events” cannot simultaneously solve two parameters θµµ and ∆m223, the bestfavored area is drawn in the (∆m2)-(θ) contour. When θµµ is assumed to be 1, the best
estimation of ∆m223 is around 2.5 × 10−3 eV2 . This point is close to the best fit of recent
atmospheric neutrino observation in Super-Kamiokande experiment [10], which is shownin Figure 1.1.
The neutrino oscillation will be concluded when the νµ energy spectrum at SK will differ
from the expected one. The distortion pattern will be analyzed according to Formula 1.10.
For this purpose, the νµ energy spectrum will be reconstructed by the analysis of near
neutrino detectors, in particular, 1kt and FGD.
Further accumulation of the neutrino events in SK will enable us to analyze the νµdisappearance with smaller statistical error, and also enable us to analyze the νµ spectrum
distortion.

174

Chapter 11
Conclusion
In order to investigate neutrino oscillation using well-monitored neutrino beam, the neutrino oscillation experiment with 250 km long base line has been performed.
Neutrino energy spectra and the ratio of the flux of far/near sites are obtained by measuring the (Pπ , θπ ) distribution of pions before decaying to neutrinos. Neutrino beam itself
is carefully measured by Muon Range Detector at the near site. The results confirm thestability of the neutrino flux, spectrum shape and the pointing accuracy toward SuperKamiokande, throughout the whole run. The beam stability is kept, on spill-by-spill basis,by proton monitors and secondary muon monitors in the beam line. The neutrino event
rate, which is the product of the neutrino flux and the cross section, is measured at 1kt
detector.
These measurements at near site allow us to extrapolate the event rate from the neardetector to the far detector, Super-Kamiokande. During the whole run of 2.29×1019 protons+3.8
on target, the expected number of event at Super-Kamiokande is 37.8±0.2(stat.) −4.0
(syst.).
It is cross checked by the event rate at Muon Range Detector.
In Super-Kamiokande, the neutrino events are clearly distinguished by the time synchronization to the accelerator using GPS system. Twenty-eight fully-contained events areobserved during the corresponding period of 37.8 expected events.
The probability of the observation without oscillation or any reduction is discussed. Comparing the expected number from 1kt detector and the observation at Super-Kamiokande,
the result shows 9.6% probability of no change. The most likely explanation is the neutrino
oscillation. Assuming the hypothesis of νµ → νx oscillation with large mixing angle, thebest estimation of ∆m2 is around sevral of 10−3 eV2 . This is consistent with the recent
assertion of the atmospheric neutrino observations.

175

Appendix A
MRD Track Finder
A muon that penetrates MRD deposits several drift-tube hits along the particle trajectory.
In order to reconstruct the muon track, MRD “track finder” code is used. The track finderconsists of four parts, “Cell fit”, “Fragment fit”, “2-D fit”, and “3-D fit”. Figure A.1
shows the flow chart of these track finding algorithm. They are explained in following
sub-sections.
In this chapter, the word ”layer” means the one iron plate (10 cm or 20 cm
thickness), or one series of X-tubes and Y-tubes inserted between the given twoiron plates. The word ”plane” means the transversely aligned cells in the given
z-position. That is, two X-planes and two Y-planes make one drift-tube layer.
MRD has 12 iron layers and 13 drift-tube layers (26 planes for each x and y).
Reconstructed track starts on one of the plane and ends on another plane.

A.1

Noise hit rejection

Averaged number of MRD hits is about 30 ∼ 40 per one spill. These hits include somefraction of noise hits caused by the electronics. They have a tendency of following;• Some particular channels frequently make these fake hits.
• Many of them record TDC count of less than 5 count.
Rejection of these noise hit is performed as follows;
1. First, noisy tubes which had hits over 10% of spills in suitable time period are masked.
These are about 50 channels (0.8%) through out the whole run (see Figure A.2).
These bad channels are randomly distributed and no localization is found.
176

Hit information

Fragment fit

Raw data

TDC cut (6<=TDC<=60count)

Divide to fragment of 4-6plane lengthwith all the hit combination and all the start point

Cell fit

Noise hit
Try other combination

Fragment fit

Linear connection of
all the combination of 2 hit cells.
Find included hit cell of (distance < 7cm)

(number of cell >=3)
Too short

Fit evaluation (Badness<1cm^2)
Bad combination

Apply time window (20count window)

2-D fit
Connect fragment form upstream(distance<10cm) & (slope diff.<0.15)

Non associated hit
Enough track length (nplane>=4)

Try next track

Too short

Penetration check

Efficiency cut
Track combination of x and y
Couple from longest overlap length( hit eff.>=0.6 for slope<0.2 )hit eff.>=0.8 for slope>=0.2

Try next combination

Bad combination
Duplication check

3-D fit

Duplicated track

Compile reconstructed track length
to muon energy
Track information(energy, direction, start & end point, etc.)

3-D track is reconstructed

Figure A.1: Flow chart of the MRD tracker algorithm.

177

number of macked ch.

100

45
40
35
30
25
20
15
10
5
0

80
60
40
20
0

0

100

200 300 400
Jun.99 to Jun.00

0

20 40 60 80 100
number of masked ch.

Figure A.2: Number of masked channels due to the high trigger rate from June 1999 toJune 2000. The left figure is the history plot, where horizontal axis corresponds to thedataset number. The right figure is the accumulated distribution. The simulation adopts
57 masked channels, which is a little conservative estimation.

x 10 2
70000

3000

60000

2500

50000

2000

40000

1500

30000

1000

20000

500

10000
0

0

20

40
60
TDC count

0

0

20

40
60
TDC count

Figure A.3: TDC distribution of hit cells (1 TDC count = 50 ns). The left figure shows
the observed data and the right figure is the neutMC simulation. Hatched area shows thehits originated by muons, in neutMC.

178

x 10 3
2000
1750
1500
1250
1000
750
500
250
0

x 10 3
10000
8000
6000
4000
2000

0

20

40

60 80 100
distance (cm)

0

0

20

40

60 80 100
distance (cm)Figure A.4: Distance from the connected track to each hit wire position. True muoncombinations are also shown by the hatched area.

2. Next, TDC cut of 6≤T ≤60 count is applied. Figure A.3 clearly shows the electricalnoise rejection by this cut. The hits from neutrino-induced event distribute from 10
count to 50 count, smeared by the drift time. There are delayed background hits,
which are mostly distributed at the top front side of the detector volume. They are
considered as low energy neutron activities, called ”sky-shine. In Figure A.3, thesimulated distribution is also shown.

A.2

Cell fit

1. All hits are connected by Cell fit. It tries all the combinations of 2 hits of morethan 4 planes apart from each other. It connects the two wire positions linearly andcounts-up the ”included” hit cells within 7 cm from the fitted line. Distributions of
the distance are shown in Figure A.4.
2. Next, Cell fit searches 20 count time window where most associated hits are included
there. 20 count (= 1µs) is the maximum drift time of the tube. With this cut, some
accidental off timing hits are rejected.
3. The hit efficiency of each passing plane is calculated. The tracks are required theefficiency more than 60% (80%) for the opening angle tan θ < 0.2 (tan θ > 0.2).
179track length
4 plane5 plane
6 plane
7 plane
8 plane
9 plane10 planeslope< 0.2 ≥ 0.2
3 hit 4 hit
3 hit 4 hit
4 hit 5 hit
5 hit 6 hit
5 hit 7 hit
6 hit 8 hit
6 hit 8 hit

Table A.1: Required hit per each track length for the efficiency cut.

Table A.1 notes the required hits per each track length. 2-dimensional view of thiscut criteria is shown in Figure A.5.

A.3

Fragment fit

1. For cell fit track, fragments with 4 to 6-plane length are picked-up. All the hits are
assigned as the start point for each fragment. All the patterns are taken when someplanes have more than one hit in one plane.
2. In each fragment, first 3 or 4 hit cells are fitted with linear line, considering drift
distance from the wire. The particle arrival time (T0 ) is searched for starting from
Tmax − 20 count to Tmin , with 1 TDC count step, where Tmax and Tmin are themaximum and minimum TDC count of the hits in each fragments, respectively. Driftdistance is calculated from the Formula 3.13. From this drift distance, 2 possibility
is exist, upper or lower side of the wire. Then all the combination is considered.
”Badness” is evaluated as following residual length;
SXX = Σ(Xi − < X >)2
SY Y = Σ(Yi − < Y >)2
SXY = Σ(Xi − < X >) · (Yi − < Y >)SXY
slope =
SXX
slice = < Y > −slope· < X >SY Y − SXY · slope
badness =Ncell − 2
180

(A.1)

2
1.5
1
0.5
0
-0.5
-1
-1.5
-2

tanθ

2
1.5
1
0.5
0
-0.5
-1
-1.5
-2

0

0.25 0.5 0.75 1
efficiency

00.25 0.5 0.75 1
efficiency

Figure A.5: Distributions of slope and efficiency of the tested tracks.

x 10 2
2000
1750
1500
1250
1000
750
500
250
0

x 10 3
1400
1200
1000
800
600
400
200

0
2
4
6
8
number of cells / fragment

0

0
2
4
6
8
number of cells / fragment

Figure A.6: Number of hit cells in each fragments. Shaded area corresponds to the muoncombinations.

181

10

5

10

6

10

10

5

4

10

4

10

3

10

2

10

3

10

2

0

0.5

1

1.5
2
badness

0

0.5

1

1.5
2
badness

Figure A.7: Badness distribution. Hatched area corresponds to the muon combinations.

All the case of hit pattern, T0 , and drift side are tested and best combination is
selected. Badness distribution is shown at Figure A.7. badness < 1 is required for
an appropriate fit.

A.4

2-D fit

1. From many fitted fragments, most upstream fragment is assumed as the start fragment of the 2-D track, at first. Next fragments are searched for whose start plane issame or before end plane of the initial fragment. To connect next one, two parameters are considered. One is the closest distance between the start point of the next
fragment and initial track (rdist), and the other is the opening angle between two
tracks (θab). The requirement is rdist < 10 cm and tan θab < 0.15 (Figure A.8).
2. After all the sequential fragments are picked-up, next upstream fragment is consideredamong remained tracks.
3. T0 is calculated as the average of fragments in each 2-D tracks.

A.5

3-D fit

1. 3-D fit process connects 2-D tracks in different view. From all the combination ofboth X-view and Y-view, the overlap length along the z-axis is considered. 3-D
182x 10 2
50000
45000
40000
35000
30000
25000
20000
15000
10000
5000
0

4000
3500
3000
2500
2000
1500
1000
500
0
0
5
10
15
20 x 10 20
5
10
15
20
distance to next start (cm)distance to next start (cm)
40000
2000
35000
1750
30000
1500
25000
1250
20000
1000
15000
750
10000
500
5000
250
0
0
-1
-0.5
0
0.5
1
-1 -0.5
0
0.5
1
tan(θ
-θ
)
tan(θ
-θ
)
a b
a b

Figure A.8: Distributions of the distance between the first track and next start point (rdist),
and angle of two tested tracks. Shaded area corresponds to the muon combinations.

183

muon total energy(GeV)

2

1.75
1.5

1.25
1
0.75
0.5
0.25
0

0

20

40

60

80

100

120
140
muon range (cm)Figure A.9: Conversion function from muon range to muon total energy.
Conversion function from muon range to muon total energy.

tracks are picked up from the best combination that has a longest overlap length
among remaining track.
2. Track slope in each view is defined from the linear line between most upstream hit
point and most downstream one in both sides view independently.
3. The start and end-points are defined as most upstream and downstream z-positionof X-view and Y-view. If 2-D track does not have hit at start or stop point, thepositions are calculated by a extrapolation using the slope.
4. Assuming the track is made by muon, muon energy is reconstructed from the path
length in the iron plates. In this path length calculation, event vertex and end point isassumed to be at the middle of the iron plate. A conversion function, which is shownin Figure A.9, is estimated by GEANT Monte Carlo simulation and good agreementwith the numerical integration of the Bethe-Bloch equation [99].
5. T0 is the average of that of two 2-D tracks in both view.
6. Some evaluation values are calculated for following event selection section; differenceof the start point, difference of the end point, and the difference of fitted T0 between
two 2-D tracks.

184

Appendix B
Neutrino Profile of
Vertex-Contained Events at MRD
For the cross check, another profile analysis is performed using the vertex-contained (VC)
neutrino events.

B.1

Event Selection

Event sample is selected with following criteria. The selection is also shown in Figure 7.2.
1. Consistency between X-view and Y-view, described in Chapter 7.1.3.
2. Longest track selection, described in Chapter 7.1.3.
3. Time window, described in Chapter 7.1.3.
9. SAMPLE-A-dash, for profile study.
The vertex point is required being in Fiducial-A, while the end point is not required
being contained.
This causes a little contamination of the cosmic ray backgrounds. But the rate is
negligibly small (it is also suggested by the T0 distribution in Figure 7.5).
iron≥This SAMPLE-A-dash includes the events that penetrate one or more iron plate (Nlayer
iron1), instead of (Nlayer ≥ 2) for SAMPLE-A. This lower threshold is necessary to keep
selection efficiency around the edge region, because some muons with large angle penetrateiron
to outside of MRD and leave hits only in two drift-tube-layers (this is Nlayer= 1). Thankto this lower threshold, SAMPLE-A-dash have better efficiency for low energy neutrinosiron= 1 contains
than SAMPLE-A, as shown in Figure 7.6. Although the events with Nlayer
about 22% of the hadron activity.

185

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

-200

0

200
efficiency x (cm)

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

-200

0

200
efficiency y (cm)Figure B.1: Selection efficiency for SAMPLE-A-dash, as a function of reconstructed vertex
point of x and y. This efficiency is estimated by neutMC of 250 kA case.

B.2

Profile of vertex-contained (VC) events

The vertex distribution of SAMPLE-A-dash is obtained for certain time periods. Since
there are drift-tube gaps at y-tubes, the selection efficiency of there (−150 < x < 50
cm and 50 < x < 150 cm) is 5 ∼ 10% lower than other area (shown in Figure B.1).
This non-uniformity is compensated by applying the efficiency correction. The efficiency
is almost uniform in each position except the gap area, and neutrinos with any energy
range also gives the uniform efficiency. This uniform efficiency is an advantage of thisanalysis method, because the systematic bias of the efficiency correction makes little effectfor profile determination.
Figure B.2 shows the vertex profile of this analysis for Nov.99 to Jun.00 run. They again
prove the neutrino beam direction pointing to SK, and the profile width is well reproducedby neutMC.

Profile reconstruction test by neutMC with shifted beam axis
The profile reconstruction is tested as Chapter ??. Simulated VC profile with shifted beamaxis are reconstructed by the same procedure. The fitted results are summarized in Table
7.4. The results agree with the nominal input axis, less than 12 cm.
18690000

90000
DATA

80000

80000

MC

70000

70000

60000

60000

50000

50000

40000

40000

30000

30000

20000

20000

10000

10000

0

-200

0

0

200

-200

x (cm)

0200

y (cm)

Vertex contained

Vertex contained

Figure B.2: Vertex profile of vertex-contained (VC) events in MRD for Nov.99 to Jun.00
run. DATA (cross) and neutMC (box) with same reconstruction are overlaid. Normalization of both figures is done by the area under the histograms. Error bars are due to data
statistics and also MC statistics of the applied efficiency correction.

beam shift
CenterX +50cm
Y +50cm
Y −50cm

method(nominal)
VC(nominal)
VC(nominal)
VC(nominal)
VC

center
(0)
−1
(+50)
+60
(0)
+5
(0)
+2

x (cm)±2±6±5±5

center
(−16)
−13
(−16)
−11
(+34)
+46
(−66)
−68

y (cm)width

x (cm)width

y (cm)

±2

291

±4

287

±4

±5

285

±9

279

±9

±6

273

±8

286

±10

±7

280

±9

294

±10

Table B.1: Reconstruction test of VC profile, with neutMC with shifted beam axis.

187profile sigma x (cm)profile center y (cm)

80
60
40
20
0
-20
-40
-60
-80
-100

500
450
400
350
300
250
200
150
100
50
0

profile sigma y (cm)profile center x (cm)

100
80
60
40
20
0
-20
-40
-60
-80
-100

500
450
400
350
300
250
200
150
100
50
0

integrated day (1 data point / 5 days)

integrated day (1 data point / 5 days)

Figure B.3: Stability of the neutrino profile center (left figure) and width (Gaussian sigma,
in right figure) from June 1999 to June 2000, obtained from VC analysis. Each definitionof figures are same as Figure 7.16

B.3

Stability of the profile

Neutrino profiles from VC events are integrated every five days and fitted with Gaussianfunction to obtain center and width (r.m.s.). The results are shown in Figure B.3. Theyshow the profile center is always pointed within 1 mrad, and the width agrees to that ofneutMC.
These results can be directly compared with the results of FC-all analysis in Figure 7.16.
Figure B.4 shows a correlation of the fitted center from two methods. They prove theconsistency of the two profile analyses.

188

center-y’ (FC)’center-x’ (FC)’

80
60
40
20
0

80
60
40
20
0

-20

-20

-40

-40

-60

-60

-80

-80
-50

0

50

-50

0

center-y (VC)

width-y’ (FC)’width-x’ (FC)’center-x (VC)
500
450
400
350

500
450
400
350

300

300

250

250

200
200

300

400

50

500

200
200

width-x (VC)

300

400

500

width-y (VC)

Figure B.4: Consistency of the neutrino profile center (top) and width (bottom), between
FC-all analysis and VC analysis. One data points correspond to the result of each 5 days.

189

Appendix C
TDC fitIn 1kt and SK, the event vertex point is reconstructed using “TDC fit” routine. “TDC fit”
routine reconstructs the vertex point using hit time (TDC) information of inner PMTs.
This routine is originally developed and used in Kamiexperiment and Super-Kamiokande
experiment [61].
TDC fit contains following three steps;
1. ”Point fit”, which searches a rough vertex from only the time information of thePMTs.
2. ”Ring edge search”, which searches the direction and opening angle of the Cherenkov
cone.
3. ”The fine vertex fit”, which determines more precise vertex by taking account of the
track length of the charged particle.
The steps 2 and 3 are iterated until the distance between the previous vertex and the latest
one becomes less than 50 cm.
When particle emits Cherenkov photons from a certain point in the water tank, theobserved TDC distribution corresponds the time of flight between the PMTs and the vertex. Therefore, the distribution of ”residual” time, which is the time after time-of-flightof Cherenkov photons of each PMT is subtracted, shows a sharp peak smeared by time
resolution. The time residual ti of the i-th hit PMT is defined as;~ <t>ti = t0i − (n/c) × |P~i − O|−(C.1)

where, n is the refractive index of water, c is the light velocity, t0i is the hit time of the i-th
~ is
PMT, < t > is the average of ti , P~i means the position vector of the i-th PMT, and O
the position vector of an assumed vertex position.
190

number of p.e.

150
100
50

second derivative

0

10

0
detected edge

-10
o

0

o

10

o

20

o

30

o

o

o

40
50
60
opening angle

o

70

o

80

o

90

Figure C.1: Effective charge CH(θ) distribution (upper) and its second deviation (lower),
as a function of opening angle θ.

In the realistic case, the time residual distribution has a certain width due to the particle
running in the water, and has also a long tail caused by scattered light.
Considering this effect, “goodness function” Gp is defined as;
t2
1 X
exp − i 2
Gp =Nhit i
2σ

!

(C.2)

where, Nhit is the number of hit PMTs in inner detector, and σ is the typical time resolutionof 2.5 ns. The point fit searches the position where Gp is maximum. The resolution of thispoint fit is about 40 cm.
~ is determined, overall particle direction d~p is calculated from theAfter the vertex O
191

weighted average of observed charge Ci as follows;
d~p =

X

~
P~i − O× Ci
i ~~|Pi − O|

(C.3)

Next, the angular distribution of effective charge CH(θ) is calculated from the defined axis
around d~p , and the result is typically shown in Figure C.1. The effective charge means theobserved charge with acceptance of PMT and water transparency correction. As shown in2
Figure C.1, Cherenkov ring edge is obtained at the nearest zero-crossing point of d CH(θ)
dθ2~ Q value is written in a following
outer than the peak of CH(θ). Assumed direction d,equation;Q=

Z θedge02dCH(θ)(θedge − θC )2
CH(θ)


× exp −dθ ×sin θedgedθ
2σθ2θ=θedge!

(C.4)

where, θC is the Cherenkov angle expected from the total charge in the corn, and σθ is its
resolution. Optimum direction d~ where Q maximizes is adopted to the next final vertex fit.
At the final fit process, two goodnesses GI and GO are calculated with following formula;
GI

1
t2i
=
exp
−
σ2
2σ 2
insideof ringedge i

GO

t2i
ti
1
max
exp
−
,
0.8
·
exp
−
=
2
σ
2σ 2
Tl
outof ring i

X

"

X

!
!



#

(C.5)

where, σi is the time resolution of the i-th PMT, which is a function of its charge. The
choice in GO means whether the observed photon hits directly or with scattering. Tl isthe typical time delay of scattered photons. Tl of 20 ns is used in the calculation. The
evaluation indicator is the sum of these two goodness values;
GT =GI + GO
P

1
i σ2

(C.6)

i

In the calculation of GI , particle path length is considered from the total charge which
are within the 70◦ cone. ti is re-calculated with unfolded emission point along the track,
instead of the unique point in initial ”point fit”.
These procedures are iterated several times, until both the vertex position and direction
are determined at the maximum GT .

192

Appendix D
Experimental Test of the Vertex
Reconstruction at 1kt
In order to check the vertex reconstruction using TDC fit, experimental test is performed
using cosmic ray [52]. A long light-tight pipe (Cosmic Ray Pipe) is installed in the watertank. Trigger scintillation counters are set at both side of the pipe. A cosmic ray muonthat hits these counters generally makes one muon-like Cherenkov rings starting at the endof the pipe. Several data are taken with the pipe end at −2 m to +3 m from the center,as shown in Figure D.1.
Figure D.2 shows the results of the fitted vertex when the pipe end was set at z(height) =+1 m. Data samples are sorted to the fully-contained muon events (whose end point iscontained in the tank), and the Partially-contained muon events (which are penetrated toout of the inner tank). The partially-contained events are identified when the maximum
signals in each PMT exceed to 200 photo-electron. Typical results of the vertex reconstruction are shown in Figure D.2. The vertex reconstruction in horizontal direction isgood, whereas the reconstruction along the particle direction (vertical direction) sometimes
makes miss-reconstruction to the forward direction, in particular for the partially-contained
events. This tendency is reproduced by the Monte Carlo simulation, although there is asmall discrepancy compare to the data. Table D.1 summarizes the mean position of thereconstructed vertices along the particle direction for each data set.
The reason of this tendency is considered that; the TDC fit gives poor constraint for thevertex determination along the particle direction, because the TDC values of hit PMTs
are close to each other. When the neutrino event sometimes makes multi-rings, the vertex
reconstruction is better than the single-ring case.

1931kt tank

Trigger scinti. counterheightCosmic Ray Pipe

+3m

0
Cherenkov Light-2m

Cosmic Ray Muon

Figure D.1: Set-up of the Cosmic Ray Pipe measurement.

Pipe end position(Vertical)
+3 m
+2 m
+1 m
0m
−1 m
−2 m

DATA
Fully
Partially+2.97 m +2.31 m+2.02 m +1.51 m+1.23 m +0.72 m+0.17 m −0.33 m−0.94 m −1.47 m−2.27 m −2.19 m

MC
Fully
Partially+3.10 m +2.46 m+2.17 m +1.67 m+1.13 m +0.84 m+0.23 m +0.07 m−0.82 m −1.09 m−1.95 m −2.14 m

Table D.1: Fitting results of the Cosmic Ray Pipe measurement, with pipe end position of+3 m (upper side) to −2 m (lower side). Cosmic ray muons go down to “minus” directionin this coordinate.

194

150

DATA
ENTRIES 720
MEAN -75.10
RMS
20.93

300

DATA

100

DATA
ENTRIES 1738
MEAN -79.74
RMS
13.55

DATA

200

Pipe size

Pipe size

50

100

0

0
X(cm)

150

DATA
ENTRIES 720
MEAN
73.17
RMS
13.11

X(cm)

300

DATA

100

DATA
ENTRIES 1738
MEAN
75.43
RMS
14.96

DATA

200

Pipe size

Pipe size

50

100

0

0
Y(cm)

Y(cm)

DATA
MC
ENTRIES 720 1181
MEAN
202.4 216.6
RMS
60.65 40.39

DATA
MC
ENTRIES 1738 3043
MEAN
150.7 167.2
RMS
66.62 62.51

Pipe end

Pipe end

DATA

DATA

MC

MC
Z(cm)

Z(cm)

Figure D.2: Fitting results of the Cosmic Ray Pipe measurement at z = +1 m heightfrom the center. Upper and middle 4 figures are distributions of the fitted vertex in thehorizontal direction, while lower 2 figures are the vertex in the vertical direction (“z” inthese figures). The left figure of each shows the events whose end-points are contained in
the detector (fully-contained), and the right figure are the events that are penetrated outof the inner vessel (partially-contained). In the vertical direction, the fitted results of theMonte Carlo simulation are overlaid (box).
195

Appendix E
Analysis of June 1999 Run
In June 1999, the experiment was performed with different target diameter and different
current of HORN magnets from other running period. Therefore, the produced pion andneutrino distributions are different. Then, data of Jun.99 run are independently analyzed,
with corresponding Monte Carlo simulations. In particular, PIMON analysis and muon
spectrum in MRD are affected by the different pion distributions and different neutrinoenergy spectrum. In this chapter, analysis results of Jun.99 run are presented.

E.1

PIMON analysis results in Jun.99 run.

The configurations of the HORN magnet and PIMON are summarized in Table 6.1. The
obtained Cherenkov photon distributions are shown in Figure E.1, with simulated distributions by beamMC. They show the agreement between the observed distributions and thesimulation based on Cho model, better than GCALOR/FLUKA model.
Figure E.1 shows the reconstructed neutrino energy spectrum and the flux ratio. The
results again show agreement between the reconstructed results and the simulated ones,
within the quoted systematic errors.
Table E.1 and Table E.2 shows the systematic error of these plots. These errors are
explained in Chapter 6.1.6. In particular, these errors are different from that in Nov. run.
4. Difference between the low and high beam intensity.
In June PIMON run, the profile was about 20 ∼ 30% (50%) narrower in the horizontal(vertical) profile comparing to the ones in normal run. Muon rate in SPD was about
30% larger. This is considered that the high energy muons are sensitive to thetargeting efficiency, and beamMC quantitatively reproduced the increase. Systematic
errors are assigned based on the comparison between these simulations with two
profiles.
196

ADC counts

ADC counts

data vs. MC
20
15
10
5
0

10

20

30

0

10

20

30

80
60
40
20
0

50
0

10

20

30

ADC counts

PMT number (n=1.00131 meas.)

200

30

0

10

20

30

75
50
25
0

200
150
100
50
0

20
10

20

30

10

20

30

0

PMT number (n=1.00179 meas.)

30

0

10

20

30

10

20

30

200
100

50
30

20

50

100
20

10

100

150

10

0

10

20

30

10

20

30

0

300
200

100
0

20

PMT number (n=1.00097 meas.)
ADC counts

ADC counts

PMT number (n=1.00076 meas.)

100

10

PMT number (n=1.00060 meas.)
ADC counts

ADC counts

20

40
20

10

PMT number (n=1.00049 meas.)

40

60

40

20
0

30

data vs. FLUKA/GCALOR

100
10

20

30

PMT number (n=1.00243 meas.)

0

Figure E.1: Comparison of the Cherenkov photon distribution with measurement (dots)
and two sets of beamMC (histograms), for Nov. 1999 run. The simulation in left figures
is based on Cho model and the simulation in right figures is based on GCALOR/FLUKA
model. Definition of these figures are same as Figure 6.3.
5. Beam stability during the PIMON measurement.
The fluctuation of the proton beam center is 3.6 mm and 0.3 mm for x and y in
V39-SPIC, 0.2 mm and 0.6 mm for x and y in TGT-SPIC, during the June run.
Fluctuation of the rate of SPD was 4.6%, and the profile center is stable within ±8
cm. These fluctuations give the systematic error.
8. Proton injection point to the target.
Muon profiles measured by SPD have less than 10 cm shift compared to the normal
run, which confirms that the proton injection point is within 2 mm in Jun. The
systematic error is estimated by the beamMC study in both case.
16. PMT saturation correction.
Another systematic error, due to the non-linearity correction is assigned, only in Junerun (see 3.2.6).

197

Jun. 1999
1
16
2
3
4
5
6
7
8
9
10
11
12
13
14

Energy bin (GeV)
Fitting error
PMT saturation correction
Mirror reflectivity
Refractive index uncertainty
Low and high beam intensity
Beam stability (PIMON run)φ asymmetry of the HORN field
PIMON alignment
Proton injection point
MIRROR-OFF subtraction
Electro-magnetic subtraction
Fitting method
Pion decay before PIMON
Radial distribution of pions
Kinematic bin of pions
Total

June 1999
Energy bin (GeV)
1
16
2
3
4
5
6
7
8
9
10
11
12
13
14

Fitting error
PMT saturation correction
Mirror reflectivity
Refractive index uncertainty
Low and high beam intensity
Beam stability (PIMON run)φ asymmetry of the HORN field
PIMON alignment
Proton injection point
MIRROR-OFF subtraction
Electro-magnetic subtraction
Fitting method
Pion decay before PIMON
Radial distribution of pions
Kinematic bin of pions
Total

Errors on spectrum at near1 − 1.5 1.5 − 2 2. − 2.5±11.7%±9.2% ±17.2%
±0.5%
±1.2%
±1.4%
−1.4%
+4.2%
−3.5%
—
—
—
−5.5%
±1.0% +10.0%
±1.9%
±4.3%
±5.0%
−2.9%
−0.9% +32.6%
—
—
—
−1.5%
+6.8% −10.0%
—
—
—
—
—
—
+6.8%
−7.7% −15.3%
±0.9%
±1.9%
±2.8%
—
—
±2.3%
+2.0%
−2.7%
−7.2%
+13.9% +13.2%+39%−13.6% −13.3%−27%

Errors on spectrum at far
1 − 1.5 1.5 − 2 2. − 2.5±14.7%
±0.8%
−1.6%
—
−7.0%
±3.2%
−2.4%
—
−2.5%
—
—
+11.0%
±2.3%
—
+1.4%
+18.8%−17.2%

±9.6%
±1.2%
+3.1%
—
−6.5%
±3.7%
−7.5%
—
+9.1%
—
—
−10.2%
±5.7%
—
−2.7%
+15.2%−18.8%±19.3%
±2.0%
—
—
+4.5%
±5.0%
+38.8%—−10.0%——−12.3%
±6.3%
±1.4%
−7.4%
+44.4%−27.1%> 2.5+25.1%
±30%
−8.7%
—
+7.0%
±12.7%−19.0%
—
+8.9%
—
−74%
+12%
−21%

±1.3%
±20%
−1.3%
+49%
−88%
> 2.5
+26.7%
±20%
−9.0%
—
+6.5%
±12.8%−10.7%
—
+3.6%
—
−60%
+1.6%
−32%

—
±21%
−13.0%+42.3%−77.5%

Table E.1: Systematic errors of neutrino spectrum at near and far detector in Jun. run.
198

Errors on flux ratio (June 1999, HORN current 200 kA)
Energy bin (GeV)
0 − 0.5 0.5 − 1 1 − 1.5+3.2%
1
Fitting error−4.5%
16
PMT saturation correction
±0.6%
—
2
Mirror reflectivity
3
Refractive index uncertainty—
4
Low and high beam intensity−6.0%
5Beam stability (PIMON run)
±1.0%
6 φ asymmetry of the HORN field+0.5%
7
PIMON alignment
—
−1.0%
8
Proton injection point
9
MIRROR-OFF subtraction—
10
Electro-magnetic subtraction
—
+4.0%
11
Fitting method
12
Pion decay before PIMON±1.4%
13
Radial distribution of pions—
14
Kinematic bin of pions
−0.6%
+5.1%
+7.3%
15
Hadron model (MC)
−9.5%
−2.5%
Total

+5.1%
−9.5%

+7.3%
−2.5%

+5.5%
−7.8%

1.5 − 2

2. − 2.5

> 2.5

+2.0%
−5.7%

+8.5%
−5.8%

±0.5%
—
—
−5.3%
±1.5%
−6.7%
—
+2.1%
—
—

±1.3%
−3.5%
—
−6.6%
±3.4%
+4.7%
—
−0.6%
—
—

+1.4%
−3.0%

+3.2%
−4.6%

±3.8%
—
—

±3.4%
±1.0%
—

±4.2%
—
—
±0.5%
±1.1%
+9.4%
—
−4.9%
—
+72%
−14.5%±1.6%±7.2%−13.0%+7.8%−11.1%+8.7%−11.1%

+6.2%
−4.9%

Table E.2: Systematic errors of neutrino flux ratio (Φf ar /Φnear ) in Jun. run.

199

+73.6%−22.5%

x 10 8KEK flux

6000

MC
Pion monitor Integrated

5000

above 2.5GeV

4000

far/near

7000

x 10

-5

0.5

0.4

3000
2000
1000
0.3

0

0.5

1

1.5

2

2.5

3

Pion monitor
MC

x 10 2

SK flux

5000

0.2

MC
Pion monitor

4000

Integrated
above 2.5GeV

3000

0.1

Integrated
above 2.5
GeV

2000
1000
0

0.5

1

1.5

2

2.5

0

3

0

0.5

E(GeV)
ν

1

1.5

2

2.5

3

E(GeV)
νLeft: Reconstructed neutrino energy spectrum at near and far site in Jun.99 run. Right:
Reconstructed ratio of far and near as a function of energy. Notations are same as Figure
6.5.

E.2

Neutrino Profile at MRD

Figure E.2 shows the acceptance-corrected vertex profile of FC-Low-Energy and FC-HighEnergy analysis (described in Chapter 7.3), in Jun.99 run. They prove that neutrino beam
is pointed towards SK, and neutMC well reproduces the profile.

E.3

Muon Distributions at MRD

Figure E.3 shows the reconstructed muon energy spectrum and angular distribution of
SAMPLE-C, for data of Jun.99 run and neutMC. The results can be reproduced by neutMC
within the uncertainty of the hadron interaction inside the iron nuclei (nuclear effect), as
discussed in chapter 4.2.7.

200

DATA

5000

5000

MC

4000

4000

3000

3000

2000

2000

1000

1000

0

-200

0

Low Energy

0

200

3000

2500

2500

2000

2000

1500

1500

1000

1000

500

500
-200

0

High Energy0

Low Energy

3000

0

-200

x (cm)

0200

x (cm)-200

0High Energy

200y (cm)200

y (cm)

Figure E.2: Corrected vertex profile in June 1999 run (HORN current 200 kA). Definitions
are same as Figure 7.15.

201

2500
1400

DATA
MC, standard

2000

MC, µ
-only

DATA
1200

MC, standard
MC, µ
-only

1000

1500
800

600

1000

400
500
200

0

0

0.5

1

1.5
Muon energy

2

2.5
3
Eµ(GeV)

0

0

10

20

30

40

50

Muon angle

60

70

80
90
θ
µ(degree)Figure E.3: Muon spectrum and polar angle distribution observed in MRD. (Ihorn = 200kA,
in Jun.99 run.) Definitions are same as Figure 7.17.

202

Appendix F
Comparison Between MRD and 1kt
F.1

Event Rate Comparison

In this thesis, two neutrino observations are presented, one is the iron interacted eventsusing MRD, and the other is the water interacted events using 1kt detector. Comparisonof them provides not only the cross check of the each detector measurement, but also therelative cross section of neutrino interaction on different nuclei. In this section comparisonof the event rate is discussed.
Iron interacted events in MRD are summarized in Table 7.6. Water interacted events in
1kt are summarized in Table 8.2. Each event rate is normalized to its fiducial mass, whichcorresponds to the number of target nucleon.
Ratio of these two normalized event rates is given by;
RM RD/1kt =

M RD
rcorr
/MM RD
1kt
rcorr /M1kt

(F.1)

M RD
1kt
where, rcorr
and rcorr
are the efficiency corrected event rates observed at MRD and 1kt,
with P.O.T. normalization. MM RD and M1kt are their fiducial mass. This ratio RM RD/1kt
means following physical explanation;

Rk ΦM RD (Eν ) · σF e (Eν )dEν
RM RD/1kt = Rk Φ1kt (Eν ) · σH2 O (Eν )dEν

(F.2)

where, ΦM RD and Φ1kt are the neutrino flux per unit P.O.T. per unit area, averaged overtheir fiducial area (MRD: 3 m radius, typically 306 m from the target, 1kt: 2 m radius,
typically 290 m from the target), σF e and σH2 O are the cross sections per one nucleon iniron or water nuclei, and k is a normalization factor corresponding to Avogadro constantNA . This comparison is free from an absolute flux uncertainty and an absolute cross section
uncertainty.
203ratio1.2

event rate ratio of MRD / 1kt
1.1

1

0.9

0.8

simulation

0.7

0.6

0.5

Jun

Nov

Jan

Feb

Mar

May

Jun
month

Figure F.1: Ratio of the observed event rate at MRD over the rate at 1kt, monthly plotted.
Error bars are only the statistical errors of the observed event. Monte Carlo prediction is
also overlaid (solid line: center value, dashed line: systematic error range).

Figure F.1 shows the RM RD/1kt in each month. Systematic errors quoted there are
discussed in the next section.
Systematic errors from neutrino event detection and event rate correction are also considered as the error of the Monte Carlo prediction ratio. They are estimated as shownin Table F.1. Systematic errors of the event detection are already discussed in Section
7.5.3 and 8.2.3. Besides them, there are correlated errors some part of which are canceled
between MRD and 1kt. They are estimated from the same discussion as Chapter 10.

F.2

Discussion about RMRD/1kt

The result shows that the event rate ratio RM RD/1kt from the observation and from thesimulation is roughly consistent within more than 10% level uncertainty. This is one ofthe demonstrations of the consistency check of MRD observation and 1kt observation. The
systematic errors dominantly come from the uncertainty of the neutrino flux below 1GeV,
and the lack of understanding of the neutrino interaction on iron nuclei.
They will be improved when further detailed analysis of neutrino interacted events in near
204

Item
1
1
2
3
4
8
5(a)
5(b)
6(a)

for Nov.99
to Jun.00+5.1 − 1.9%
±5.3%
±1.0%
±0.9%
−0.5%
−0.3%
+2.1 − 0.0%

for Jun.99

MRD measurement (Table 7.7)
1kt measurement (Table 8.3)
P.O.T. normalization
Neutrino profile (direction)
Proton targeting stability
σF e /σH2 O including p and πinteraction in nuclei
NC/CC uncertainty
in-elastic cross section
Neutrino energy spectrum
Total+3.4 − 7.3%
+3.1 − 2.7%
+3.0 − 3.3%
+8.3 − 8.1%
±6.5%
+12.6%+11.5%−13.0%−12.1%

Table F.1: Systematic error estimation against the Monte Carlo prediction of RM RD/1kt.

detector give more knowledge about both our neutrino beam and the neutrino interaction
process. This can be achieved, in particular, by analyzing Fine Grain detector (FGD)
measurements.

205

Appendix G
Various Distributions of the
Observed Events in SK
Various distributions of the observed 28 events in SK are shown here. So far, statistics ofobserved events have not been enough. Thus, no physics results are discussed, yet.
Visible energy (Evis ) distribution
Figure G.1 shows the reconstructed visible energy distribution. The distribution of simulated events (no oscillation) is overlaid, which is normalized by the expected number of
events derived from 1kt analysis. Visible energy has a correlation to the initial neutrinoenergy, although some fraction of energy may be lost by invisible particles, like neutrinos,
neutrons, and protons, or may be pent to the produced muons and mesons.
Number of ring, particle identification
Standard ring-counting routine and the particle identification routine [61] are applied forthe observed events. Following table summarizes the number of events in each category.
SK
Expected number of events without oscillation (Nexp) are also shown.

Fully-contained events (total)
1-ring, µ-like
1-ring, e-like
multi-ring206

SK
DATA Nexp
28
37.8
14
20.9
1
2.0
13
14.9

Evis F.C. 22.5kt
15

10

5

0

0

1000

2000

3000

4000

5000
MeV

Figure G.1: Visible energy distribution for SK event. Observed events are shown by closed
circles, and histogram shows the Monte Carlo expectation in null oscillation hypothesis,
normalized by the expected number of events derived from 1kt measurement.

Momentum and angular distribution
Figure G.2-(A),(B) shows the momentum and the angular distribution for 1-ring µ-likeevents. The simulated (neutMC) distributions without oscillation are overlaid.
If the µ-like ring is really the muon, and it comes from Quasi-elastic scattering, neutrinoenergy Eν can be calculated by following formula;Eν =mN · Eµ − m2µ /2
mN − Eµ + pµ cos θµ(G.1)

where, mN (∼ 0.94 GeV) and mµ (∼ 0.106 GeV) are nucleon and muon mass, Eµ , pµ , θµ are
the measured muon energy, momentum, and polar angle with respect to the neutrino beam
direction. For the event selection criteria, the simulation (neutMC) says 53% of events
come from CC quasi-elastic scattering, when the oscillation does not occurs. Therefore, if
the oscillation occurs, entries in some particular energy bins are significantly decreased.
Figure G.2-(C) shows the reconstructed neutrino energy distribution for 1-ring µ-likeevents, by the Formula G.1. Current number of events is not enough to discuss the spectrum
distortion.
207

10

(A)
reconstructed8
momentum
6(B)polar angle

10 (C) reconst.d
neutrino
energyfrom
10 beam direction

DATA
neutMC

4

5

2
0

0

2

4
GeV/c

0
-1

0
0

cos θ

1

0

2

4
GeV

Figure G.2: (A) Reconstructed momentum distribution for 1-ring µ-like events in SK. (B)Reconstructed polar angle distribution with respect to the beam direction, for 1-ring µ-likeevents. (C) Reconstructed neutrino energy distribution, assuming the Quasi-elastic scattering, for 1-ring µ-like events. In each figure, simulated distributions without oscillation
are overlaid (histogram).

208

List of Tables
1.1
1.2
1.3
1.4

The present limit of the each neutrino mass. . . . . . . . . . . . . . . . . .
Comparison of the various neutrino oscillation experiments. . . . . . . . . .
Summary of the measured R values in various experiments. . . . . . . . . .
Results of the solar neutrino measurement. . . . . . . . . . . . . . . . . . .

7
9
12
14

2.1 The measured position of the KEK and SK. . . . . . . . . . . . . . . . . .
2.2 The history of K2K experiment. . . . . . . . . . . . . . . . . . . . . . . . .

21
23

3.1
3.2
3.3
3.4
3.5

Specification summary of KEK-PS for K2K experiment. . . . . . . . . . . .
Freon gas pressure set in PIMON measurement. . . . . . . . . . . . . . . .
The Cherenkov threshold momentum in the water. . . . . . . . . . . . . .
The specifications of the 20-inch PMT. . . . . . . . . . . . . . . . . . . . .
Arrangement of the drift-tubes and iron layers in MRD. . . . . . . . . . . .

25
36
50
51
56

4.1 Parameters for our standard simulation. . . . . . . . . . . . . . . . . . . .
4.2 Parameters of Sanford-Wang formula, for Cho model. . . . . . . . . . . . .

67
69

5.1 Chart of the used spill definition. . . . . . . . . . . . . . . . . . . . . . . .
5.2 Summary of the analyzed p.o.t. . . . . . . . . . . . . . . . . . . . . . . . .

86
86

6.1
6.2
6.3
6.4

Summary of the beam condition and PIMON operations. . . . . . . . . . . 88
Systematic errors of neutrino spectrum at near and far detector in Nov. . . 94
Systematic errors of neutrino flux ratio in Nov. . . . . . . . . . . . . . . . . 95
Proton targeting dependence of the observed events. . . . . . . . . . . . . . 102

7.1
7.2
7.3
7.4
7.5
7.6
7.7

Summary of the event selection process. . . . . . . . . . . . . . . . . . . .
Summary of the selection efficiency for each interaction type. . . . . . . . .
Summary of the fitted center and width of the neutrino profile (FC-all). . .
Reconstruction test of FC profile. . . . . . . . . . . . . . . . . . . . . . . .
Relative event rate at 1kt, MRD and SK when beam is off-direction. . . . .
Summary of the number of observed event in MRD. . . . . . . . . . . . . .
Systematic errors from MRD detection scheme. . . . . . . . . . . . . . . .
209

116
117
129
130
131
135
137

7.8 Event rate comparison with different fiducial volume. . . . . . . . . . . . . 138
7.9 Error estimation of the MRD event selection. . . . . . . . . . . . . . . . . . 138
7.10 Comparison corrected number of track with estimated tracking efficiency. . 139
8.1
8.2
8.3
8.4
8.5

Summary of the number of events at each selection stage. . . . . . . . . . .
1kt event summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systematic errors of 1kt measurement. . . . . . . . . . . . . . . . . . . . .
Event rate comparison with various fiducial volume z-definition. . . . . . .
Effects caused by the FADC threshold change. . . . . . . . . . . . . . . . .

142
147
149
150
151

9.1 Summary of the number of selected events in each step. . . . . . . . . . . . 156
10.1 Calculated number of expected event at SK from 1kt measurement. . . . .
SK
10.2 Systematic error for Nexp
from 1kt measurement. . . . . . . . . . . . . . .
10.3 Efficiency change caused by the cross section change. . . . . . . . . . . . .
SK
10.4 Errors on Nexp
from the near spectrum and the flux ratio uncertainty. . . .
10.5 Calculated number of expected events at SK from MRD measurement. . .
SK
10.6 Systematic errors for Nexp
from MRD measurement. . . . . . . . . . . . .

166
166
168
170
172
172

A.1 Required hit for the efficiency cut. . . . . . . . . . . . . . . . . . . . . . . . 180
B.1 Reconstruction test of VC profile. . . . . . . . . . . . . . . . . . . . . . . . 187
D.1 Fitting results of the Cosmic Ray Pipe measurement. . . . . . . . . . . . . 194
E.1 Systematic errors of neutrino spectrum at near and far detector in Jun. . . 198
E.2 Systematic errors of neutrino flux ratio in Jun. . . . . . . . . . . . . . . . . 199
F.1 Systematic error estimation of RM RD/1kt . . . . . . . . . . . . . . . . . . . . 205

210

List of Figures
1.1 Allowed region of νµ,e → νx oscillation. . . . . . . . . . . . . . . . . . . . .
1.2 Zenith angle distribution of the µ-like and e-like events. . . . . . . . . . . .

10
13

2.1 The schematic view of K2K experiment. . . . . . . . . . . . . . . . . . . .
2.2 Neutrino profile and energy spectrum at SK site. . . . . . . . . . . . . . . .

1821

3.1 Neutrino production beam line and monitors. . . . . . . . . . . . . . . . .
3.2 Typical beam time structure measured by CT. . . . . . . . . . . . . . . . .
3.3 The schematic view of the Segmented Plate Ionization Chamber (SPIC). .
3.4 Schematic view of the two horn magnets. . . . . . . . . . . . . . . . . . . .
3.5 Expected neutrino flux with/without HORN current. . . . . . . . . . . . .
3.6 β distribution of p, π, µ, and e± . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Focusing optics of the spherical mirror. . . . . . . . . . . . . . . . . . . . .
3.8 Advantage of the pie-shaped mirror. . . . . . . . . . . . . . . . . . . . . . .
3.9 The schematic view of PIMON. . . . . . . . . . . . . . . . . . . . . . . . .
3.10 Typical Cherenkov photon distributions in Monte Carlo simulation. . . . .
3.11 Analysis strategy of PIMON. . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Wavelength dependence of the refractive index. . . . . . . . . . . . . . . .
3.13 The schematic view of the interferometer. . . . . . . . . . . . . . . . . . . .
3.14 Cherenkov photon distribution with proton component. . . . . . . . . . . .
3.15 The schematic view of the beam dump and MUMON location. . . . . . . .
3.16 Observed muon distributions in MUMON. . . . . . . . . . . . . . . . . . .
3.17 Relative gain constant of ICH. . . . . . . . . . . . . . . . . . . . . . . . . .
3.18 K2K near detector system. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.19 The schematic view of 1kt barrel and PMTs. . . . . . . . . . . . . . . . . .
3.20 Result of the energy scale calibration using cosmic ray muons. . . . . . . .
3.21 The schematic diagram of 1kt data acquisition system. . . . . . . . . . . .
3.22 The schematic view of Muon Range Detector and its drift-tube. . . . . . .
3.23 DAQ system of the near detector. . . . . . . . . . . . . . . . . . . . . . . .
3.24 The schematic view of Super-Kamiokande detector. . . . . . . . . . . . . .
3.25 The data acquisition system for the inner detector. . . . . . . . . . . . . .

25
26
27
28
29
31
33
33
34
35
37
39
40
41
43
44
46
48
49
52
53
57
58
60
63

211

3.26 Overview of the GPS in SK. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.27 History plot of the difference of UTC and LTC. . . . . . . . . . . . . . . .

65
65

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

The schematic view of the proton emittance calculation. . . . . . . . . . .
Pion yield of experimental result and the fit by Cho model. . . . . . . . . .
Simulated neutrino flux at near site and far site. . . . . . . . . . . . . . . .
Neutrino cross section for water and iron target. . . . . . . . . . . . . . . .
Cross section of CC quasi-elastic scattering. . . . . . . . . . . . . . . . . .
Cross section of CC single-pion production. . . . . . . . . . . . . . . . . . .
CC-total cross section and σ(νn)/σ(νp) . . . . . . . . . . . . . . . . . . . .
Cross section for pi+ and π 0 on oxygen nuclei. . . . . . . . . . . . . . . . .

68
70
71
73
75
77
80
81

5.1 Number of proton accumulation. . . . . . . . . . . . . . . . . . . . . . . . .

85

6.1
6.2
6.3
6.4
6.5

89
90
91
92

Typical example of the MIRROR-OFF subtraction. . . . . . . . . . . . . .
Measured Cherenkov photon distribution in Nov. run. . . . . . . . . . . . .
Cherenkov photon distributions measured in Nov. and beamMC. . . . . . .
Fitted results of pion kinematic region and their error. . . . . . . . . . . .
Predicted neutrino spectrum and flux ratio of Far/Near, compared with thesimulation based on Cho model, in Nov. . . . . . . . . . . . . . . . . . . .
6.6 Comparison with the simulated neutrino spectrum and Far/Near ratio using
GCALOR/FLUKA model, in Nov. . . . . . . . . . . . . . . . . . . . . . .
6.7 Typical proton profile measured by SPIC. . . . . . . . . . . . . . . . . . .
6.8 Spill-by-spill stability of the profile center and width of TGT-SPIC. . . . .
6.9 Stability of the proton profile in front face of the target. . . . . . . . . . .
6.10 Typical muon profile of MUMON-SPD and MUMON-ICH. . . . . . . . . .
6.11 Spill-by-spill fluctuation of the mean of MUMON-ICH profile. . . . . . . .
6.12 Time variation of the muon profile center measured by MUMON. . . . . .

96
99
101
103
106
106
107

7.1 The typical MRD event and fiducial volume definition. . . . . . . . . . . .
7.2 Flow chart of the event selection. . . . . . . . . . . . . . . . . . . . . . . .
7.3 Difference of T0, start point, and end point in X-view and in Y-view. . . .
7.4 2-dimensional distribution of V T Xdist or ENDpoint and T IM Edist . . .
7.5 Reconstructed T0 distribution. . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Selection efficiency of the function of Eν , Eµ , and θµ . . . . . . . . . . . . .
7.7 The effective hit efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.8 Method of the re-tracking test. . . . . . . . . . . . . . . . . . . . . . . . . .
7.9 Typical distributions of the cosmic ray sample used for analysis. . . . . . .
7.10 Tracking efficiency from the re-tracking test. . . . . . . . . . . . . . . . . .
7.11 Residual of the 2-D tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.12 Difference distributions of the re-fitted track and the original one. . . . . .

109
111
113
114
115
117
119
120
121
122
123
123

212

93

7.13 Reconstruction resolution of the vertex, energy and angle . . . . . . . . . .
7.14 Time variation of the track rate from the off-spill data. . . . . . . . . . . .
7.15 Corrected vertex profile of fully-contained events in MRD. . . . . . . . . .
7.16 Stability of the neutrino profile center and width (FC-all analysis). . . . . .
7.17 Eµ spectrum and θµ distributions in MRD. . . . . . . . . . . . . . . . . . .
7.18 Muon energy and angle distributions on monthly basis. . . . . . . . . . . .
7.19 Reduced chi-square of the muon spectrum and angle distortion from theaveraged ones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.20 Stability of the MRD event rate. . . . . . . . . . . . . . . . . . . . . . . . .

124
125
127
128
133
134
134
136

8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8

A typical neutrino event in 1kt detector. . . . . . . . . . . . . . . . . . . . 142
FADC efficiency curve around the threshold height. . . . . . . . . . . . . . 143
Number of peaks and the timing distribution. . . . . . . . . . . . . . . . . 144
Definition of the fiducial volume in 1kt. . . . . . . . . . . . . . . . . . . . . 145
Selection efficiency for events in fiducial-C. . . . . . . . . . . . . . . . . . . 146
1kt detector event rate stability. . . . . . . . . . . . . . . . . . . . . . . . . 148
Vertex profile of x, y, and z direction in 1kt detector. . . . . . . . . . . . . 150
Comparison of of the total photo-electron distribution of DATA with neutMC.153

9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9

Typical neutrino event in Super-Kamiokande. . . . . . . . . . . . . . . . .
Total photo-electron distribution in 300 ns time window. . . . . . . . . . .
Ratio of (maximum p.e.)/(total p.e.). . . . . . . . . . . . . . . . . . . . . .
Number of outer PMTs in largest hit cluster. . . . . . . . . . . . . . . . . .
Visible energy distribution at SK. . . . . . . . . . . . . . . . . . . . . . . .
Reconstructed vertex distance from the tank wall. . . . . . . . . . . . . . .
Time difference distribution for selected events in each step. . . . . . . . .
The selection efficiency at Super-Kamiokande. . . . . . . . . . . . . . . . .
Reconstructed vertex distribution of SK event. . . . . . . . . . . . . . . . .

155
157
158
158
159
160
161
162
162

10.1 Results of the statistical test. . . . . . . . . . . . . . . . . . . . . . . . . . 174
A.1
A.2
A.3
A.4
A.5
A.6
A.7
A.8
A.9

Flow chart of the MRD tracker algorithm. . . . . . . . . . . . . . . . . . .
Number of masked channels. . . . . . . . . . . . . . . . . . . . . . . . . . .
TDC distribution of hit cells. . . . . . . . . . . . . . . . . . . . . . . . . .
Distance from the Cell fit track to hit wire position. . . . . . . . . . . . . .
Distributions of slope and efficiency of the tested tracks. . . . . . . . . . .
Number of hit cells in each fragments. . . . . . . . . . . . . . . . . . . . .
Badness distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distance and angle difference between two tested tracks. . . . . . . . . . .
Conversion function from muon range to muon total energy. . . . . . . . .
213

177
178
178
179
181
181
182
183
184

B.1
B.2
B.3
B.4

Selection efficiency for SAMPLE-A-dash. . . . . . . . . . . . . . . . . . . .
Vertex profile of vertex-contained events in MRD. . . . . . . . . . . . . . .
Stability of the neutrino profile center and width (VC analysis). . . . . . .
Consistency of the profile center and width, between FC-all analysis and VC
analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

186
187
188
189

C.1 Effective charge CH(θ) distributions . . . . . . . . . . . . . . . . . . . . . 191
D.1 Set-up of the Cosmic Ray Pipe measurement. . . . . . . . . . . . . . . . . 194
D.2 Results of the Cosmic Ray Pipe measurement. . . . . . . . . . . . . . . . . 195
E.1 Cherenkov photon distribution with measurement in Jun. and beamMC. . 197
E.2 Corrected vertex profile in Jun.99 run. . . . . . . . . . . . . . . . . . . . . 201
E.3 Muon spectrum and polar angle distribution observed in MRD. (Ihorn =200kA). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
F.1 Event rate ratio of MRD/1kt. . . . . . . . . . . . . . . . . . . . . . . . . . 204
G.1 Visible energy distribution for SK event. . . . . . . . . . . . . . . . . . . . 207
G.2 Reconstructed momentum, angle, and neutrino energy distribution. . . . . 208

214

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220

Acknowledgement
I would like to express my great appreciation to my adviser, Prof. Koichiro Nishikawa. He guides
me in fascinating “High Energy Physics” world, and always supports my reserch activities. I
admire his smart viewpoint to the physics, and his lead of the K2K experiment. I wish to extend
my appreciation to Prof. K.Nakamura, Prof. Y.Totsuka, Prof. Y.Suzuki, Prof. C.K.Jung, andDr. M.Sakuda. Their management of K2K experiment enables me to accomplish my works.
My study depends on the hard work of many collaborators. Chapter 7 is supported by MRD
group, Dr. T.Ishii, Dr. A.Sakai, Mr. K.Shiino, Mr. K.Tauchi, Dr. S.B.Lee, and Mr. J.H.Choi.
Chapter 6 is supprted by Beam Monitor group, Dr. T.Hasegawa, Dr. T.Maruyama, Dr. J.Hill,
Dr. W.Gajewski, Dr. M.Kohama, Mr. T.Kadowaki, Mr. E.Seo, and Mr. H.Yokoyama. Chapter 8
is supported by 1kt group, Dr. Y.Itow, Dr. M.Miura, Dr. S.Mine, Dr. T.Nakaya, Mr. C.Mauger,
Mr. S.Nakayama, and Mr. A.Shima. Chapter 9 is supported by K2K-SK group, Dr. K.Kaneyuki
and Mr. S.Yamada, as much as the Super-Kamiokande collaborators. I have great thank forthe complete data-taking works performed by Dr. T.Kobayashi, Dr. Y.hayato, Dr. M.Yoshida,
and Mr. H.G.Berns. Many times I have a support of FGD group, Dr. T.Ishida, Dr. Y.Oyama,
Dr. A.C.Suzuki, Dr. T.Chikamatsu, Dr. H.Ishino, Dr. H.Park, Dr. S.Boyd, Dr. B.J.Kim, Dr. V.Tumakov,
Mr. E.Sharkey, Mr. T.Iwashita, Mrs. E.J.Jeon, and Mrs. H.Yokoyama. I got an advice and discussion of the physics of neutrino interaction from Mr. J.Kameda. I would like to express mygratitude to all of these collaborators, giving me a lot of discussion of the analysis as much as theneutrino physics. I am deeply grateful to KEK-PS accelerator group and Beam-channel group,for their hard work on providing stable neutrino beam. I always appreciate to Mr. M.Taino
and Beam-channel group members, for supporting the experiment and care about us. I am very
happy to accomplish this experiment with all of the collaborators, including Mr. M.Nakamura,
Mr. M.Etoh, Mr. S.Echigo, Mr. S.Kenmochi, Mr. T.Umeda, Mrs. E.M.Jeong, Mrs. H.K.Lee, Mr. M.Kitamura, Mr. T.Inada, Mr. G.Kume, Mr. M.Onchi, Mr. S.Kishi, and Mrs. M.Takatsuki.
I am grateful to our laboratory members in Kyoto University, especially, Prof. N.Sasao,
Dr. H.Sakamoto, Dr. T.Nomura, Dr. T.Nakaya, Mr. M.Suehiro, Dr. H.R.Sakai, Dr. Y.Ushiroda,
Mr. T.Akky.Fujiwara, Mr. S.Mukai, Mr. H.Yokoyama, Mr. I.Kato, Mr. A.Shima, Mr. H.Maesaka,
Dr. A.K.Ichikawa, and Prof. K.Nishikawa, for a many physics (and beyond-physics?) discussion.
I thank KEK, ICRR, and the Japan Society for Promotion of Science, for financial support andpromotion of this study.
Finally, I gratefully acknowledge my family and my best friends, for a lot of encouragement
and support throughout my physicist life.

221