Proposal for KL → π 0νν Experiment at J-Parc
April 28, 2006
Revised: May 2, 2006

Joseph Comfort and Jeremy Figgins
Arizona State University, Physics Department
Tempe, Arizona 85287 USA

Mircea Bogdan, Jiasen Ma, Fukun Tang, Harold Sanders, and
Yau W. Wah
Enrico Fermi Institute, The University of Chicago
5640 South Ellis Avenue, Chicago, Illinois 60637, USA

Alexandr S. Kurilin, Evgeni S. Kuzmin, Sergey V. Podolsky, andAnton A. Shuteev
Joint Institute for Nuclear Research (JINR)
Dzhelepov Laboratory of Nuclear Problems
Joliot-Curie St., 6, Dubna Moscow Region 141980, Russia

Mikhail Yu. Doroshenko, Takao Inagaki, Nobuhiro Ishihara,
Takeshi K. Komatsubara, Gei-Youb Lim, Hideki Okuno,
Takahiro Sato, Michiko Sekimoto, Hiroaki Watanabe, andYoshio YoshimuraHigh Energy Accelerator Research Organization (KEK)
Oho 1-1, Tsukuba-shi, Ibaraki 305-0801, Japan

Hideki Morii, Yasuhiro Nakajima, Hajime Nanjo, Tadashi Nomura,
Noboru Sasao, and Toshi Sumida
Kyoto University, Department of Physics
Kitashirakawa-Oiwake, Sakyo, Kyoto 606-8502, Japan1

Toru Matsumura and Takao Shinkawa
National Defense Academy, Department of Applied Physics
1-10-20 Hashirimizu, Yokosuka 239-8686, Japan

Kai-Feng Chen, Yee Bob Hsiung, Yu-Chen Tung, and Meng-Lin Wu
National Taiwan University, Department of Physics
1, Roosevelt Rd., Sec.4, Taipei, Taiwan 10617 ROC

Eito Iwai, Atsushi Kakehashi, Ken Sakashita, Mitsuhiro Yamaga, andTaku Yamanaka
Osaka University, Department of Physics
1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan

Jung Keun Ahn, Hyo Sang Lee, and Kwang Yoon BaikPusan National University, Department of Physics
Pusan 609-735, Korea

Shiro Suzuki, Shigeharu Kobayashi, Risa Ogata, Tetsushi Shimogawa,and Masayuki Yoshimi
Saga University, Department of Physics
1 Honjo-machi, Saga 840-8502, Japan

Macharashvili Gogi and Tsamalaidze Zviadi
Tbilisi State University, Department of Physics
I. Chavchavadze Avenue, 3, 0128, Tbilisi, Georgia

Toshio Numao
TRIUMF
4004 Wesbrook Mall, Vancouver, British Columbia, Canada, V6T 2A3

Takahiro Iwata1 , Yasuhisa Tajima2 , and Hiroshi Yoshida2
Yamagata University,
1
Department of Physics, and 2 Networking and Computing Service
Center
1-4-12 Kojirakawa-machi, Yamagata 990-8560, Japan

Spokesperson: Taku Yamanaka
Email: taku@hep.sci.osaka-u.ac.jp, Phone: +81-6-6850-5356
2

Contents
1 Executive Summary

5

2 Physics Motivation
2.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Beyond the Standard Model . . . . . . . . . . . . . . . . . . .
2.3 KL0 → π 0 νν and Flavor Physics in the next decade . . . . . .
2.4 Other physics decay modes . . . . . . . . . . . . . . . . . . .
2.4.1 KL0 → π 0 π 0 νν . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Light sgoldstinos in KL0 → π 0 π 0 X 0 . . . . . . . . . . .
2.4.3 KL0 → π 0 γγ . . . . . . . . . . . . . . . . . . . . . . . .

6
6
9
10
16
16
17
17

3 Strategy
19
3.1 Basic strategy of the experiment . . . . . . . . . . . . . . . . 19
3.2 E391a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Step 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 Step 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Step 1
23
4.1 Goal of Step 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3.1 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3.2 Barrel Photon Veto . . . . . . . . . . . . . . . . . . . 34
4.3.3 Charged Veto . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.4 Collar Counters . . . . . . . . . . . . . . . . . . . . . . 42
4.3.5 Beam Hole Veto . . . . . . . . . . . . . . . . . . . . . 43
4.3.6 Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 Frontend electronics, Trigger, and DAQ . . . . . . . . . . . . 47
4.4.1 Electronics . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4.2 Trigger and DAQ . . . . . . . . . . . . . . . . . . . . . 49
4.5 Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.6 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6.1 Detector acceptance . . . . . . . . . . . . . . . . . . . 51
4.6.2 Acceptance Loss . . . . . . . . . . . . . . . . . . . . . 53
4.6.3 Single event sensitivity . . . . . . . . . . . . . . . . . . 55
4.7 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.7.1 KL → π 0 π 0 background . . . . . . . . . . . . . . . . . 56
4.7.2 KL → γγ background . . . . . . . . . . . . . . . . . . 60

3

4.7.3
4.7.4
4.7.5
4.7.6
4.7.7

KL → π 0 π 0 π 0 background . . . . . . . . . . . . . . . .
KL → π + π − π 0 Background . . . . . . . . . . . . . . .
KL → π − e+ ν Background . . . . . . . . . . . . . . . .
Neutron Background . . . . . . . . . . . . . . . . . . .
Accidental halo neutron background . . . . . . . . . .

60
62
63
65
67

5 Step 2
69
5.1 New beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 Sensitivity and Background . . . . . . . . . . . . . . . . . . . 72
5.4 Detector R&D . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.4.1 Endcap Calorimeter . . . . . . . . . . . . . . . . . . . 74
5.4.2 Charged Veto . . . . . . . . . . . . . . . . . . . . . . . 75
5.4.3 Pipeline readout . . . . . . . . . . . . . . . . . . . . . 78
6 Schedule and Cost
79
6.1 Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7 Conclusion

81

A Appendices82
A.1 Beam Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 82
A.2 Photon Veto Ineﬃciency . . . . . . . . . . . . . . . . . . . . . 87
A.3 Charged Particle Veto Ineﬃciency . . . . . . . . . . . . . . . 90
A.4 Expected Performance of Beam Hole Photon Veto . . . . . . 93

4

1

Executive Summary

The very rare decay KL0 → π 0 νν is a sensitive probe for direct CP violation in
the quark sector. The decay is a Flavor Changing Neutral Current processthat is induced through electroweak loop diagrams. The branching ratio
for KL0 → π 0 νν is predicted to be (2.8 ± 0.4) × 10−11 in the Standard
Model, and the theoretical uncertainty is estimated to be only a few percent.
The decay is also sensitive to new physics scenarios beyond the Standard
Model such as Supersymmetric theories. A comparison of the CP-violation
parameters from KL0 → π 0 νν with the values obtained from experiments at
the B factories is therefore a precise tool for discovering and understanding
the ﬂavor structure in new physics.
We propose to measure the branching ratio of the KL → π 0 νν decay
with an uncertainty less than 10%. We will take a step-by-step approach toachieve our goal.
We have already run a pilot experiment, E391a, at the KEK 12-GeV Proton Synchrotron. We propose to reuse the beamline and detector, and apply
necessary modiﬁcations based on our experience with E391a. In particular,
we plan to replace the CsI crystals in the Calorimeter with the smaller-size
crstals used in the Fermilab KTeV experiment. We will start running at
Time 0 of the J-PARC slow extraction beam, by using the common T1 target on the A-line and a neutral beam line with a 16◦ extraction angle; thisstage will be the Step 1 of our experiment. Our goal of Step 1 is to makethe ﬁrst observation of the decay. We expect to observe 3.5 Standard Model
events (with a 50% acceptance loss due to tight extra-photon rejection) with
1.8 × 1021 protons on target in total. The expected S/N ratio is 1.4. The
beamline and detector in Step 1 can be realized with reasonable costs.
In the Step 2 stage, we plan to upgrade the beam line and the detector,
and accumulate more than 100 Standard Model events with an S/N ratio of
4.8.
This proposal is focused on the Step 1 experiment, but will also show
our plan for Step 2.

5

2

Physics Motivation

CP violation is currently recognized as one of the forefront issues in elementary particle physics. Together with obtaining a better understanding ofquark mixing as well as neutrino mixing phenomena, it is one of the central
goals of particle physics and has been pursued vigorously in many experiments. The very rare decay KL0 → π 0 νν [2] provides one of the best probes
for understanding the origin of CP violation in the quark sector [3, 4]. The
decay is a Flavor Changing Neutral Current (FCNC) process from strange
quark to down quark, and its observation will provide new positive evidence for direct CP violation. It has been established that studies of FCNC
processes are extremely useful for understanding the underlying physics phenomena.
The decay KL0 → π 0 νν is a unique and clean process. The decay has been
considered as an ideal “golden mode” in quark ﬂavor physics for a critical
test of the Standard Model (SM), as well as a search for new physics beyond
the SM [5, 6]. The ultimate goal of this proposal is to achieve a sensitivity ofbetter than 3×10−13 for the branching ratio, corresponding to an observationof more than 100 events for the Standard Model prediction. This result
would determine the height of the CKM unitarity triangle, represented by
the imaginary part η of the CKM matrix, to better than 5% accuracy.

2.1

Standard Model

Understanding the phenomenology of quark mixing and CP violation requires examining the CKM ansatz of the Standard Model through precise determination of its basic parameters, several of which are still poorly known.
To assure a clear interpretation of the experimental results, the ideal observable must not only be sensitive to fundamental parameters, but it mustalso be calculable with little theoretical ambiguity.
The rare decay KL0 → π 0 νν provides such an opportunity and is uniqueamong potential SM observables. It is dominated by direct CP violationand is entirely governed by short-distance physics involving the top quark.
Long-distance contributions have been shown to be negligible. Theoreticaluncertainties are extremely small in SM calculations.
The KL0 → π 0 νν decay is a FCNC process that is induced through loop
eﬀects. A direct term, which proceeds through a ∆S = 1 transition as
expressed by the electroweak penguin and box diagrams shown in Fig. 1,
dominates an “indirect” mixing term that proceeds through a ∆S = 2 tran0
sition where KL0 changes into KS0 via K 0 − K mixing [7]. The KL0 → π 0 νν6

decay therefore oﬀers information of the ∆S = 1 process. The hadronicmatrix element can be factorized as the well-known branching ratio of the
K → πeν decay [8]. The higher-order QCD corrections that couple to thevirtual top quark are calculable but small due to the large mass of the top
quark [9]. A long-distance interaction contributes little to the KL0 → π 0 νν
decay [7, 10, 11], because neutrinos are weakly interacting particles. Consequently, an uncertainty in the theoretical calculation is estimated to be only
a few percent, and the KL0 → π 0 νν decay will oﬀer clean information on an
important basic parameter of current elementary particle physics.

           

Figure 1: SM diagrams for the KL0 → π 0 νν decay.

In the Standard Model, the decay amplitude of KL0 → π 0 νν is proportional to the imaginary part of a product of CKM matrix elements,
Im(Vts∗ Vtd ), which corresponds to the height of the unitarity triangle asshown in Fig. 2. The unitarity of the CKM matrix has been considered as
one of the most critical checks for new physics beyond the Standard Model.
The pure and clean information obtained by the KL0 → π 0 νν decay is crucial
for checks of the SM as well as those by B decays. By using current estimates for SM parameters, the branching ratio for KL0 → π 0 νν is predicted
to be
(

)8 [

]

2
Im(Vts∗ Vtd )
X(x
)
,
t
λ5
(1)
−11
and is expected to lie in the range (2.8 ± 0.4) × 10[12]. Here λ ≡ |Vus |,X(xt ) = 1.464±0.041 is the value of Inami-Lim loop function [13] (including
the QCD correction), and the parameter xt is the square of the ratio of the
top quark and W masses. Because η in Im(Vts∗ Vtd ) = −A2 λ5 η measuresdirectly the height of kaon unitarity triangle, the decay amplitude KL0 →π 0 νν violates CP directly and oﬀers the best opportunity for measuring theJarlskog invariant:

B(KL0 → π 0 νν) = (2.20 ± 0.07) × 10−10λ0.2248(∗
JCP ≡ −Im(Vts∗ Vtd Vus
Vud ) = −λ

7

λ2
1−
2

)

Im(Vts∗ Vtd ) ,(2)which is proportional to twice the area of the unitarity triangle [14].

Figure 2: Kaon unitarity triangle.
Although the best direct experimental information on the KL0 → π 0 ννmode will be from the full E391a data set, the ﬁrst preliminary result forthe branching ratio is B(KL0 → π 0 νν) < 2.1 × 10−7 as a 90% conﬁdencelevel (C.L.) upper limit [15]. A more stringent constraint can be derived byusing the information on the charged mode [16] and isospin symmetry, andis called “Grossman-Nir (GN) bound” [17]:which gives

B(KL0 → π 0 νν) ≤ 4.4 × B(K + → π + νν)(3)

B(KL0 → π 0 νν) < 1.4 × 10−9 .

(4)As discussed in Ref. [17], this bound is valid in virtually any extension of theStandard Model. By comparing this model-independent bound and the SM
prediction, it is clear that there is still considerable room for new physics in
KL0 → π 0 νν. But even if the experimental measurement of B(KL0 → π 0 νν)was found to be in agreement with the SM expectation with a small relative
error, this information would translate into a unique and precious insightabout the CP and ﬂavor structure of any extension of the SM. These features
make the experimental search for KL0 → π 0 νν, at the SM level and below,
a must-do experiment.
The super-weak model, which causes CP violation only in the mixing(∆S = 2 transition), is almost ruled out by the recent ϵ′ /ϵ experiments at
Fermilab [18] and CERN [19]. However, the other primary explanation, theCKM matrix (i.e. the Standard Model), accommodates the experimental
8

results but has basic problems, such as the strong CP problem and the lackof strength for baryogenesis. Problems of CP violation are not solved yet.
One of the best ways to understand profoundly the physics of CP violation
is to measure precisely its strength in all FCNC processes, ∆S = 1, 2 and∆B = 1, 2. For ∆B = 1, 2, B-factory experiments such as Belle, Babar and
LHCb can provide answers at the level of a few percent. For ∆S = 2, latticecalculations may soon solve the problem of the large theoretical ambiguityfor ϵ. However, the precise value of ∆S = 1 can only be obtained from ameasurement of KL0 → π 0 νν decay.
A recent paper by Buras, Gorbahn, Haisch, and Nierste [12], who completed the next-to-next-to-leading order (NNLO) QCD calculation of thecharmed penguin contribution to K + → π + νν, has improved the theoretical accuracy by a factor of 4 and reduced the error of the charmed penguin
uncertainty in the charged mode from ±9.8% down to ±2.4%. Their results
are translated into the following theoretical uncertainties in the K → πννsystem on the quantities of interest as:σ(|Vtd |)= ±1.0%, σ(sin 2φ1 ) = ±0.006, and σ(φ3 ) = ±1.2◦ ,|Vtd |(5)

implying a better constraint on the CKM parameters in the future.

2.2

Beyond the Standard Model

Extensions of the Standard Model in principle can modify the physics discussed above in many ways. Extended models usually introduce a variety of
new degrees of freedom and many unknown parameters, and it is therefore
diﬃcult to obtain deﬁnite predictions. However, one can make some general
remarks relevant for KL0 → π 0 νν and the comparison with information fromthe B sector.
Various models beyond the SM predict sizable eﬀects on the KL0 →π 0 νν decay. For example, in the Minimal Supersymmetric extensions of theSM (MSSM) with new sources of ﬂavor mixing, there is considerable room
for possible enhancements in the KL0 → π 0 νν branching ratio even after
taking into account all of the available constraints from other CP-violating
observables and rare decays [20, 21].
A clean SM test is provided by comparing η from KL0 → π 0 νν with themeasurements of |Vub /|Vcb | in b → u versus b → c decays, and xd /xs in
Bd –Bd vs. Bs –Bs mixing. Similarly, if the branching ratio B(K + → π + νν)is measured precisely, a very clean test is to compare the value of sin 2φ1

9obtained from the two kaon rare decays with that determined from the CPasymmetry in B → J/ψ KS . Other incisive tests involve comparisons of
the Jarlskog invariant obtained from B(KL0 → π 0 νν) with indirect determinations of the same quantity from the B system. Any discrepancy would
clearly indicate new physics.
In some new physics scenarios, such as multi-Higgs doublets models [22]or the speciﬁc MSSM in which the CKM matrix remains the sole source ofCP violation (called the “Minimal Flavor Violation” hypothesis) [23, 24], theextraction of sin 2φ1 and sin 2φ2 from CP asymmetries in B decays would
be unaﬀected. Such eﬀects might show up in a comparison with KL0 →π 0 νν, where the charged Higgs contributions modify the top quark loop
contribution [25]. In other new physics scenarios, such as Supersymmetric
ﬂavor models [26] or extra dimensions [27], the eﬀects in K → πνν tend tobe small, while there can be large eﬀects in the B (and also in D) systems. In
these models, the rare K decays are the only clean way to measure the true
CKM parameters. Examples for new physics scenarios that show drastic
deviations from the SM are provided by some of the extended Higgs models[28], topcolor-assisted technicolor models [29], left-right symmetric models[30], models with extra quarks in vector-like representations [31], lepto-quark
exchange [17], and four-generation models [32]. Figures 3 [33, 3] and 4 [24]show examples of possible new physics scenarios [5] that can drasticallychange the SM predictions.
Even in the K-decay observables, the additional beyond-the-SM eﬀects
change the SM predictions in diﬀerent directions. For example, the ϵ param0
eter in K 0 –K mixing and in KL0 → π 0 νν decay change values in opposite
directions [34, 35]. Thus, measuring the KL0 → π 0 νν decay branching ratio
to an accuracy of a few percent will provide a critical check on eﬀects beyond
the Standard Model.

2.3

KL0 → π 0 νν and Flavor Physics in the next decade

Observation of KL0 → π 0 ν ν̄ enables us to perform the stringent test of
the quark ﬂavor sector in the Standard Model. Figure 5 shows how we
can discover or discriminate several new physics scenarios by improving thesensitivity. An experiment with 100 SM events tells us whether the s → dtransition is consistent with the SM or not. If signatures of new physics areobserved in the LHC experiments beginning in 2007, we can study whether
the ﬂavor structure is in the Minimal Flavor Violation hypothesis or moregeneric ones.
An experiment with a sensitivity of 3 × 10−13 determines η and sin 2φ1
10

BR(K + → π + ν ν̄)+DφK
v0 = 0.1
v0 = 0.4∆0 = 0◦
90◦
180◦
270◦
BaBar
Belle
BR(K + → π + ν ν̄)BR(KL → π 0 ν ν̄)SMexp. range
βX = 99◦
βX = 111◦ 1.6·10−10
βX = 123◦ 1.4·10−10exp. range

1.2·10

−10

1·10

−10

8·10

−11

6·10

−11

4·10

−11

2·10

−11

150◦
50◦

βX = 25◦

111◦

70◦

130◦

SM
GN bound

1·10

−10

2·10

−10

3·10

−10

BR(KL → π 0 ν ν̄)

−10

5·10

 

 

4·10

−10











 


 
!"# !"#
!  # 



$%











 

 

Figure 3: Top: correlation of B(KL0 → π 0 νν) and B(K + → π + νν) for
various values of βX , which is the diﬀerence of φ1 in the SM from the new
CP-violating phase θX beyond the SM [33]. Bottom: ratio of B(KL0 → π 0 νν)to B(K + → π + νν) as a function of βX for |X| = 1.25, 1.5, 2.0, where X ≡|X|eiθX is the short-distance function, instead of the Inami-Lim function,
beyond the SM [3].

11Figure 4: Comparison of the eﬀectiveness of diﬀerent observables in rare K
and B decays in setting future bounds on the energy scale of new physics
operators [24]. The vertical axis indicates the relative precision of a hypothetical measurement of the observable, with the central value equal to the
SM expectation. The curves are obtained by assuming an uncertainty of 1%
precision on the corresponding overall CKM factor.

12Figure 5: A 5σ discovery region (shaded area) and 95% CL upper and lower
exclusion limits versus the number of KL0 → π 0 νν events, assuming theSM, from the study by Bryman, Buras, Isidori and Littenberg [5]. The
maximal enhancement of the branching ratio (BR) expected in various nonSM scenarios are also included.

13

Figure 6: Constraints in the ρ − η plane from future measurements of
B(KL0 → π 0 νν) and B(K + → π + νν) with an accuracy of ±10%. The
constraints from the CKM global ﬁt obtained by the CKMﬁtter Group [36]are overlaid.

14

in the SM with the accuracies of 6.3% and 7.0%, respectively [3]. These
precisions are comparable to those obtained by the CKM global ﬁts in 2005
(6.8% and 4.7%, respectively1 ) [36, 37], as shown in Fig. 6. In order to identify the signature of new physics, deviations of sin 2φ1 measured in several
B and K decay modes (≡ Sm ) from that in B → J/ψ KS0 (≡ SJ/ψK 0 ), ∆Sm
S≡ Sm − SJ/ψK 0 , are useful because SJ/ψK 0 will be precisely measured inSS
the near future. The precision of ∆Sπ0 ν ν̄ with the sensitivity of 3 × 10−13 is±0.05 [3],2 while the precision of ∆SφK 0 from the B → φKS0 decay, which isS
the most promising mode for new physics in the future Super-B factories, is
expected to be ±0.08 with 5 ab−1 and ±0.03 with 50 ab−1 integrated luminosity, respectively [38]. We would point out that a σ(∆Sπ0 ν ν̄ ) of ±0.05 iscomparable to σ(∆SφK 0 ) from Super-B running for a few years (15 ab−1 ),S
which indicates the competitiveness of the J-PARC KL0 program to the otherﬂavor-physics experiments in the 2010’s (Fig. 7).

Figure 7: Schematic determination of (ρ, η) from the B system (Bd →J/ψ KS and ∆mBd /∆mBs ) and from K → πνν [39].

The KL0 → π 0 ν ν̄ measurement determines η directly, while B-factory experiments
measure sin 2φ1 from the B → J/ψKS0 and related decays. The precision of sin 2φ1 in B
experiments is always better than the precision of η.
2
Here we assume the number of KL0 → π 0 ν ν̄ events to be 100 as in the SM. The
precision gets better if the branching ratio is larger than the prediction in the SM.
1

15

2.4

Other physics decay modes

Table 1 is a list of kaon decays anticipated as byproducts in the KL0 → π 0 ννexperiment. The physics of the ﬁrst three topics in the table are explainedin this subsection.
Table 1: Other physics decay modes in the J-PARC KL0 experiment. ”NP”
means the prediction in New Physics.

decay mode
KL0 → π 0 π 0 νν
0KL0 → π 0 π 0 Xinvisible000
KL → π π Xµ0+ µ−0
KL0 → π 0 π 0 Xγγ00KL → π γγ

physics
FCNC, ρlight sgoldstino
HyperCP events
HyperCP events
ChPT

KL0 → π 0 π 0 γ

ChPT

KL0 → γνν
KL0 → π 0 γννKL0 → γγγ

new physics
new physics
Bose/gauge sym.

2.4.1

(past result)prediction
1.4 × 10−13
10−3 in NP
10−8 in NP
10−4 in NP
Mγγ spectrum(1.5 × 10−6 )7 × 10−11∼ 1 × 10−8(< 5.6 × 10−6 )0.7 × 10−11
4.4 × 10−15
3 × 10−19(< 2.4 × 10−7 )

Ref.
[40]
[41, 42][44, 45, 46, 47][44, 45, 46, 47][49, 50][51][52, 53, 54][55, 56]

KL0 → π 0 π 0 ννThe CP conserving decay KL0 → π 0 π 0 νν is a Flavor Changing Neutral Current process and involves an s → dνν transition. Similar to the KL0 → π 0 νν
decay, this mode is not sensitive to long-distance contributions. The branching ratio, which is proportional the square of the CKM matrix parameter ρ(Fig. 2), is predicted to be (1.4 ± 0.4) × 10−13 with little theoretical uncertainty [40]. We have started working on this decay mode with the E391a
data set, and expect to improve the upper limit further at J-PARC.

16

2.4.2

Light sgoldstinos in KL0 → π 0 π 0 X 0

The decay mode KL0 → π 0 π 0 X 0 , where X 0 is a neutral weakly-interacting
particle, allows one to search for a low-mass supersymmetric particle, called
the “sgoldstino” [41, 42].3 The masses of scalar and pseudoscalar sgoldstinos are model dependent and could be below a few GeV/c2 or a few
MeV/c2 . Sgoldstinos are light in some gravity-mediated theories and gaugemediated models. If the pseudoscalar sgoldstino P is light enough, (mP <mKL − 2mπ ), then the decay of a neutral kaon to 2π 0 and the pseudoscalarsgoldstino, identiﬁed as KL0 → π 0 π 0 X 0 , is a very interesting probe of thephysics.4 Depending on the phases of the quark-sgoldstino coupling, theallowed branching ratio can be as high as 10−3 .
The Fermilab HyperCP experiment recently reported [43] evidence forthe decay Σ+ → pµ+ µ− and suggested that the µ+ µ− pair was due to the
decay of a new neutral particle X 0 at 214 MeV/c2 . A boson of such mass
has never been searched for in the past. Theoretical studies [44, 45, 46, 47]
pointed out that the branching ratios of K → ππX 0 following X 0 → µ+ µ−
and X 0 → γγ could be as high as 10−8 and 10−4 , respectively. We havestarted a search with the E391a data set [48], and will continue at J-PARC.
2.4.3

KL0 → π 0 γγ

Two experiments, Fermilab E832 [49] and CERN NA48 [50], measured
KL0 → π 0 γγ and showed strong evidence for the decay in the region of
low γγ invariant mass, as predicted by recent O(p6 ) calculations in chiralperturbation theory (ChPT) that include vector meson exchange contributions. However, their results diﬀer by three standard deviations in boththe branching ratio (∼ 1.5 × 10−6 ) and the pole parameter aV . This decay
mode is important for the determination of the CP conserving amplitude of3

The spontaneous breaking of any global symmetry results in a massless NambuGoldstone mode with the same quantum numbers as the symmetry generator. In the caseof supersymmetry, the symmetry generator is fermionic resulting in a Nambu-Goldstone
fermion named “goldstino.” The exact nature of the goldstino depends on the speciﬁcmodel of supersymmetry. For example, in the case of supegravity theories, the superpartner of the graviton, the gravitino, absorbs the goldstino and thereby acquires a mass. As
the goldstino is√part of a superﬁeld, it should have a superpartner, the complex scalar ﬁeld
z = (S + iP )/ 2 named “sgoldstino.” The real component S is the scalar sgoldstino, andthe imaginary part P is the pseudoscalar sgoldstino.
4
This possibility is not an unreasonable one as it arises in a variety of models. The
coupling constants are constrained by the limits on the mass diﬀerence between KL and
KS and requiring that the contribution to the CP violation parameter ϵ in the kaon system
is less than its measured value.

17

KL0 → π 0 e+ e− , which has a large direct CP-violating component. A highstatistics study (∼ 104 events) of KL0 → π 0 γγ is needed to resolve this issue.
We expect to do such a measurement in the J-PARC experiment.

18

3Strategy

3.1

Basic strategy of the experiment

The KL → π 0 νν decay is a theoretically clean decay mode, but also a
diﬃcult decay mode to study experimentally. The incoming KL cannot be
observed before decaying, and only two photons are visible. The branchingratio expected from the Standard Model is very low, ≅ 3×10−11 . One of the
major backgrounds is KL → π 0 π 0 , where two of the four photons are missed.
Because the branching ratio of KL → π 0 π 0 is 8.83 × 10−4 , the backgroundhas to be suppressed by 8 orders of magnitude or more.
In order to cope with these diﬃculties, we will use the following basic
techniques.
• Use a detector with a high acceptance.
This requirement is necessary for increasing the signal yield from a limited number of KL decays. We will place an electromagnetic calorimeter downstream of the decay region to catch two photons from the
KL → π 0 νν decay. There will be a beam hole at the center of thecalorimeter to let neutral particles go through.
• Cover the decay region with hermetic photon veto counters with a low
detection ineﬃciency.
This technique will suppress the KL → π 0 π 0 decay backgrounds by
detecting the extra two photons. Note that the background level is
proportional to the product of the detection ineﬃciencies for those
extra photons.
• Place detectors inside high vacuum
The decay volume has to be evacuated, in order to suppress the number of π 0 ’s produced by neutrons interacting with residual gas. Also,
placing the detector components inside instead of outside the vacuumtank eliminates dead material (e.g., the vacuum tank) that could absorb photons before hitting the detector.
• Use a KL beam with a small size.
There are two reasons.
– First, a small size allows us to minimize the beam hole in thecalorimeter, and reduces the chance that photons from KL →π 0 π 0 decays go through the beam hole. Such photons are likely
to hit a veto detector with a higher ineﬃciency due to its highrates.
19

– Second, the error on the transverse momentum of π 0 , PT , will be
kept small. The decay vertex along the beam is reconstructed byassuming that the two photons hitting the Calorimeter has theinvariant mass of π 0 . The PT is calculated by assuming that the
decay vertex is at the center of the beam, so the error on PT due
to the ﬁnite beam size will be limited with a small beam size.
• Require events with only two photons that together have a large transverse momentum.
We require PT to be large (>120 MeV/c). This requirement is useful:– to suppress background from KL → γγ decays,– to require missing photons to have higher energies, and reduce
the probability of missing them, and– to suppress KL → π 0 π 0 backgrounds where two higher-energy
photons from diﬀerent π 0 ’s are detected.
In order to collect more than 100 signal events, we have to improve thesensitivity from the current KTeV limit BR(KL → π 0 νν) < 5.9 × 10−7
(90% CL)[1] using π 0 → e+ e− γ in the ﬁnal state, by 6 orders of magnitude
or more. Because such improvements cannot be done easily in a single step,
we will pursue the experiment in a step-by-step approach as follows.

3.2

E391a

We ran a ﬁrst experiment dedicated for the KL → π 0 νν decay, the KEK
PS E391a experiment, using the existing 12-GeV Proton Synchrotron at
KEK. As shown in Fig.8, the detector consists of a pure CsI electromagnetic
calorimeter at the downstream end, and photon veto detectors surrounding
the decay region, all located inside a vacuum tank. There was also a set ofphoton veto detectors located downstream of the calorimeter. The typicalbeam intensity was 2.5 × 1012 /pulse, and the average KL momentum was
2.6 GeV/c.
We had three data taking runs, totaling 6 months. The ﬁrst preliminary
result BR(KL → π 0 νν) < 2.1 × 10−7 (90% CL)[15] was obtained from oneweek sample of the ﬁrst physics run.

3.3

Step 1The Step 1 experiment will be the ﬁrst one to be run at J-Parc. We will use
the KL beam line coming oﬀ the T 1 target on the A-line, along with the20Figure 8: KEK PS E391a detector.

E391a detector with necessary modiﬁcations. The purpose of this experiment is to• make the ﬁrst observation of the signal event,• search for new physics events with branching ratios higher than predictions from the Standard Model, and• gain experience at the J-Parc beam line environment, in preparation
for the next Step 2 experiment.
Running the Step 1 experiment at Time 0, before going to the ultimate
Step 2 experiment, is also practical from the point of view of laboratory
resources. We can produce physics results while the beam intensity is still
low initially, and the budget for the beamline and experiments is still limited. Also, because the same target is shared by multiple slow extraction
experiments, we can run simultaneously without interfering each other.

3.4

Step 2After Step 1, we plan to build an optimized KL beam line with higher yieldand energy, and build a larger detector with a longer decay volume andcapability for higher rates. The purpose of Step 2 is to collect more than21

100 signal events, as per the Standard Model, and measure the KL → π 0 ννbranching ratio to <10%. In this proposal, we will describe our plan on how
to proceed to Step 2.

22

4

Step 1

4.1

Goal of Step 1

The goal of Step 1 is the ﬁrst observation of KL → π 0 νν decay with asensitivity of 8.0 × 10−12 . With this sensitivity, we should be able to detect
3.5 events if its branching ratio is 2.8 × 10−11 as predicted by the Standard
Model with the currently known parameters.
As described in Chapter 2, the KL → π 0 νν decay is very sensitive to new
physics beyond the Standard Model. A number of observed events that issigniﬁcantly diﬀerent from the Standard Model prediction will be evidence
for new physics.

4.2

Beamline

Figure 9: Layout of the hadron hall and KL beamline.
Figure 9 shows the layout of the hadron hall and KL beam line for Step 1.
The common T1 target will be shared with other secondary beamline experiments, and with simultaneous running. Because there is a geometricallimitation in the layout of the experimental hall, the KL beam line is extracted at 16◦ from the primary proton beam line.
The KL beam is collimated to have a solid angle of 9 µsr. The KL ﬂux atthe exit of the beamline (20-m downstream of the target) is estimated to be
8.1 × 106 per spill assuming 2 × 1014 protons on the T1 target. Compared to
the 4◦ extraction angle at the KEK-PS K0 beam line (PS-K0), the KL yield
23

per solid angle per incident proton is reduced and its momentum distribution
is softer than at PS-K0. As shown in Fig. 10, the KL momentum has a peakat 1.3 GeV/c and the average momentum is 2.1 GeV/c, lower than 1.8 GeV/cand 2.6 GeV/c at the PS-K0 line.
However, the extraction at a larger angle is an advantage because highmomentum neutrons are signiﬁcantly suppressed as shown in Fig. 10. Because the higher momentum neutrons have a larger probability for contributing to background, the softer momentum distribution reduces the numberof neutron-induced background events.
Table 2 summarizes the parameters of the beam line.

Figure 10: Momentum distribution of KL (left) and neutron (right). The
solid line is for the KL beamline in Step 1, and the dashed line is for the
PS-K0.
The total length of the beam line is 20 meters which is long enoughto remove hyperon contamination and to install additional collimators forfurther suppression of halo neutrons.
The PS-K0 beam line has the greatest suppression of beam halo in theworld, about ﬁve orders of magnitude lower than the beam core. This suppression is obtained with ﬁve stages of thick tungsten collimators as shown in
Fig. 11. The amount of the beam halo is well reproduced by GEANT-basedMonte Carlo calculations. Most of beamline components will be reused.
Because the collimators are thick enough to prevent neutrons from passing
through, the upgrade of the beamline is focused on removing a source of
halo neutrons identiﬁed in the E391a experiment.
The main source of halo neutrons in the PS-K0 beam line is multiple
24

Table 2: Parameters of the KL beamline for Step 1
Item
Primary proton energy
Proton intensity
Spill length / Beam repetition
Production Target

J-Parc Step 1
30 GeV
2 × 1014
0.7 s / 3.3 s
Common T1 target

Extraction angle
Solid angle
KL yield/spill (beam exit)
Average momentum of KL
Decay probability in 3 < z(m) < 5
Core Neutrons/spill
En >0.1 GeV
En > 1 GeV

16◦
9 µsr
8.1 × 106
2.1 GeV/c
3.6%

KEK E391a
12 GeV
2.5 × 1012
2s/4s
Pt rod(L=60 mm, 8-mm φ)4◦12.6 µsr
3.3 × 105
2.6 GeV/c
2.7%

3.4 × 108
6.9 × 107

2.0 × 107
1.4 × 107

Figure 11: Schematic view of KEK-PS K0 beam line for E391a.

25

Figure 12: An example of a halo neutron event found in the Monte Carlosimulation for the PS-K0, which is caused by multiple scattering at thesurface of collimators.

Figure 13: Conceptual design of the beam line for Step 1.

26

scattering at the surface of the collimator as shown in Fig. 12. In orderto remove the halo neutrons, the collimators in Step 1, will be arranged asshown in Fig. 13. With this design, the neutrons scattered in the ﬁrst halfof the ﬁrst collimator will not hit the inner surface of the second collimator.
(The rate of neutrons scattered at the second half of the ﬁrst collimatorshould be low, because its inner surface is not visible from the target.) Our
goal is to reduce the ratio of halo to core neutrons by another factor of 5.
If this goal is achieved, the number of halo neutron increases by only factorof 3.4, while the number of KL ’s increases 24.5 times compared to those of
the PS-K0.

4.3

Detector

Figure 14 shows a schematic view of the detector setup after upgrading theexisting E391a detector. Here, we deﬁne our coordinate system. The z
axis is the center of the neutral beam line, +z pointing downstream. The
origin is set at the upstream surface of the ”Front Barrel”. The positive ydirection points vertically up, and the positive x direction is deﬁned in theright-handed coordinate system.
We will use the same concept as in E391a, which is summarized as follows:• Hermetic veto system completely enclosing the decay region;• Double decay chambers;• Highly evacuated decay region;• High detection eﬃciency for photons and charged particles.
The π 0 in the KL → π 0 νν decay is detected by measuring the positions
and energies of two photons with the CsI Calorimeter. Because most of
the other KL decays are multiparticle ﬁnal states (e.g., 2π 0 ), they will berejected by detecting additional photons and/or charged particles with ahermetic veto system. In order to reject KL ’s that decay upstream of the
ﬁducial region, we adopt a double decay-chamber scheme. The main decay
chamber is enclosed by Main Barrel (MB), and an upstream chamber consists of counters CC01, CC02, and a Front Barrel (FB). In order to detectphotons escaping through the beam hole, a series of collar counters (CC04,
CC05, and CC06) and the Beam Hole Veto (BHCV and BHPV) counters
are located downstream of the Calorimeter.

27

Another background is π 0 production from beam neutrons interactingwith residual gas in the decay region. In order to suppress this background,the decay volume is evacuated to 10−5 Pa, as was obtained in E391a byseparating the detector and the decay region with a thin ﬁlm.

Figure 14: Schematic view of detector setup.

4.3.1

Calorimeter

The electromagnetic calorimeter measures the positions and energies of photons to reconstruct π 0 in the KL0 → π 0 νν decay. In the E391a experiment,
the Calorimeter was made of 576 pure CsI crystals. Each crystal was 7.0×7.0
cm2 and 30-cm long (16 X0 ) [59].
For the experiment at J-PARC, we plan to replace these crystals with thepure CsI crystals used in the calorimeter of the Fermilab KTeV experiment.
The crystals, called “KTeV CsI crystals” hereafter, are smaller in the crosssection and longer in the beam direction (50 cm, 27 X0 ) than the crystals in
E391a, which ensures us much better performance in the new experiment.
Figure 15 shows the layout of the new Calorimeter, which then consists of2576 crystals. These crystals are of two sizes, 2.5 × 2.5 × 50 cm3 for thecentral region (2240 blocks), and 5.0 × 5.0 × 50 cm3 for the outer region (336
blocks) of the Calorimeter.
The reasons for replacing the calorimeter are as follows.
• Reduce the probability of missing photons due to fused clusters.
If two photons hit the Calorimeter close to each other, the generated
showers will overlap and be misidentiﬁed as a single photon. Figure 16
shows an event display for two photons that enter the CsI Calorimeterwith 6-cm separation. By using the KTeV CsI crystals, two photons

28

Figure 15: Layout of the Calorimeter for the J-PARC experiment with the
KTeV CsI crystals. The 2.5 × 2.5 × 50-cm3 crystals are used for the inner
region, and 5.0 × 5.0 × 50-cm3 crystals are used for the outer region.

as close as ∼5 cm can be identiﬁed as two clusters, compared to ∼15
cm in E391a. Each cluster is required to have a transverse energy
distribution consistent with an electromagnetic shower, which is easierto achieve with KTeV crystals.
• Eliminate the photon detection ineﬃciency due to punch-through.
In the case of the 30-cm-long (16 X0 ) crystals used in E391a, the probability that a photon passes through a crystal without interacting iscomparable to the ineﬃciency due to photonuclear interactions. However, with the 50-cm-long (27 X0 ) crystals, the probability is reduced
to a negligible level as shown in Fig. 17.
• Reduce background due to shower leakage.
When a photon hits a calorimeter, some part of the shower leaks fromthe back. The amount of the leakage depends on the depth where theﬁrst e+ e− pair in the shower is created. Because the decay vertex isreconstructed by assuming a π 0 mass, the energy leakage shifts the
decay vertex downstream. The π 0 ’s produced by halo neutrons in
CC02 are then reconstructed as if they were from the decays inside of
the ﬁducial region. As shown in Fig. 18 (Left), the longer KTeV CsI
29

crystals will have signiﬁcantly less leakage, and thus suppress such abackground.
In E391a, we performed a special run to calibrate Calorimeter withknown vertex position, in which a 5mm-thick aluminum plate wasinserted in the beam at 5.5 cm downstream of CC02, as a π 0 production target. As indicated in Fig. 18 (Right), we observed a long tailin the reconstructed vertex distribution, extending far downstream.
This can be explained by the energy leakage behind the Calorimeter.
By using longer crystals, we can reduce the tail, as indicated by thehatched histogram (expected by our simulation) in the ﬁgure. As wellas narrower width by better position resolution, this improvement of
the vertex reconstruction is quite eﬀective to reduce backgrounds due
to halo neutrons interacting with CC02, which is one of the major
backgrounds observed in E391a.

Figure 16: Event display for two photons in the calorimeter close to eachother for Step 1 (Left) and E391a (Right).

The Calorimeter has a square beam pipe at the center to let the neutralbeam pass through. The beampipe is made of an ultra-high modulus carbon
ﬁber/epoxy combination (4mm thick). It serves the purpose of supporting
the weight of the crystals (∼210 kg) with minimum dead space. The beam
pipe is surrounded by an upgraded veto counter (Collar counter, CC03) as
described in Sec. 4.3.4. Figure 19 shows one of the conﬁgurations aroundthe square beampipe. In this option, the two most inner rows and columns
30Figure 17: Photon detection ineﬃciency of the Calorimeter due to punchthrough. In the KTeV CsI crystals, the ineﬃciency is negligible comparedto that due to photonuclear interactions, while these ineﬃciencies are comparable in the E391a CsI crystals.

31

Figure 18: Monte Carlo study of the shower leakage. Left: the ratio between
the deposited energy in the CsI crystals and the true incident energy for thephotons in the energies between 0.1GeV and 1GeV. The dotted line is forE391a crystals (16 X0 ), and the solid line is for KTeV crystals in Step 1 (27X0 ). Right: reconstructed vertex distribution for π 0 events produced by analuminum plate located downstream of CC02 (true position = 280.5 cm inthe plot) only during calibration runs for E391a (open histogram) and for
Step 1 (hatched histogram).

32

surrounding the beampipe will have 112 blocks of 1.25 × 1.25 × 50 cm3
PbWO4 crystals. Another option is to use a spaghetti-type counter.

Figure 19: Layout of the CsI around the beam-hole region of the Calorimeter. In this conﬁguration, the inner-most 2.5-cm layer consists of 1.25 ×1.25 × 50.0-cm3 PbWO4 crystals, a total of 112 blocks. The square carbon
ﬁber pipe is 4 mm thick.
In the KTeV experiment, the scintillation light from each CsI block
was collected by 5-stage 3/4” R5364 Hamamatsu phototubes for the small
crystals, while 6-stage 1.5” R5330 tubes were used for the larger crystals.
The signal was read out by a device named “digital photomultiplier tube”(DPMT), in which the PMT anode was connected by a very short cable (afew cm) to a circuit that digitized the signal, buﬀered the digitized value,
and transmitted it on demand. It involved two ASICs and was operated
synchronously with the beam RF of Tevatron at 53 MHz. However, it isimportant to note that this technique provided the timing of only ∼5-ns
precision. The position and energy resolutions achieved were ∼1 mm and∼2%, respectively, for 1-GeV electromagnetic showers. Details of the calibration and performance of the calorimeter in the KTeV experiment are
documented in Ref. [58].
Due to the requirements on vacuum, cooling, and timing for the proposed33

experiment, we plan to reinstrument each CsI block, retaining only the crystals and the phototubes from the KTeV calorimter system. New bases, HVand signal cables, and front/back-end electronics will be redesigned. To
reduce the total number of HV cables, a special system to distribute HV
directly to the dynodes may be employed. A short length (∼1 meter) of
anode cable carries the signal from a phototube base to a pulse shaper andan asynchronous waveform digitizer located outside the vacuum vessel, as
described in Sec. 4.4. We expect the timing resolution of better than 1 ns
while retaining the position and energy resolutions by the new calorimeterwith KTeV crystals.
4.3.2

Barrel Photon Veto

The Barrel Photon Veto surrounds the decay volume to detect additional
photons from KL decays. In order to cover the large volume of the ﬁducial
region, this detector is made as a sampling calorimeter with alternating leadand plastic-scintillation plates. Two diﬀerent sets of detectors are used toform a double decay chamber, the Front Barrel and the Main Barrel.
We will transfer the Front and Main Barrels for the KEK PS E391a
experiment to J-Parc, and apply necessary modiﬁcations for Step 1 .
The Main Barrel for E391a is made of 32 modules. Each module consistsof 5-mm-thick scintillator plates and lead plates that are 1-mm thick for the
inner 15 layers and 2-mm thick for the outer 29 layers. The total thicknessof the module is 14 radiation lengths (X0 ), and the length is 5.5 meters.
In the most inner part of the Main Barrel, a pair of scintillators (Barrel
Charged Veto, or BCV) are located to identify charged particles. Figure 20
shows drawings of the Main Barrel module and of the full assembly.
Wavelength shifting (WLS) ﬁbers are used to read out the scintillation
light. We have developed a Green-extended high-QE PMT having a prismtype photo-cathode, which increases the photoelectron yield by a factor of
1.8 [60]. We attached PMTs to both ends of the module, separately for the
BCV, inner, and outer modules (6 channels for one module). A light yieldof 13.8 photoelectrons was obtained at the center of a module for a 1-MeV
energy deposit (Fig. 21). By using cosmic ray data, the timing resolution
was obtained as 0.6 ns for the inner module and 0.5 ns for the outer module,
respectively. Details of main barrel preformance is reported in [61]. In theE391a data, the response of the Main Barrel down to a 1-MeV deposit iswell reproduce by Monte Carlo simulation as shown in Fig. 22.
For Step 1, we will improve the Main Barrel in two ways:
34

Figure 20: Left: A module of the Main Barrel. Right: Cross section of theMain Barrel.

50
40

Np.e.(p.e./MeV)

30
20

10
9
8
7
6
5

Inner 15 layers
Outer 30 layers

0

100

200

300

Upstream PMT
Downstream PMT
Upstream PMT
Downstream PMT

400

500

600

Position (cm)Figure 21: The light yield of the Main Barrel as a function of distance fromthe PMT.

35

Figure 22: Top: The distribution of the energy deposit in the Main Barrel
for the data (dots) and Monte Carlo (M.C.) results to KL → π 0 π 0 decay(blue hatched) and KL → π 0 π 0 π 0 decay (red hatched). Bottom: Ratio ofthe data to M.C.
• Pipeline readout of the pulse shape with waveform digitizers.
• Addition of extra layers behind the Main Barrel.
Because the Main Barrel is a long detector, timing provides important information to prevent acceptance loss due to accidental hits and back-splash.
In E391a, we observed back-splash that arises from particles generated asa part of the Calorimeter shower that enter back into the Main Barrel, as
shown in Fig. 23. This back-splash, which is a main source of acceptance loss
due to vetoing from the Main Barrel, is well identiﬁed when we use timing
information. As shown in Fig. 24, the correlation between incident position
and time of the back-splash is opposite to that of real photons. However, thetiming information obtained from TDC is frequently destroyed in a high-rateenvironment due to pile-up of signal specially for a large detector like Main
Barrel. It is important to get timing information for small signals without signiﬁcant dead time caused by discrimination, which will be achieved
through a pipeline readout of the pulse shape with waveform digitizers.
To improve the eﬃciency for photon detection, more layers will need tobe added because the thickness of Main Barrel is only 14 X0 . By adding
additional layers behind the current Main Barrel, the photon detection inef36

Figure 23: Schematic view of a shower back-splash.

Figure 24: Distribution of incident time (horizontal axis) and the eﬀective incident position (vertical axis; downstream points up) for photons hitting theMain Barrel for the events in which 4 photons are detected in the Calorimeter in the E391 data. The black dots represent the photons from decays.
The red dots represent the back-splash, as the timing is later for upstream
hits.

37

ﬁciency due to punch-through will be greatly improved as shown in Fig. 25.
We will use the current vacuum chamber with a little modiﬁcation.

Figure 25: Comparison of the γ-detection ineﬃciency of the Main Barrel
between E391a and Step 1. In Step 1, we will add additional modules made of
5 layers of alternating 5-mm-thick lead and 5-mm-thick scintillation plates.
Black points are the ineﬃciency of the E391a Main Barrel, and red ones arefor Step 1.
As shown in Fig. 26, the Front Barrel and the collar counters CC01 andCC02 form an upstream decay chamber in order to suppress KL decays infront of the ﬁducial region. As shown in Fig. 27, the Front Barrel consistsof 16 trapezoidal-shaped modules that are made of 59 layers of alternating
lead and plastic-scintillator plates (16.5 X0 thickness and 2.75 meters long).
The light yield is obtained as 20 (10) photoelectrons per 1-MeV deposit at
the nearest (farthest) point from the PMT.
Table 3 summarizes the parameters of the Barrel Photon Vetos.
4.3.3

Charged Veto

Most KL decays include charged particles such as KL → π + π − π 0 (12%),KL → π ± µ∓ ν (27%), and KL → π ± e∓ ν (40%), and these decays can become
backgrounds both in the trigger stage and in the analysis stage. For example,
KL → π + π − π 0 contains a π 0 in the ﬁnal state and can fake the signalof interest if the two charged pions are missed. Thus, the decay region
must be surrounded by charged particle veto detectors, as well as photon
veto detectors. There are three categories of charged detectors: the main38

Figure 26: Schematic view of the role of the upstream decay chamber.

Figure 27: Left: A module of Front Barrel. Right: Cross section of the
Front Barrel.

39

Table 3: Parameters of Barrel Photon Vetos. The thicknesses of the leadand scintillator sheets are show in parentheses.
Front Barrel
Length (m)Outer diameter (m)Inner diameter (m)No. of modules
No. of channels
No. of Scin. layers
No. of lead layers

2.75
1.6
0.6
16
32
59 (5 mm)
58 (1.5 mm)

Thickness (X0 )Module mass (kg)

16.5
850

Main Barrel(E391a)
5.5
2.8
2.0
32
128
45 (5 mm)
15 (1 mm)
29 (2 mm)
14.0
1,500

Main Barrel(Step 1 )
5.5
3.0
2.0
32
192
51 (5 mm)
15 (1 mm)
29 (2 mm)
5 (5 mm)
18.5
1,940

Charged Veto (CV) which covers the Calorimeter, the Barrel Charged Veto
(BCV) which lines the Barrel Photon Veto, and the Beam Hole Charged
Veto (BHCV), which will be described in a later section.
The CV consists of two layers of hodoscopes, each of which is a 5-mmthick plastic scintillator array aligned in horizontal and vertical directions,as shown in Fig. 28. In the region that does not include the beam hole, there
are twelve 15-cm-wide scintillator slabs in a layer. Both ends of a slab are
bent and extended to the downstream region along the outer circumferenceof the Calorimeter and are read out by photomultipliers. The region in
the horizontal (vertical) line of the beam hole is covered by two 7.5-cm-wide
counters in each side. In order to be read from both ends, their inner ends areextended to the downstream region, lining the inside wall of the Calorimeter,while their outer structure is the same as others. This scheme of reading out
from both ends enables us to obtain good timing information, and thus to set
tight veto windows which are important in the high-rate environment of theexperiment. Furthermore, we can calculate the hit position in one scintillator
by using the time diﬀerence of both ends, which is useful for distinguishing
signals and back-splashes from the Calorimeter. The CV is located 50 cm
upstream of the Calorimeter surface in order to resolve two photons frome+ annihilation and/or π 0 s from π − charge exchange interactions in the CVmaterial, and thus to prevent KL → π ± e∓ ν from faking a real signal.
40

Figure 28: The schematic drawing of the Charged Veto in front of theCalorimeter (CV).

41

The BCV is a liner of the Barrel Photon Veto Counter, the same as usedin the E391a experiment. It consists of 32 plastic scintillators 20-cm wideby 550-cm long by 1-cm thick. There are 38 wavelength shifting ﬁbers ineach slab, embedded in a longitudinal direction, and they are collected onto
photomultiplier tubes with a prism photocathode at both ends.
From the E391a experiment we have learned the performances of charged
particle detectors, such as the achieved light yield and counting rate, and we
can use these parameters for estimating the performances in the J-PARC
experiment. The expected eﬃciency of the Charged Veto counter will be
described in Appendix A.3.
4.3.4

Collar Counters

We will arrange collar counters, which are sensitive to both charged particles
and photons, along the beam as in E391a. Their crucial roles are not only
to cover the gap near the beam region tightly, but also to prevent a truesignal from being rejected by beam-induced activities. Typical examples ofthe latter role are a reduction of the halo neutrons by CC01 and CC02,
a shield against products from KL0 decays along the beam near the CsI
calorimeter by CC03, and a shield against the back-splash from the BHPV
by the downstream collar counters. The ﬂexibility to take care of special
demands for each collar counter is a principal merit of the present plan toarrange several separate collar counters. Another merit is that they are
relatively small in size to fabricate and to modify later.
At present we have a basic plan for the collar counters as follows. We
will reuse the CC02 of E391a and add CC01. Both are Shashlik-type counters with the lead sheets in the direction perpendicular to the beam. We
are considering two options for CC03, PWO crystals or a spaghetti-type
counter that has tungsten and scintillator ﬁbers as shown in Fig. 29. The
lamination direction of CC04 must be perpendicular to the beam, because
it must mask the stacking gaps in CC03. For the downstream collar counters after CC04, we are planning to reuse the CsI blocks used for the E391a
calorimeter. A single and separate readout of the ﬁrst layer of scintillator ofthe downstream collar counters is necessary to make a tight veto for charged
particles, especially to reject the background from the decay KL0 → π + π − π 0 .
A smaller leakage from the rear end of the CsI calorimeter is a very important advantage compared to E391a, where we were perhaps overly cautious
about the leakage of true photon signals through relatively thin CsI crystals.
The single-counting rates, estimated by extrapolating the rate observedin E391a, are kept at a tolerable level for all of the collar counters except
42

Tuogsyeo wmre
Scmoymllaymog ﬁber

Figure 29: An option of CC03 which is made of alternating tungsten wires
and scintillating ﬁbers.
for CC07. The most downstream counter CC07 received very strong backsplash from the BA (name of BHPV at E391a). We will install the BHPV
inside the cave as shown in the setup.
4.3.5

Beam Hole Veto

The purpose of the Beam Hole Veto detector is to detect extra particles in
the KL decay which escape through the beam hole. It is placed in the neutralbeam at the end of our detector system. Because it is exposed to a high ﬂux
of neutrons, KL ’s, and beam photons, there would be a high probability ofgenerating fake hits, which inhibit a proper function of the detector. Thus,
the detector should be insensitive to those unwanted particles, while keeping
a high sensitivity to products from KL decays in the ﬁducial volume. The
detector consists of two components; one is for the detection of charged
particles, and the other is for photons.
Beam Hole Charged Veto counter (BHCV) The BHCV is set at 4 m
downstream of the CsI Calorimeter, where the neutral beam size is about
10 cm in diameter. The current design of the BHCV is based on the usualtechniques of charged particle detection. It is composed of 2 (horizontal) by
8 (vertical) slabs of plastic scintillators, each of which has a dimension of
10 cm (horizontal) by 2.5 cm (vertical) by 3 mm (thickness), and thus covers
the region of ±10 cm from the beam axis. Each scintillator is read out bya photomultiplier tube attached at one end. According to the experience inthe E391a experiment, its counting rate is estimated to be about 1 MHz per
counter for energy deposits of more than 300 keV. As discussed in Appendix
A.3, the expected eﬃciency of the BHCV is estimated to be 99.5%, where

43the source of ineﬃciency is dominated by masking eﬀects due to the highcounting rates.
Beam Hole Photon Veto (BHPV) The Beam Hole Photon Veto counteris at the downstream end of our detector system. It starts at 6.3 m downstream of the CsI calorimeter, corresponding to about 34 m from the target.
At this point, the diameter of the neutral beam is 11.6 cm and the BHPV
should cover this region. In order to suppress shower components going backto the Calorimeter, the BHPV will be placed in a shield.
The BHPV is designed on a new concept of photon detection. One feature utilizes Čerenkov radiation to detect electrons and positrons produced
by an electromagnetic shower. This feature enables us to be blind to heavy(and thus slow) particles, which are expected to be the main products inneutron interactions. The other feature is to use directional information.
Photons to be caught and vetoed come from the ﬁducial region 6 m or more
upstream through a narrow beam hole, and thus their electromagnetic showers are spread over in the forward direction. On the other hand, secondary
particles from neutron interactions tend to go isotropically. Therefore, neutron signals can be reduced further, without losing photon eﬃciency, by
requiring shower development along the beam direction.
Based on this concept, the BHPV is designed to be an array of PbAerogel counters. Figure 30 shows the schematic view of the BHPV module.
Each module is composed of 2-mm-thick lead as a photon converter, a stackof aerogel tiles as a Čerenkov radiator, a light-collection system of a mirror
and a Winston cone, and a 5-inch photomultiplier tube. In order to identify
a genuine signal when it is smeared by accidental hits, 500-MHz waveform
digitizers are used in the readout.
The aerogel array has a cross section of 30 cm by 30 cm, a thickness of 5
cm, and the refractive index of 1.03. These modules are lined up in 25 layers
along the beam direction, each of which is placed 35 cm apart as shown in
Fig. 31. The total length and thickness of the BHPV are 8.75 meters and
8.9 X0 , respectively. This conﬁguration enables us to select events thathave their shower development in the forward direction, and thus reduce
the sensitivity to neutrons. The parameters of the BHPV are summarizedin Table 4.
A full-size prototype of the BHPV module was constructed and tested
in the actual neutral beam during the third period of the E391a experiment(Run III). Even though the intensity was 25 times of lower than that expected in Step 1 at J-PARC, we were able to examine various performances,

44

30cm































mirrorBeam

Pb 2mmAerogel 5cm

Winston−type funnel

5 inch PMT
Figure 30: Schematic view of the BHPV module.

Beam
1



















/

-

'





)





+

!

#

%

01




















./

,-

&'





()





*+
!

"#

$%

0



















.

,

&





(





*

"

$

Figure 31: Schematic side view of the BHPV arrangement.

45

Table 4: The base parameters of the BHPV.
Items
size of module
Pb converter
aerogelParameters
30 cm (H) by 30 cm (V)2-mm thickrefractive index=1.03
30 cm (H) by 30 cm (V)10-mm-thick×5 tiles
ﬂat, 45◦ degree inclined
Winston cone(din =30 cm, dout =12 cm)
Hamamatsu R1250 (5-inch)
25
35 cm
875 cm
8.9 X0main mirror
light funnel
photomultiplier
number of modules
layer spacing
size in beam direction
radiation length

such as the light yield for photons and the gain stability, and found that
it worked according to expectations. In addition, the counting rate waswell reproduced, without unknown excess, by a E391a beam simulation and
BHPV detector simulation. This result enables us to conclude that we canunderstand the BHPV performance in the beam line and to be convinced of
the validity of our expectation in Step 1 at J-PARC, which is described indetail in Appendix A.4.
4.3.6

VacuumThere are two tight requirements for the vacuum in the proposed experiment: a high vacuum of 10−5 Pa along the beam axis, and a very thin (≤ 50
mg/cm2 ) layer of dead material in front of the detectors. The former is required for reducing interactions of the beam with the residual air. The latter
requirement is for reducing the detection ineﬃciency for decayed particles
that could be absorbed in the dead material. We will use the “diﬀerential
pumping method” developed in the E391a experiment, where we have two
diﬀerent vacuum levels across a thin layer.
We will be able to reuse much of the equipment from E391a, such as
the pumps, duct, etc.. The separator between the high- and low-vacuum
regions, a membrane, should be newly fabricated to match the changes of46

the detector setup and to improve its supporting system.

4.4

Frontend electronics, Trigger, and DAQ

In the proposed experiment, events will be accumulated not only for the
KL → π 0 νν decay, but also for other decays such as KL → π 0 π 0 and
KL → π 0 π 0 π 0 for calibration and monitoring. The rates from KL decays
are expected to be several MHz. Upgrades of the frontend electronics, trigger
and DAQ are major parts of the upgrades from the E391a.
4.4.1

Electronics

Waveform digitization will be necessary to distinguish pile-up signals fromlegitimate two-photon signals under the high-rate conditions we expect tohave. The precise timing information for each signal will help to identify
and separate the events, and to reduce losses arising from accidentals in thehigh counting rates of the detectors. Multihit TDCs will also be necessary
with these conditions.
VME-based frontend electronics are currently being considered for theentire DAQ system, instead of the FASTBUS, CAMAC and TKO systems
that have been widely used in the past, in order to avoid complications of
the system management between diﬀerent electronics standards, either forthe hardware or the software.
In order to reduce the dead-time during data acquisition, fully-pipelined
electronics modules are required.
Waveform Digitizer. The number of channel for the waveform digitizer
is dominated by the CsI calorimeter. Basically there are two known techniques. The ﬁrst is the “digital scope” method, i.e. each phototube signal
will be digitized by a ∼500-MHz FADC. The major concerns here will becost and the immediate processing power for the throughput. The second
method takes advantage of a sophisticated electronic ﬁlter. That is, thewell deﬁned pulse shape from the CsI light/phototube, when input to a 7pole Bessel low-pass LC ﬁlter, will produce a ﬁxed-width Gaussian shaped
output pulse. This technique has been used by the LHC ATLAS hadroncalorimeter Tilcal group, and considerable data have been published about
the performance. With a Gaussian shaped output, one could use a lowerspeed FADC for the sampling for both timing and charge information. For
the CsI calorimeter, ∼50 MHz will be adequate. A timing resolution of
better than 1 ns was achieved by the Tilcal group. For overlapping pulses,

47the ﬁlter technique seems to work as well as the conventional one. Studies on performance, cost, and system issues are needed before a choice canbe made. The digital backends for the FADC implementation include a
COPPER-II platform [62] where add-on modules can be added, or FPGA
(ﬁeld-programmable gate array)-based digital processors. We plan to build
prototypes and measure the performance with beam tests.
The cables to and from the waveform digitizers should be as short as
possible to avoid undesirable noise on the signal lines so that the signal
pulse shapes are not signiﬁcantly distorted. Because the detector is locatedinside the vacuum, vacuum feedthroughs for the signal cables are mandatory. The waveform digitizers must be located outside the vacuum, and thefeedthroughs might distort the pulse shapes. The eﬀect of feedthroughs on
the distortion of the signal shape for the waveform digitizers will also be
examined in the beam tests.
Multihit TDC. We will measure the timing of signals with multihit TDCs
with a timing resolution of ∼1 ns. Although this timing measurement isredundant with that provided by the waveform digitizers, it has some advantages. First, the timing resolution is better than the resolution obtained
from a waveform analysis using 500-MHz FADCs. Second, multihit TDCs
will also be able to record longer time periods such as tens of µs and with lessdata output than those waveform digitizers. Because accidental activities
will be one of the limitations of the experiment, particularly for high-rate
conditions, it is crucially important to have redundancy checks with diﬀerent
systems such as waveform digitizers and multihit TDCs.
A prototype of pipeline TDC modules [63], which was originally developed for the CDF experiment, is a possible candidate. It has 96 channels
per board, each channel of which has 10-hits of buﬀer depth per trigger, andhas ∼1.2 ns of timing resolution. The FPGA-based signal processor allow us
the further modiﬁcation of the signal processing scheme if we require better
performance.
Another possibility is the COPPER-II platform. It has recently beendeveloped at KEK as the next-generation DAQ system for near-future experiment at such as Super B-factory, J-PARC, LHC, etc.. It consists of a
VME 9U-size mother-board which mounts the add-on modules for analog-todigital(A/D) signal processor, trigger controller, CPU and network-interface
modules. Various kinds of signal processors such as FADCs and TDCs arebeing developed and tested. Among them, Time Memory Cell(TMC)-based
pipeline-TDC add-on module, which utilises the AMT3 chip developed for48

LHC ATLAS experiment, will be applicable for our experiment. It has 24channels per add-on module, and each channel has 0.8 ns of timing resolution with at maximum 256 depth of buﬀer. If we require even better
performance, custom-made add-on module could be developed with little
diﬃculty and costs, because only the A/D processing part, not the entire
function of the module, has to be developed as a small add-on module,
thanks to the “add-on” scheme of the COPPER-II platform.
4.4.2

Trigger and DAQ

A multi-stage triggering scheme has been adopted to reduce event rates
so that the events of interests can be selected with high eﬃciency. The
scheme will also reduce the amount of recorded data by discarding most of
the unnecessary background events, which would otherwise dominate thetriggered events in the early stages of processing.
Level-1 Trigger. The ﬁrst-level trigger is used to store the waveforms andthe timing of the signals from each detector to the pipelined FIFO buﬀers on
the FADC/TDC modules. The trigger signal is produced by hardware logic
modules. Data from the CsI Calorimeter crystals and other veto systems
are used to count roughly the number of photons in the CsI crystals alongwith additional activities in the veto systems. The goal for the rate after
the Level-1 trigger is a few hundreds kHz.
Level-2 Trigger. The Level-2 trigger signal is produced by FPGA modules. A clever cluster counting for the CsI crystals will be performed inorder to identify not only the two-photon signals that are candidates for the
events of interest, but also four-photon or six-photon events for calibrationand monitoring. The goal for the rate after the Level-2 trigger is a few tens
kHz.
Level-3 Trigger. Data in the Level-2 buﬀer will be sent to an online PC
farm. The computers will build the event by using all the data from thesubdetectors. A more thorough event reconstruction and ﬁltering will be
performed at this stage. The event processing will be done in parallel by
distributing the data to the CPUs of the PC farm via fast network switches.
All of the events after this ﬁlter will be recorded to long-term storage for
oﬄine analysis. The goal for the event rate after this ﬁltering is a few kHz.

49

Data Acquisition System. Figure 32 shows the basic schematics of thedata acquisition system. The data size is expected to be about 30 kB per
event, which requires a data recording speed of 30 MB/sec. The accumulated
data size on long-term storage media for one-year (i.e., 107 seconds) ofoperation will be about 0.3 PB.
Sub detetor

Waveform Digitizer
Multihit TDC

Level1 Trigger
Trigger Logic

Pipeline Buffer

Level2 Trigger
FPGA

Readout Controller

Level2 Buffer

Event Builder
Level3 Trigger

Storage

Figure 32: Schematics of data acquisition system

4.5

Rates

We estimated the rates at J-Parc by scaling the E391a data.
In E391a, we measured the accidental rates in the detector system witha 1-MeV visible-energy threshold. Table 5 summarizes the singles counting
rates per channel for various detector elements in E391a. The rates in theneutral beam was 165 kHz for KL ’s, and 10 MHz for neutrons (En > 0.1
GeV).
50

The Beam Hole Photon Veto has the highest rate, and the rate in CC07
is also high because of back-splash from the BHPV. This problem will besolved by using the new version of BHPV placed inside a shield.
Table 6 shows the multiplicity of accidental hits in a 100-ns time window
for the full E391a detector except for Beam Anti, CC06, and CC07. Summing the rates for diﬀerent multiplicities, we get the overall veto rate of 450
kHz.
In Step 1, with 2 × 1014 protons on target per pulse, we expect 11.6 MHz
of KL ’s and 486 MHz of neutrons (En > 0.1 GeV), i.e., a 49 times higher
beam ﬂux. We estimate the accidental rate to be 450 kHz × 49 = 22 MHzfrom the beam, and an additional 4 MHz from KL decays in the 21-m region
between the front of the detector and the end of BHPV. Thus the overall
accidental rate is estimated to be 26 MHz.
Table 5: Summary of counting rates for detector components in E391a witha 1-MeV detection threshold. For the BCV, BHCV, and CV, we applied a
100-keV threshold.
Detector
Main Barrel
Front Barrel
Charged Veto (CV)
Inner CV
Barrel CV
Beam hole CV
CC02
CC03
CC04
CC05
CC06
CC07
Beam Hole Photon Veto

4.6
4.6.1

Counting Rates (kHz)
7.5
10
3.5
11
15
45
8
11
24
28
50
125
600

Sensitivity
Detector acceptanceIn order to identify events for the KL → π 0 νν decay, the following kinematic
selection cuts are required. Detailed descriptions of the applications of these51

Table 6: Multiplicities of accident hits for all detector components except
for Beam Anti, CC06, and CC07, with 100-ns time windows.
Multiplicity
1
2
3
4
5
>5

Counting Rates (kHz)
312
67
25
14
8
30

cuts for suppressing backgrounds are given in Sec. 4.7.
• Eγ cut:
There are two photons in the Calorimeter with the energy greater than
0.1GeV each. This requirement rejects most of accidental hits. Besides
these two photons, there are no clusters with energies above 1MeV.
• Photon veto counters have no energy deposit above 1 MeV. Charged
veto counters, BCV, BHCV and CV, have no energy deposit larger
than 100 keV.
• Calorimeter ﬁducial cut:
The incident position of photons on the Calorimeter should be between
17.5 cm and 85 cm from the center of the beam. This is to ensure thatthe shower is well contained in the Calorimeter, and the energies andpositions of the photons are properly reconstructed.
• Vertex cut:
The reconstructed vertex position, assuming a π 0 mass is between 300
cm and 500 cm in the detector coordinate system.
• PT cut:
The reconstructed π 0 has transverse momentum between 0.12 GeV/c
and 0.25 GeV/c. The vertex cut and PT cut optimize the backgroundrejection and signal acceptance.
• Collinearity angle cut:
The collinearity angle is deﬁned as the projected angle of two photons

52

in the Calorimeter plane (x − y plane). The collinearity angle isrequired to be less than 150◦ to reject KL → γγ background events.
• E-θ cut:
The relationship between the incident angle of each photon calculated
from the reconstructed vertex and the energy of a photon should satisfy
π 0 kinematics. This cut is to reduce the odd-pairing KL → π 0 π 0background, as shown in Fig. 36.
• E-ratio cut:
The ratio between the lower and the higher energy of the two photons isgreater than 0.2. This cut further rejects the odd-pairing backgroundfor KL → π 0 π 0 decays, as will be described in Sec. 4.7.1.
• E-total cut:
The sum of the energies of the two photon is greater than 0.5 GeV.
This cut rejects π 0 ’s produced downstream of the Calorimeter, withphotons traveling back upstream.
Figure 33 shows the distribution of PT vs. the reconstructed z position
for the KL → π 0 νν signal events. For the KL ’s that exit the beam line at 20m from the production target, 3.6% of them decay within the ﬁducial region(300 cm < z < 500 cm in our coordinate system). The signal acceptancefor the KL → π 0 νν decays in the ﬁducial region, after all the above cuts, is
9.4%.
4.6.2

Acceptance Loss

In addition to the selection cuts explained above, we have to take into account the acceptance loss caused by tight vetoing. We simply estimate theeﬀects by scaling the E391a values, although they surely depend on various
experimental conditions.
• Accidental activities: 27%.
Accidental activities in the detector originate from the high intensityof the beam and back-splash from the Calorimeter.
With a total accidental rate of 26 MHz, as estimated in Sec. 4.5, anda 10-ns resolving time for vetos, we expect a 26% loss in acceptance.
As described in Appendix A.4, the acceptance loss due to the BHPV
is expected to be 2%.

53

Figure 33: Distribution of PT vs. the reconstructed z position for the KL →π 0 νν signal events. The box shows the signal region.
• Cluster shape cut: 20%.
In order to identify photon clusters from hadronic showers, and to
identify fused clusters, we require the transverse energy distribution
within a cluster to be consistent with an electromagnetic shower. A
tight shape cut will reject photons and introduce an acceptance loss.
The loss should be less for the KTeV CsI crystals, and we assume 20%
for it.
• Collateral clusters: 10%.
Sometimes, a photon cluster in the Calorimeter is associated with
an isolated low-energy cluster nearby (“collateral cluster”). As we
carefully studied the E391a data [64], we concluded that these collateral clusters are made by low-energy neutrons and photons within
the shower. Such a collateral cluster will veto the signal event itself.
However, the acceptance loss due to this eﬀect can be reduced by relaxing the veto thresholds in the close vicinity of energetic clusters.
We assume that the loss is 10%.
As a result, we expect/assume a 50% acceptance loss in total.

54

4.6.3Single event sensitivity

In Step 1, assuming 2 × 1014 protons every 3.3 seconds and three Snowmass
years (3 × 107 s) of data taking, we expect a total of 7.3 × 1013 KL ’s at theexit of the beam line. With a decay probability of 3.6% in the ﬁducial region(300 cm < z < 500 cm) and 9.4% acceptance, the single event sensitivity is:
S.E.S. = 1/(NK × decay probability × acceptance) = 4.0 × 10−12With a Standard Model prediction of B(KL → π 0 νν) = 2.8 × 10−11 , we
expect to observe 7.0 events in Step 1. If the acceptance loss is 50% as
we estimated, the S.E.S. is 8.0 × 10−12 and 3.5 Standard Model events are
expected.

4.7

Backgrounds

There are several background sources for the KL → π 0 νν decay, as follows.
• Other kaon decays with particles escaping detection.
All other KL decays except for the KL → γγ decay have four or more
photons, or two or more charged particles in the ﬁnal state. If two or
more of these particles are not detected, and the remaining particles
are identiﬁed as two photons, then the decay will become a source of
background. For example, KL → π 0 π 0 , KL → π + π − π 0 , KL → π ± e∓ ν,
etc. fall into this category. Therefore, it is crucial to have photon vetoand charge veto counters with extremely low ineﬃciencies. In this
proposal, we used the photon veto and charged veto ineﬃciencies as
described in Appendices A.2, A.3, and A.4.
• KL → γγ.
The KL → γγ decay has the same observable ﬁnal-state particles withthe signal decay. However, this decay will be rejected by requiringhigh transverse momentum (PT ) of the π 0 .
• π 0 ’s produced by neutron interaction.
Single π 0 ’s can be produced by a neutron interaction, nA → π 0 A′ .
Such examples include neutrons in the beam interacting with residual
gas in the decay region, and neutrons outside the beam (halo neutrons)interacting with detector materials. Therefore, the decay volume has
to be highly evacuated, and detector materials should be placed far
from the ﬁducial region.

55• Λ → nπ 0 .
Λ’s in the beam can decay into nπ 0 . This background can be reducedby placing the detector far from the production target to let Λ’s decay
away, and by requiring the PT of π 0 to be larger than the maximum
PT for the Λ decay.
Table 7 summarizes the estimated background levels. The estimatedlevels for these backgrounds will be described in the following subsections.
Table 7: The estimated number of background events for Step 1. The single
event sensitivity is 4.0 × 10−12 , with which 7.0 standard model events are
expected. With a 50% of acceptance loss, both the number of expectedsignal events and background events would be scaled accordingly.
Background source
Other KL decays
KL → π 0 π 0
KL → π + π − π 0
KL → π − e+ νKL → γγKL → π 0 π 0 π 0
Neutron Interaction
With Residual gas
At the CC02
At the C.V.
Accidental Coincidence

4.7.1#Background events
3.65
0.93
0.01
negligible
negligible
0.07
0.26
negligible
0.20

KL → π 0 π 0 background

The KL → π 0 π 0 (Kπ2 ) decay mode is considered to be the main source of
background because of its relatively large branching ratio (8.83 × 10−4 ) [65]and its 4-photon ﬁnal state. There are two kinds of Kπ2 backgrounds: evenpairing and odd pairing according to the missed two photons, which havediﬀerent characteristics in the event reconstruction.
The even-pairing events are those in which two photons generated froma single π 0 decay enter the Calorimeter, and the other two photons fromanother π 0 enter the veto system. The π 0 ’s are correctly reconstructed andhave similar vertex (Zvert ) and transverse momenta distributions (PT ) to56

those of the signal. As shown in Fig. 34, at least one photon has relatively
high energy (> 50 MeV) and enters veto counters that provide a high eﬃciency of vetoing.

Figure 34: Left: reconstructed vertex and PT distribution for even pairing
KL → π 0 π 0 background. It has a distribution similar to that of the KL →π 0 νν decay. Right: Energy distribution of gammas that enter the vetocounters. At least one photon has suﬃciently high energy to trigger thecounter with a high detection eﬃciency.
On the other hand, the odd-pairing events have two photons from different π 0 decays in the Calorimeter. As a result, the events have smaller
probabilities of entering the signal-gating box because the reconstructed vertex is incorrect (moved upstream) and the PT distribution tends to be low,
as shown in Fig. 35. Even though many events have two low energy photons entering the veto counters, the events are rejected through the high-PT
selection. As a result, the photons that need to be rejected by the vetocounters have distributions similar to those for even pairing. However, there
is an additional kinematical constraint related to the wrong reconstructedvertex, as shown in Fig. 36. The incident angle of photons deduced fromthe reconstructed vertex is incorrect and is located in an unphysical region
for a given incident energy (E-θ cut). Also, the high-PT selection requires alarge imbalance between the energies of the two photons as shown in Fig. 36(E-ratio cut). These constraints provide further suppression for odd-pairing
events.
The Kπ2 background level is estimated by using 7.3 × 107 KL → π 0 π 0 ’s
decaying between z = 0 m and 6.15 m in the Monte Carlo simulations. For
each event, we assigned an event weight as a product of detection ineﬃcien57

Figure 35: Left: reconstructed vertex and PT distribution for odd-pairing
KL → π 0 π 0 background. The reconstructed vertex is not correct which makethe PT lower than the signal box. Right: Energy distribution of photons
that enter the veto counters. Even though many events have low energies forboth of the photons, the events are rejected through the high-PT selection.
As a result, the photons needed to be rejected by the veto counters have
distributions similar to those for even pairing.
cies for all the photons that entered veto counters. The ineﬃciencies area function of energy and incident angle of the photon, as described in Appendix A.2. The background level is obtained from the sum of the weights
for the events passing all the signal selection cuts.
In the case that three photons enter the Calorimeter, we treated themas one even-pairing and two odd-pairing events according to the assumed
missing photon at the Calorimeter. With separate analyses as explained
above for each case, the event weights are summed up as a backgroundlevel.
Another background source is fused events. Among the three photons
in the Calorimeter, two photons are mis-identiﬁed as one cluster when they
enter very close together. These ’fused’ clusters can be identiﬁed by requiringthat the transverse energy distribution within each cluster is consistent witha typical electromagnetic shower. The probability of failing to identify thefusion was studied by the KAMI experimental group, as shown in Fig. 37[66].
We used the fusion probability curve, together with the detection ineﬃciencyof the photon entering the veto counters, to estimate the background.
Table 8 summarizes the sequential acceptance factors for signal eventsand the KL → π 0 π 0 background, normalized to the number of KL ’s entering
58

Figure 36: Top-left: Relation between incident energy and reconstructed
angle for even-pairing KL → π 0 π 0 background events in the event-gatingbox. Because the incident angle is correctly reconstructed, the events arelocated in the allowed region, which is same as that of the signal. Top-right:
Relation between incident energy and reconstructed angle for odd-pairing
background. The relation is broken due to wrong vertex reconstruction andmany events are shifted to an unphysical region. Bottom-left: Energy Ratio
between two photons in even pairing, which has the same distribution as
signal events. Bottom-right: Ratio between two photons in odd pairing. A
large diﬀerence between the energies of two photons is needed to satisfy thecondition of high PT .

59the detector setup. Based on 1.8 × 1021 protons on the T1 target in Step 1
with 3 × 107 seconds data taking, 3.65 Kπ2 background events are expected,
compared to 7.0 Standard Model signal events. If the 50% acceptance loss on
the signal is imposed, the number of background events will be also reduced
to 1.8.

Figure 37: Monte Carlo study of the fusion probability as a function of the
distance between two incident photons for the KTeV CsI crystals. [66]4.7.2

KL → γγ background

The KL → γγ decay is easily rejected by kinematic constraints. First,
as shown in Fig. 38(right), the reconstructed PT of two photons is small.
Second, as shown in Fig. 38(left), the collinearity angle between the two
photons in the Calorimeter plane (Fig. 39) is peaked at 180◦ . This would
be true even if the energy of a photon is mismeasured due to photonuclear
interaction within the Calorimeter. Third, the reconstructed vertex with theassumption of a π 0 mass is shifted upstream. As a result, the backgroundfrom the KL → γγ decay is negligible.
4.7.3

KL → π 0 π 0 π 0 background

Even though the KL → π 0 π 0 π 0 decay has a large branching fraction of
21%, it is not a serious background source because there are four additional
photons. In order to suppress the KL → π 0 π 0 π 0 decay down to 0.1 eventsin Step 1, we need a rejection factor of 6.4 × 10−14 , which is not diﬃcult

60

Table 8: Summary of sequential acceptance factors for signal events and the
KL → π 0 π 0 background normalized to the incident KL ’s into the detector
setup (including decay probabilities). The decay probability and acceptances
are shown for the kaon decays in 3 m< z <5 m for KL → π 0 νν, and
0 m< z <6.15 m for KL → π 0 π 0 decays. For fusion events, the fusion
probability is included in the photon veto cut. The number of events isdeduced based on 1.8 × 1021 protons on the T1 target.
KL → π 0 ννEVEN
Decay Probability
Eγ > 0.1 GeVCalorimeter ﬁducial
VertexPT
Collinearity angle
Eγ1+Eγ2 >0.5GeV
E-θ, E-ratio
Photon Veto
Branching Ratio
Number of events−2

3.6 × 101.53 × 10−2
1.05 × 10−2
6.98 × 10−3
5.12 × 10−3
4.89 × 10−3
4.71 × 10−3
3.41 × 10−3
3.41 × 10−3
9.56 × 10−14
7.0

2.05 × 10−2
1.48 × 10−2
9.60 × 10−3
7.73 × 10−3
7.43 × 10−3
7.25 × 10−3
5.28 × 10−3
5.09 × 10−11
4.49 × 10−14
3.28

KL → π 0 π 0ODD11.4 × 10−2
3.46 × 10−2
2.56 × 10−2
1.23 × 10−2
2.41 × 10−3
2.25 × 10−3
2.16 × 10−3
8.48 × 10−4
1.95 × 10−12
1.72 × 10−15
0.12

Fusion4.65 × 10−5
3.01 × 10−5
1.48 × 10−55.95 × 10−6
5.77 × 10−6
5.55 × 10−6
4.42 × 10−6
3.95 × 10−12
3.49 × 10−15
0.25

Figure 38: Monte Carlo study for the KL → γγ decays. Left: Distributionof collinearity angle vs. PT . Right: PT distribution. The total number ofgenerated events is equvalent to 9.7 × 1010 of the KL ’s entering the detector
setup, which is 0.05% of the total number of KL ’s in Step 1.
61

γaoggelbSresy Slcgb

γ

TbSm

Figure 39: The collinearity angle is the opening angle between the momentaof two photons projected on the Calorimeter plane (x-y plane).
to achieve with the four photons. There is a also a further rejection by
imposing the high-PT selection.
4.7.4

KL → π + π − π 0 Background

One of the major decay modes of the KL is KL → π + π − π 0 . Because it
contains one π 0 , it could fake the signal of interest if two charged pions
escape detection. There are two methods for reducing this background.
One is the kinematic limit of KL → π + π − π 0 . The transverse momentumof the π 0 (PT ) is relatively low, limited to 0.133 GeV/c, and thus the PT
cut, described in the Sensitivity section, can greatly reduce this background.
Second, the charged particle veto counters surrounding the decay region can
detect additional charged pions and reject faked events.
Figure 40 shows the distribution of PT versus the reconstructed Z position before and after the charged veto cut. We use here the ineﬃciency
functions for charged particles which are discussed in Appendix A.3 (seeFig. 57), and weigh the remaining events by the ineﬃciencies of the two
pions. As can be seen in Fig. 40, only a small fraction of KL → π + π − π 0
comes in the high PT region even though the PT ’s are mis-measured dueto the Calorimeter resolution and ﬁnite beam size. After applying all the
cut and veto weights, the estimated number of background events for the
3π mode in the signal box is found to be small, namely 0.93 after requiring
PT > 0.12GeV /c.

62

Figure 40: Distributions of PT vs. the reconstructed Z position for the KL →π + π − π 0 background. The left and right plots indicate the distribution before
and after charged veto cuts, respectively. The boxes indicate the selection
region for the KL → π 0 νν decay mode.
4.7.5

KL → π − e+ ν Background

The KL → π − e+ ν background is caused by detection ineﬃciencies of the π −and e+ particles. The momentum distributions of the π − and e+ generated
from the decay are given in Fig. 41. We generated π − and e+ following
the distributions for particles that enter a 1-cm-thick plastic scintillator andobtained a detection ineﬃciency as 1.4 × 10−4 for π − , and 7.5 × 10−5 for e+with a 100-keV detection threshold.
Because the ineﬃciency is due to charge-exchange interactions, the events
not rejected by the Charged Veto involve multi-photon ﬁnal states whichfake 2-photon events. Thus, the most probable background source is thatthe π − is missed due to a π − p → π 0 n interaction and e+ is missed due toannihilation into two photons. In order to identify these interactions, wewill place the Charged Veto 50 cm away from the Calorimeter. After thisdistance, the two photons from the π 0 and annihilation will open up large
enough to be identiﬁed as two clusters, as shown in Fig. 42.
Monte Carlo calculations for the Charged Veto ineﬃcient events estimate
the acceptance as 7.6 × 10−6 after passing the event selection and photon
vetoing. As a result, we expect 0.01 events as a background in Step 1.
The case in which an e+ enters the beam hole and a π − enters the
Calorimeter would be another source of background because the Beam Hole
Charged Veto has a slightly worse detection eﬃciency. However, the accep63

Figure 41: Incident momentum distribution of π − (Left) and e+ (Right).

Figure 42: Separation of two photons according to incident momentum byplacing the Charged Veto 50 cm away from the Calorimeter as illustrated
in the case of π − (left) and e+ (right).

64

tance of the events is estimated as negligibly small.
4.7.6

Neutron Background

The production of π 0 ’s by neutron interactions through nA → π 0 A′ is an
important source of background. Since the cross section of π 0 production
is very small for low energy neutrons less then 1 GeV, we take into accountthe ﬂux of neutrons with energies above 1GeV. As shown in Table 2, theneutron ﬂux per spill increases by a factor of 4.9 at the Step 1 compared toE391a, while the KL ﬂux increases by a factor 25. This corresponds to a
5-fold reduction of the neutron to K ratio (n/K).
In order to reject π 0 production by neutrons that interact with residual
gas, the decay region is evacuated to 10−5 Pa, which was achieved in theE391a experiment. In E391a, we used three diﬀerent simulation packages toestimate this background level. Even with the largest number of expectedbackground events among the three calculations, we get 0.06 events for the
standard model sensitivity (3 × 10−11 at the E391a study). With the improvment of the n/K ratio of 0.2, we estimate 0.07 events as a backgrounddue to beam neutron interaction in Step 1 .
Another background source is an interaction of halo neutrons with detector materials, especially at the CC02 (CC02 event) and the Charged Veto
(CV event) because these detectors are located close to the ﬁducial region.
In E391a, we observed a clear enhancement of π 0 events at the position ofthese detectors. Because the events are isolated in the reconstructed vertex,
we can reject the events with the condition that the ﬁducial region should
be far from these interaction points.
The momentum spectrum of halo neutrons shown in Fig.43 was obtainedby calculating the ratio of halo neutrons to beam neutrons in the E391a
experiment as a function of the neutron momentum[67], and multiplying
the ratio to the beam momentum spectrum for the Step 1.
As shown in Fig. 44, the CV events are negligibly small in Step 1 withthe ﬁducial region 50-cm distant from the position of CV.
On the other hand, the CC02 events have a long tail in the reconstructedvertex distribution, which extends into the ﬁducial region due to shower
leakage explained in Sec. 4.3.1. As shown in Fig. 18, we can get rejection of
3.7 × 10−5 against the events after considering the shower leakage. There isanother reduction factor for the CC02 events at the Step 1. The calorimeter
acceptance for two photons of the CC02 events increases according to theincident momentum of halo neutrons (Fig. 45). Since the neutron spectrumin Step 1 is softer than E391a, the acceptance at Step 1 is 13% of the65Figure 43: Momentum spectrum of halo neutrons at Step 1 (solid line)
which is scaled by E391a M.C. result (dashed line) according to the ratioof momentum spectra of beam neutrons between Step 1 and E391 those aregive in Fig. 10.

66

acceptance at E391a.
The number of the CC02 events in E391a is 83 for 9.6 × 1011 neutrons
entering detector. With 1.8 × 1021 protons in total for Step 1, we expect
6.2 × 1014 neutrons and 5.4 × 104 CC02 events. As a results, we estimate
0.26 events as CC02 background.

Figure 44: Reconstructed vertex for the π 0 events produced at the Charged
Veto. In E391a, the background level is estimated to be ∼ 9 × 10−10 for theexperiment with a single event sensitivity of 9 × 10−8 . The π 0 backgroundfrom Charged Veto is still negligible in Step 1 with 10−12 sensitivity.

4.7.7

Accidental halo neutron backgroundIf two halo neutrons hit the Calorimeter accidentally at the same time andproduce showers that mimics electromagnetic showers, they can be a sourceof background. In the E391a Monte Carlo study, we estimated a 12.5-Hz
rate of accidental hits for energy deposits greater than 100 MeV at the CsI
together with 1-MeV veto thresholds for other detectors (events mainly fromhalo neutrons). With a random combination of two generated halo neutron
events, we estimated the probability for the event to pass all of the selection
cuts, which is found to be 5.9 × 10−2 . The acceptance change according to
the neutron momentum is estimated as 0.88.
67Figure 45: Acceptance of CC02 events as a function of neutron momentum.
For the E391a data, we have developed a neural net analysis to separate
the CsI responses to neutrons and true photons based on shower shapes.
It removes about 72% of neutron events with a 15% loss of photon events.
With the ﬁner segmented CsI crystals in Step 1 , the performance will be
improved.
With 4.9 times larger number of neutrons during the 0.7 s beam spill in
Step 1, the singles hit rate due to halo neutrons of 12.5×4.9×(1/0.7) = 87.5
Hz, which is reduced to 24.5 Hz by using the shower shape analysis. The
number of background events is given by
NB.G. = Rate2 × 2 · ∆τ × T × Acceptance= 24.52 × 10−9 × ((0.7/3.3) × 3.0 × 107 ) × (5.19 × 10−2 )= 0.20where ∆τ is a coincidence resolving time and T is the eﬀective running timefor 3 × 107 s of data taking. As a result, we expect 0.23 event in Step 1 dueto accidental coincidences.

68

5

Step 2In this section we brieﬂy describe the KL0 experiment deﬁned as Step 2 inSec. 3, to be done subsequently to the Step 1 experiment. The goal of Step
2 is to do a precise measurement of the branching ratio for KL0 → π 0 ν ν̄
so as to fully determine the direct CP violation in the s → d transition.
We assume here that such a measurement has a single event sensitivity of
3 × 10−13 , which is equivalent to about 100 signal events in the Standard
Model. We plan to proceed to Step 2 once we understand the beam-related
issues at J-PARC and establish the experimental techniques to achieve ourphysics goal.

5.1

New beamline

With the area in the current design of the Hadron Experimental Hall forthe neutral beamline and detector, the KL yield is not large enough toachieve our physics goal. Thus we will propose, in Step 2, to have a newprimary proton beam (B-line), target, and beam dump in the hall (Fig. 46)
and construct a new and optimized KL0 beam line. The detector will belocated 50 m from the target, and KL0 ’s will be transported through a narrow“pencil” beam as in the E391a and Step 1 experiments.
The basic parameters of the beamline, whose study is now in progress,
are summarized in Table 9. The proton energy is 30 GeV. A distinct advantage of 50-GeV protons over 30 GeV is not yet observed in our studies ofdetector simulation. We might request, for the accelerator, a longer beam
spill and higher duty cycle instead. A new nickel production target (oneinteraction length) and a lead absorber (7-cm thick) will be used to produce a higher KL0 ﬂux with lower photon contamination, respectively. With
30-GeV protons and an extraction angle of 5◦ , the n/KL0 ratio is 30 at theentrance of the detector. The average KL0 momenta are higher than thosein E391a and Step 1, which is an advantage for removing the KL0 → π 0 π 0background with its extra photons. A 50-m-long beamline is necessary to
suppress the background from Λ’s. With several stages of collimators in thelong beamline, the ﬂux of beam-halo neutrons to the detector can also be
suppressed.
In order to design the new target and beam dump5 in the hall, we need
advice from experts on technical issues, in particular on radiation safety.
5

The beam dump should be located as close as reasonably possible to the target inorder to absorb pions before they decay into muons.

69

Figure 46: Plan view of the Hadron Hall layout with the B-line, target(circle in red) and beam dump (rectangles in brown and pink). If the hall
is not extended further, the area for the detector (rectangle in blue) will belocated outside the hall.

Table 9: Parameters of the new KL0 beamline for Step 2.
item
Primary proton energy
Proton intensity
Spill length / Beam repetition
Production Target
Extraction angle
Solid angle
0
KL Yield/spill (beam exit)
Average momentum of KL0
Decay probability in 2 < z(m) < 13Core neutrons/spill70

J-PARC Step 2
30 GeV
3 × 1014
0.7 s / 3.3 s
new Ni Target (1 λI )Pb absorber (7 cm)
5◦
2 µsr
4.4 × 107
5.2 GeV/c6%
1.3 × 109

5.2

Detector

The concept of the new KL0 detector (Fig. 47) is basically the same as those inE391a and in Step 1. A crystal-based Endcap Calorimeter, with a diameterof 3 meters, detects two photons from the π 0 in the KL0 → π 0 ν ν̄ decay.
Other photon detectors are located at the front, barrel, collar, and beamhole regions in order to obtain hermetic photon detection6 and suppress the
background from KL0 → π 0 π 0 .

Figure 47: Conceptual view of the new KL0 detector for Step 2.
The size of the detector (3 meters radius) and the length of the decay
volume (15 meters total) are much larger than those for Step 1, which are
based on the existing E391a detector, in order to achieve better sensitivity(the number of KL0 decays and π 0 acceptance) as well as tighter backgroundrejection. The KL0 decays along the beam axis between 2–13 meters fromthe entrance of the detector, in vacuum, are used for the measurements.
This region is 2m away from the upstream Collar Counter and the Charged
6
A note: We pursued the idea of using the Barrel Calorimeter, covering the long decay
volume, for measurements of the π 0 ’s from KL0 → π 0 ν ν̄. We concluded that, because
shower leakage from the Barrel Calorimeter hits the Endcap Calorimeter and vetos thesignal event itself, the sensitivity of the experiment is not improved.

71

Veto counters at the downstream, to avoid π 0 backgrounds produced byhalo neutrons in those counters. The large volume of the CsI crystals in the
Step 1 Endcap Calorimeter will be reused, unless we observe some limitations and conclude that we need smaller and/or faster crystals. The Barrel
Calorimeter, which is totally 15 m long, should be segmented in the beam
direction in order to take care of the back-splash from the showers in the
Endcap as well as to have a better rate capability. The Collar and Beam
Hole counters, which are located close to or in the beamline, will be designed
carefully based on their performance at Step 1. The beam hole is set to be as
narrow as possible to minimize the number of photons and charged-particles(in particular the π + and π − from the KL0 → π 0 π + π − decay) that escape
downstream.

5.3

Sensitivity and Background

The latest but not yet ﬁnalized results of our simulation studies of the beamline and detector for Step 2 are reported here. We assume the neutral
beamline parameters listed in Table 9 and the running condition of 3 × 1014
protons per spill for three Snowmass years (3 × 107 s), which corresponds
to 2.73 × 1021 protons on the target and 4 × 1014 KL0 ’s at the entrance tothe detector. In order to detect the photons and charged-particles escaping
downstream, the Beam Hole Charged Veto and Photon Veto counters, withdiameters of 15 cm, are located in the beamline at 10 meters downstreamof the Endcap Calorimeter. The same oﬄine selection criteria and photon
and charged veto cuts as used in the Step 1 studies are imposed.
Some results from the simulation studies are shown in Fig. 48. The larger
box in the plots indicates the signal region we assume for Step 2:
200 < Z < 1300 cm

and0.12 < PT < 0.25 (GeV/c).

We expect to observe 133.2 ± 0.4 KL0 → π 0 ν ν̄ events in the SM with a S/Nratio of 4.8, and with background levels of 19.4 ± 0.7 from KL0 → π 0 π 0 and
8.13 ± 0.11 from KL0 → π 0 π + π − . The background from hyperon decays(Λ → nπ 0 , ..) is negligible. By understanding the characteristics of the
distribution of each background source in the PT vs. Z plane and by using
likelihood techniques, we would be able to measure the branching ratio witheven higher signiﬁcance.
An optimization for Step 2, however, will not be completed until we fully
understand the expected single rates and the energy spectrum of accidental
hits in the detector, which seriously depend on the quality of the slowextracted proton beam, the radiation environment of the experimental area,72

Figure 48: Distributions of PT vs. the reconstructed Z position for KL0 →π 0 νν signal events (top), KL0 → π 0 π 0 (middle) and KL0 → π 0 π + π − (bottom)
background events before (left) and after (right) imposing the photon vetocuts, respectively.
73

and halo neutrons in the collimation of the pencil beamline. What we canlearn from the Step 1 experiment in the early stage of J-PARC is therefore
very crucial for the success of the Step2 experiment.

5.4

Detector R&D

For the Step 2 detector, we are also thinking about introducing new techniques such as photon direction measurements, straw chambers in front of
the Endcap, new photo-sensors, etc. in order to improve the performance ofthe detector and the S/N ratio for KL0 → π 0 ν ν̄ in the experiment. These
techniques will be tested, if possible, as an option or as a potential upgrade
within Step 1.
5.4.1

Endcap Calorimeter

PWO crystals. One of the options for Step 2, if and when the CsI Endcap Calorimeter in Step 1 needs to be changed, is the use of lead-tungstate
crystals (PbW04 , PWO). PWO has higher density, a shorter Moliere radius, and faster response than CsI. The electromagnetic shower in PWO
is more localized in space and time, thereby reducing the backgrounds due
to fusing and blinding eﬀects. Due to the large atomic numbers in PWO,
the electromagnetic interaction is much more enhanced in comparison withthe photonuclear interaction. Thus a smaller photonuclear ineﬃciency is
expected than for CsI.

Figure 49: PWO crystals for the Beam Hole Photon Veto of E391a before(left) and after (right) being wrapped up.
The manufacturing method of PWO is well established now that a large
number of such crystals have been produced for the CMS and ALICE ex74

periments at the LHC. Drawbacks to the material are its small light yield(less than 10% of CsI) and large temperature coeﬃcient (−2%/◦ C at room
temperature). It was reported [68] that the light yield is enhanced by a factor of 2.5 if the temperature is decreased from 20◦ C to −25◦ C. However, theshort decay time is lengthened (from 10 ns to 20 ns) and the temperaturecoeﬃcient becomes larger (to −4.5%/◦ C). In the case of the J-PARC KL0
experiment, an operation at −25◦ C with high temperature stability is nota fundamental problem, because the crystals are installed in vacuum. We
have already studied the performance of PWO when we constructed seventy
PWO modules for the Beam Hole Photon Veto in Run 3 of E391a (Fig. 49),and concluded that PWO is a prime option for the Step 2 Calorimeter,should it be upgraded.
Spaghetti detector. One of the serious background sources is the KL0 →π 0 π 0 decay if two photons coming from it are lost due to ineﬃciencies of thedetector system and or cluster fusion in the Endcap Calorimeter. The solution for reducing the cluster-fusion events is to install a photon detector witha good positional isolation capability just in front of the Endcap crystals.
A spaghetti calorimeter, consisting of many scintillating ﬁbers embedded inlead, would be a possible candidate.
The R&D for a spaghetti calorimeter has been started for the future
Step 2 experiment (Fig. 50). The construction procedure was established byassembling a prototype detector. The performance of the prototype detector
with a CCD readout was checked by the beam test held at SPring-8 in March
2006. The main objectives for further R&D were: (1) development of a fasterand cheaper readout system by using multi-pixel photon-counters (MPPC),
and (2) optimization of the ﬁber arrangement through Monte-Carlo simulations in order to achieve higher photon-detection eﬃciency, along with
better position and angular resolutions.
5.4.2

Charged Veto

Straw tubes. At the University of Chicago, R&D for the possible implementation of vacuum straw tubes (Fig. 51) would proceed forward. The advantages of having tracking capabilities in the experiment are numerous andimportant. With straw-tube tracking, the π + and π − tracks and the vertex
from the copious KL0 → π + π − π 0 decay can be reconstructed. Together withthe two photons from the π 0 , we can (a) calibrate and determinate the absolute energy scale of diﬀerent detector elements; (b) determine the absolute
ineﬃciencies (with the π 0 Dalitz decay); (c) have additional and necessary75Figure 50: Prototype of the spaghetti calorimeter (top); ﬁber alignment inlead (middle left); cross section of the prototype (middle right) and shower
development of 1-GeV photons recorded in the beam test (bottom).

76

charged particle vetos to those of the current plastic scintillator panels withredundancy checks on charged-particle veto eﬃciencies; and lastly, perhaps
most importantly, (d) measure the beam shape and halo distributions withthe reconstructed tranverse positions of the copious Ke3 , Kµ3 , and K+−0
decays.

Figure 51: Design of vacuum straw tubes.
Some work has been done already by using the existing Fermilab’s straws
for the CKM experiment. A beam test was mounted (Fermilab T950) anddata were taken in November/December of 2005. The purpose of the beam
test is to measure the intrinsic ineﬃciency (absorption cross sections) ofstraws.7 Our physics requirements for straws will be diﬀerent from those
for CKM, and therefore further R&D and likely a second beam test will beneeded.8 A Prototype of full length and with 1/20 full width, double-layer
vacuum straws will be tested in a vacuum box. This step is an important
one for R&D in that no 2-meter straw tube assembly has ever been tested
for performance.
Due to the high density and vacuum requirement of the straws, we wish
to start the R&D on the preamps/discriminator circuit and related mechanical infrastructure. This work will be interfaced with the new prototype
above, and only 32 channels on one board are needed for evaluation of the7

The work was a collaboration of Fermilab, Osaka University, and the University of
Chicago. Data analysis is on-going, and we plan to publish the results in the coming
months.
8
We will continue the studies based on the Japan-U.S. Cooperative Research Programin High Energy Physics.

77

gain/noise performance.
5.4.3

Pipeline readout

VME pipeline TDC modules, which are FPGA programmable with an existing prototype, need extensive software modiﬁcation to suit our needs. We
would like to set up a test bench and build a simple tester system to validate
the various properties and proper functions of the module [63].

78

6Schedule and Cost

6.1

Schedule

Table 10 shows our current schedule to prepare and run the experiment.
Table 10: The experiment schedule.
• Start preparing the beam collimators.
2006• Prepare for transferring and shipping CsI crystals.
• Start designing the new CsI readout electronics.
• Start designing the new DAQ.
• Build beam collimators.
• Start assembling the additional MB layers.

2007• Ship KTeV CsI crystals.
• Move some of the E391a detector parts to J-Parc.
• Start assembling the new DAQ.
• Finish installing the beam line by the summer shutdown.
• Move most of the E391 detector components from KEK to J-Parc.

2008• Construct the CsI Calorimeter.
• Build the DAQ system.

2009
2010

6.2

• December: Start a beam survey during night.
• Construct and install rest of the detector components.
• Continue beam survey, and tune the detector.
• The ﬁrst physics data taking run.

Cost

Table 11 shows the estimate on the cost for the Step 1 experiment. The
numbers can still change by a factor of two as detailed designs are developed.

79

Table 11: Cost estimate for Step 1. Unit: $1k.
Item
Beam line

Calorimeter

Main Barrel upgrade

Vacuum system
BHPV

Collar Counters
Trigger and DAQ

Transportation from KEK
Assembling of detector
Total

sum
600

breakdown

cost

Collimator
Beam shutter
Neutron absorber
Beam pipes and their housing, etc.
Construction

200
20
20
260
100

Disassembling / shipping from FNAL
Storage / fabrication
Front end and ET trigger
Readout
HV
Mechanical infrastructure
Calibration system

100
200
600
100
50
50
10

Scintillator, lead sheets, WLS ﬁbers
PMT’s
Scintillator machining
Mechanical structure, fabrication

156
55
38
85

$11k/module × 25
PMTs: $3k × (25 - existing 18)

275
25

HV for non-CsI
Front end for non-CsI
Readout system + CPU
Local Storage

200
100
150
100

1,110

334

250
300

200
550

500
200
3,744

80

7

Conclusion

In order to measure the CP-violation parameters in the ∆S = 1 transition
and to study the ﬂavor physics beyond the Standard Model, we will take a
step by step approach to measure the branching ratio of KL → π 0 νν.
As Step 1, we will use the common T1 target on the A-line, and use
a neutral beam line with a 16◦ extraction angle. We will use the KEK
PS E391a detector with modiﬁcations to improve the background rejection.
With a total of 1.8 × 1021 protons on target (equivalent to 2 × 1014 protons/spill ×3 × 107 seconds of running), we expect to observe 3.5 Standard
Model events. The S/N ratio is expected to be 1.4.
As Step 2, we plan to build a dedicated beam line and upgrade thedetector. We expect to observe 133 SM events with a S/N ratio of 4.8 with
2.73 × 1021 protons on target in total.
This experiment will be one of the most precise tools to study CP violation and the physics beyond the Standard Model in the LHC era.

81

A

AppendicesA.1

Beam Simulation

A solid understanding of the neutral beam is very important for this typeof KL rare-decay experiments. To calculate our sensitivity, we need good
information for the KL yield and spectrum. Higher beam intensities are
preferable with regards to sensitivity, but we must then handle a high ﬂux
of unwanted particles such as neutrons and beam photons. In order toestimate the beam properties, we have performed Monte Carlo simulations
based on the GEANT4 framework. We used the GEANT4/QGSP package
for hadronic interactions.
In our calculations, the momentum of primary proton is assumed to be
30 GeV/c, and its yield to be 2 × 1014 protons on target (P.O.T.) per beam
spill. The spill length and repetition are taken to be 0.7 and 3.3 seconds,
respectively.
In Step 1, we use the common target, called the “T1 target”, which
is a set of nickel disks, as shown in Fig. 52 [69]. In the simulation, there

Figure 52: Schematic drawing of the T1 target, prepared by the J-PARC
Target Monitor Group.

82are ﬁve nickel disks of diﬀerent thickness, 21.7, 11.2, 8.3, 6.8 and 5.9 mm
each, and they are placed 3 mm apart. The total thickness is 54 mm, whichcorresponds to a 36% interaction length (λI ). Each disk has a diameter of
280 mm, and the primary protons are injected at 10 mm from the edge.
The primary beam size at the target is assumed to be inﬁnitesimal in thecalculation.9
We adopt the production angle and solid angle of the neutral beam to be16◦ and 9 µsr, respectively. To save CPU time, we gathered the secondary
products coming between 15◦ and 17◦ and calculated the yield by making
solid-angle corrections.
As can be seen in the following results, the beam just after the target isdominated by soft photons, which are harmful to the detectors in the beamhole. To reduce such photons, we put the photon absorber made of lead at
2 m downstream from the target.
Figures 53, 54, and 55 show the resultant spectra of our simulations at
the detector entrance, i.e. 20 m from the target. The Pb absorber cangreatly reduce the photon yield, while sacriﬁcing part of the KL yield. Table
12 summarizes the calculated yields of KL ’s, neutrons, and photons, withvarious thicknesses of the absorber. Considering a realistic handling of theﬂux, we have decided to use 7-cm-thick lead.
Table 12: Summary of the calculated yields of KL ’s, neutrons, and photons.
All of the numbers are described as the yield per spill, i.e. per 2 × 1014
P.O.T.
Absorber thickness
N (KL ) (×107 )N (neutron) (×108 )N (photon) (×108 )

0 cm
1.9
7.4
1.4
230
103
21

5 cm
1.0
4.3
0.84
13
2.4
0.07

9

7 cm
0.81
3.4
0.69
4.5
0.61
<0.01

9 cm
0.64
2.7
0.56
1.6
0.16
<0.01

Notes
En >0.1 GeV
En >1 GeV
>2 MeV>10 MeV>100 MeV

The size would be 1.3 mm (RMS) according to communications with the Beam Channel Group.

83Figure 53: KL spectrum with various thicknesses of Pb absorber.

84

Figure 54: Neutron spectrum with various thicknesses of Pb absorber.

85

Figure 55: Beam photon spectrum with various thicknesses of Pb absorber.

86

A.2

Photon Veto Ineﬃciency

The detection ineﬃciency for photons can be caused by the following mechanisms.
Photonuclear interaction The ineﬃciency due to photonuclear interactions is caused by events in which a photonuclear interaction occurs in
the Calorimeter prior to an electromagnetic cascade shower, and thesecondary particles thus produced do not generate large signals above
the detection threshold. For example, neutrons can be produced whichthen escape the calorimeter.
Sampling eﬀect The sampling ﬂuctuation is another source of the ineﬃciency in sampling calorimeters such as Main Barrel, which consists ofalternating lead and plastic scintillation plates. The electromagnetic
shower generated in the inactive converter can be totally absorbed anddoes not produce any signal in the active layers of the detector.
Figure 56 shows the photon detection ineﬃciencies for CsI and a sampling calorimeter as a function of the incident photon energy. The graphs
were used for background estimates. The photon detection ineﬃciency of theCalorimeter arises when the energy deposition in the Calorimeter is smaller
than a given detection threshold. We adopt a 3-MeV detection threshold for
the CsI, and 1 MeV for the sampling calorimeter. There are three sources ofineﬃciency: punch-through, photonuclear interactions, and sampling ﬂuctuations. The punch-through, in which the incident photon penetrates the
Calorimeter without any interaction, is well simulated by Monte Carlo calculation and suppressed by having a thick Calorimeter. In Step 1, the fullcalorimeters are thicker than 16 radiation lengths (X0 ) and make the punchthrough eﬀect suﬃciently small.
Even though the total cross sections for photonuclear interactions incalorimeter materials can be evaluated from experimental data [70, 71], it isvery diﬃcult to simulate an actual calorimeter response to the produced secondaries with accuracy. Because detection ineﬃciencies due to photonuclear
interactions were measured in a dedicated experiment, they can be used toestimate the backgrounds.
We deﬁne the ineﬃciency functions to represent the ineﬃciency of theCalorimeter for background estimations. The solid curve in the Left plot in
Fig. 56 shows a model ineﬃciency function that ﬁts the data with a simple
power function, f = pE q , where E is the incident photon energy. Because
we do not have experimental data for photon energies greater than 2 GeV,87

Figure 56: Photon detection ineﬃciencies for CsI crystals (Left) and a sampling calorimeter (Right) as a function of incident photon energy. The open
black circles are experimental data for photonuclear interactions. Monte
Carlo results for the ineﬃciencies due to punch-through and sampling ﬂuctuations are shown in the Right ﬁgures as colored points. Diﬀerent colors
indicate diﬀerent incident angles on the detector. The solid curves are themodel ineﬃciency functions obtained by ﬁtting the data and Monte Carlo
results.

88

we assumed the ineﬃciency at 2 GeV to be a constant value in the higher
energy region. For the very low-energy region where the ﬁt function gives
ineﬃciency values greater than one, we them to the constant value 1, i.e.
completely ineﬃcient states. Thus we obtain the photon ineﬃciency function
f for the CsI Calorimeter as


 1

f=

(E < 1.4 MeV)
(1.4 MeV < E < 2.0 GeV)
(2.0 GeV < E)

3.54 × 10−7 E −2.23

 7.30 × 10−8

(6)

For the sampling calorimeter, we evaluated the ineﬃciency due to punchthrough and sampling ﬂuctuations by using Monte Carlo simulations. It is
dominant for low-energy photons. We can also expect ﬂuctuations in thephotonuclear interaction. They are already included in the obtained data.
In the right plot in Fig. 56, the open black circles show the experimental
data for photonuclear interactions. A dependence of the photon ineﬃciency
on incident angle arises for the sampling calorimeter because the eﬀective
thickness of the inactive converter would be diﬀerent for the diﬀerent incident angle photons. Monte Carlo results for the ineﬃciencies due to punchthrough and sampling ﬂuctuations are shown in the right ﬁgures as coloredpoints. Diﬀerent colors indicate the diﬀerent incident angle to the detector.
The solid curves show the model ineﬃciency functions that ﬁt the data andMonte Carlo results with a sum of power function f = pE q and exponentialfunction f = aebE , where the power function represents the photonuclear
interaction and the exponential function represents the punch-through andsampling ﬂuctuations, respectively. Because we again do not have experimental data for the photon energies greater than 2 GeV, we assumed theineﬃciency at 2 GeV to be a constant value for the higher energy region. For
the energy region between 5 MeV and 2 GeV, we used the incident-angledependent ﬁt functions that categorize the incident angle in nine regions
from 0◦ to 90◦ in 10◦ intervals. Below 0.5 MeV, we assumed that the detector is completely ineﬃcient. The energy region between 0.5 MeV and 5
MeV is assumed to be represented by an exponential function connecting theineﬃciencies at 5 MeV and 0.5 MeV. Thus we obtain the photon ineﬃciency
function f for sampling calorimeter as


1




p1 ep2 Ef=
4.37E −1.83 + p3 ep4 E1.23 × 10−7

89

(E < 0.5 MeV)
(0.5 MeV < E < 5 MeV)
(5 MeV < E < 2.0 GeV)
(2.0 GeV < E)(7)

where the parameters p1 ∼ p4 change for diﬀerent photon incident angles.
These parameters are summarized in the Table 13.
θ (deg)
5
15
25
35
45
55
65
75
85

p1
1.13
1.13
1.13
1.13
1.13
1.14
1.14
1.14
1.14

p2
-248
-238
-245
-249
-251
-253
-255
-256
-256

p3
0.491
0.645
0.729
0.784
0.822
0.845
0.861
0.869
0.873

p4
-85.4
-130
-162
-180
-192
-199
-204
-207
-208

Table 13: Parameters of the ineﬃciency functions for the sampling calorimeter deﬁned by Eq. (7). The photon incident angle θ = 90◦ means perpendicular to the detector surface.

A.3

Charged Particle Veto Ineﬃciency

Detection ineﬃciencies for charged particles are due to several reasons. First,
it can arise from photoelectron statistics. If the light yield per energy deposit
is not suﬃcient, the probability that pulses will be below the detection
threshold is not negligible even if charged particles properly pass through thedetector. A second source is the charge-exchange process π − p → π 0 n before
and/or in the charged particle detector. The π − can disappear through theprocess into neutral particles and go undetected. This eﬀect dominates theπ − ineﬃciency, especially in low-energy region near the large ∆ resonance. A
third source is the e+ annihilation process in the detector material. Data are
available from ineﬃciency measurements by charged particle beams at KEK[72] and PSI[73]. The former experiment provides data around 1 GeV/c,and the latter around 300 MeV/c. We can model the ineﬃciency function
based on these results.
One of the important issues for applying these data to the situation in the
J-PARC experiment is the detection threshold. To reduce the ineﬃciency
due to the charge-exchange and annihilation processes, we have to detect a
π − and/or e+ before it interacts. By setting a lower detection threshold,we can obtain better eﬃciency. On the other hand, a threshold too low willproduce too high a counting rate. We have already had experience with thelight yields and counting rates in the E391a experiment, and thus we can90

safely estimate reasonable detection thresholds for the J-PARC experiment.
In addition, all the sources described above contain charged particles orphotons in their ﬁnal states. The detection eﬃciency can be improved byusing the information of the photon counters behind the charged particle
counters. Therefore, the estimates here result from a combination of charged
and photon counters.
We performed a Monte Carlo simulation, based on the GEANT4 framework, to obtain ineﬃciencies for π + and π − ,10 as shown in Fig. 57. Because
the result does not reproduce the measured data very well, we decided touse only the shape of the ineﬃciency curve from the simulation and scale it
to ﬁt the data. In these plots, we assumed a detection threshold of 100 keV.
Also, we assumed that there exists a 20-mg/cm2 layer of dead material infront of Charged Veto counters, which accounts for the membrane.

Figure 57: Ineﬃciencies for negative (left) and positive pions (right), withthe combination of charged particle detectors and photon counters behindthem. The shape of the curve is obtained by ﬁtting the simulation result,as indicated by the lower curve in the plots. We scaled it to reproduce themeasured data by thePSI group, as indicated with dashed line, and used itas the model function of pion ineﬃciency.
Note that we do not show e+ /e− ineﬃciency functions here because
we do not use model functions, unlike the case for charged pions. In ourestimates of the KL → π ± e∓ ν backgrounds, we have fully simulated the10

We used the GEANT4/QGSP package for hadronic interactions.

91

events, including physics processes such as e+ annihilation, electromagnetic
showers, and decay and hadronic interactions of charged particles.
The situation is diﬀerent for the case of the Beam Hole Charged Veto
(BHCV) counter. The BHCV suﬀers from a high counting rate due to beam
photons and neutrons. If a fake signal happens to come just before the particle that we want to veto, wrong timing information is recorded and masks
the genuine signal. Even though the BHCV is equipped with waveform digitizers in the readout and has a capability to resolve two adjacent pulses, thiseﬀect would be the dominant source of BHCV ineﬃciency. Extrapolating
the counting rate of the Beam Hole Charged Counter in the E391a experiment to the J-PARC environment, we estimate the BHCV ineﬃciency to be
0.5%, independent of particle species and the energies of the particles.

92

A.4

Expected Performance of Beam Hole Photon Veto

In order to estimate the performance of the Beam Hole Photon Veto (BHPV),
we have built a simulation tool based on the GEANT3 framework. All of theČerenkov photons are traced by using our own subroutines. The simulation
includes the eﬀects of the measured optical properties of aerogel tiles such astransmittance and Rayleigh scattering length, and the expected reﬂectivityof the mirror and the Winston cone. The quantum eﬃciency of the photomultiplier is taken as given in the Hamamatsu catalog, with some correction
factors obtained from our beam tests.
Figure 58 shows the expected photon ineﬃciency as obtained from ourMonte Carlo simulations. Here, a hit is deﬁned as a module in which fouror more photoelectrons are detected, and we require coincident hits in threeconsecutive layers. We expect to obtain 99% eﬃciency for 0.6-GeV photons,
and 99.9% for photons of more than 1 GeV, respectively.
Figure 59 shows the hit probabilities for neutrons.11 As can be seen in theﬁgure, our detection condition gives about 0.2% hit probability for 2-GeV/cneutrons, which are the main contributors to the false veto probability as
described below. By multiplying this neutron sensitivity with the expected
neutron spectrum, we can calculate the false hit rate due to neutrons, as
shown in the right plot of Fig. 59. Integrating over the neutron momentum,
the estimated false hit rate of the BHPV is about 540 kHz.
Figure 60 shows the hit probabilities for KL ’s that do not decay in theﬁducial decay region but rather decay further downstream or interact directly with the BHPV. Similar to the discussion about neutrons, the false
hit rates due to neutral kaons were also estimated, as shown in the rightplot of Fig. 60. Integrating over the entire momentum region, it is found to
be 700 kHz.
In addition to the neutrons and KL ’s, there exist photons that are produced directly in the production target. These photons also contribute to
the false hit rate. From the expected energy spectrum and ﬂux for the beam
photons as shown in Appen. A.1, the hit rate due to beam photons is calculated to be 860 kHz, which dominates the false coincidence rate of the
BHPV.
A high counting rate in the beam environment causes three problems.
One problem is the acceptance loss of KL → π 0 νν events. Because the
BHPV is a veto counter, a false hit accidentally kills the real event. Thiseﬀect can be estimated from the counting rate. From the results above, weestimate the false counting rate due to unwanted beam particles (n, KL , γ)11

We use the GEANT3/GCALOR package for hadronic showers.

93

Figure 58: Expected photon ineﬃciency of the BHPV. We require threeor more consecutive hits along the beam direction, where the thresholdof each module is set to be 4 photoelectrons. In the calculation, photons
are injected randomly in a region of 15-cm diameter and normal to the
BHPV face. The red curve indicates our ineﬃciency function Ineﬃciency= p0 + exp(p1 + p2 ∗ Eγ ), which is used later for background estimations.

94

Figure 59: BHPV response to neutrons as a function of momentum. The
left plot shows the BHPV hit probabilities for neutrons. The hit conditionis the same as the one used in the photon ineﬃciency calculations, i.e. threeor more consecutive modules with ≥4 photoelectrons. Again, the value here
is an average over the area of φ 15 cm. Right plot shows the estimated false
hit rate due to neutrons. The upper line with black circles indicates the
expected neutron yield. Multiplying by the coincidence hit probability inthe left plot, the false hit rate can be calculated, shown as the lower linewith red boxes.

Figure 60: BHPV response to KL ’s as a function of momentum. Each ﬁgureshows the hit probability of the BHPV (left) and the estimated count rate
due to KL ’s.
95to be 2.1 MHz in total. Assuming a veto timing window to be 10 ns, theacceptance loss is estimated to be 2%.
Second is the operation of the photomultiplier itself, which is a matterof the singles counting rate of each module. Figure 61 shows the counting
rates in the modules as a function of layer number. As can be seen in

Figure 61: Estimated BHPV counting rates as a function of module ID,
where ID 0 (24) means the most upstream (downstream) module. The
detection threshold is set to be 4 photoelectrons. The square, triangle,
and inverted triangle points show the contributions from beam photons,
neutrons, and KL ’s, respectively, and the circle points indicate their sum.
the ﬁgure, the counting rate is dominated by the contribution from beam
photons, which reaches a maximum of 8 MHz in the most upstream module.
To handle this extremely high rate, each module in the upstream 10 layers isplanned to be segmented into quadrants. In addition, there are some options
for reducing the singles rates. For example, the photomultiplier tubes canbe operated with very low gain and with high speed ampliﬁers, so as not tosuﬀer a loss in gain. Or the detection threshold can be raised to be 8 p.e. if
necessary.
96The third problem is the blinding eﬀect. A real photon signal from KL
decay that we want to catch and veto might be smeared (and thus lost) by
adjacent (early or late) particles. In particular, when unwanted signals arelarger than the real signal and come just before it, they are likely to causea loss in eﬃciency. If we simply assume that a module will be blind for
10 ns once a signal has been generated, based on the double-pulse resolution of the waveform digitizers, we may suﬀer an eﬃciency loss of about 1%
due to 1-MHz (in average) singles counting rates, as discussed above. The
main contributer to the rate is soft photons which do not generate consecutive hits in the BHPV. If the shower size of the photons to be determined,
the eﬃciency loss by accidentals, deﬁned as the probability of destroying
coincidences, is expected to be about 0.1%.
We summarize the estimated BHPV performance in Table 14.
Table 14: The summary of the estimated performance.
photon eﬃciency
neutron hit probability
false hit rateeﬃciency loss by blindness

≥ 99%
99.9%
0.2%
540 kHz700 kHz860 kHz
0.1%

97

above 0.6 GeV
above 1 GeV
at 2 GeV/cneutrons
KL ’s
beam photons
beam photons

References[1] A. Alavi-Harati et al., Phys. Rev. D 61, 072006 (2000).
[2] L.S.Littenberg, Phys. Rev. D39, 3322 (1989).
[3] A.J.Buras, F.Schwab, and S.Uhlig, hep-ph/0405132, and references
therein.
[4] G.Isidori, hep-ph/0307014, eConf C0304052, WG304 (2003), and references therein.
[5] D.Bryman, A.J.Buras, G.Isidori, and L.S.Littenberg, hep-ph/0505171,
Int. J. Mod. Phys. A21, 487 (2006), and references therein.
[6] G.Isidori, hep-ph/0301159, Annales Henri Poincare 4, S97 (2003), andreferences therein.
[7] G.Buchalla and G.Isidori, Phys. Lett. B440, 170 (1998).
[8] W.J.Marciano and Z.Parsa, Phys. Rev. D53, R1 (1996).
[9] G.Buchalla and A.J.Buras, Nucl. Phys. B548, 309 (1999); ibid. B412,
106 (1994).
[10] G.Isidori, F.Mescia, and C.Smith, Nucl. Phys. B718, 319 (2005).
[11] G.Isidori, G.Martinelli, and P.Turchetti, Phys. Lett. B633, 75 (2006).
[12] A.J.Buras, M.Gorbahn, U.Haisch, and U.Nierste, hep-ph/0603079;
Phys. Rev. Lett. 95, 261805 (2005).
[13] T.Inami and C.S.Lim, Progr. Theor. Phys. 65, 297 (1981); Erratumibid. 65 1172 (1981).
[14] C.Jarlskog, Phys. Rev. Lett. 55, 1039 (1985).
[15] K.Sakashita, Ph.D Thesis, Osaka University, 2006; E391a Collaboration, in preparation.
[16] V.V.Anisimovsky et al., Phys. Rev. Lett. 93, 031801 (2004).
[17] Y.Grossman and Y.Nir, Phys. Lett. B398, 163 (1997).
[18] A.Alavi-Harati et al., Phys. Rev. D67, 012005 (2003); Erratum-ibid.
D70, 079904 (2004).
98

[19] J.R.Batley et al., Phys. Lett. B544, 97 (2002).
[20] G.Isidori, F.Mescia, P.Paradisi, C.Smith, and S.Trine, hep-ph/0604074.
[21] A.J.Buras, T.Ewerth, S.Jager, and J.Rosiek, Nucl. Phys. B714, 103(2005).
[22] G.Belanger, C.G.Geng, and P. Turcotte, Phys. Rev. D46, 2950 (1992).
[23] C.Bobeth, M.Bona, A.J.Buras, T.Ewerth, M.Pierini, L.Silvestrini, andA.Weiler, Nucl. Phys. B726, 252 (2005).
[24] G.D’Ambrosio, G.F.Giudice, G.Isidori, and A.Strumia, Nucl. Phys.
B645, 155 (2002).
[25] G.Isidori and P.Paradisi, Phys. Rev. D73, 055017 (2006).
[26] Y.Nir and M.Worah, Phys. Lett. B423, 319 (1998).
[27] See, for example, S.J.Huber, Nucl. Phys. B666, 269 (2003).
[28] C.E.Carlson, G.D.Dorata, and M.Sher, Phys. Rev. D54, 4393 (1996).
[29] Z.Xiao, C.Li, and K.Chao, Eur. Phys. J. C10, 51 (1999).
[30] X-G.He and G.Valencia, Phys. Rev. D70, 053003 (2004).
[31] N.G.Deshpande, D.K.Ghosh, and X-G.He, Phys. Rev. D70, 093003(2004).
[32] W-S.Hou, M.Nagashima, and A.Soddu, Phys. Rev. D72, 115007 (2005).
[33] A.J.Buras, R.Fleischer, S.Recksiegel, and F,Schwab, Nucl. Phys. B697,
133 (2005); Phys. Rev. Lett. 92, 101804 (2004). Updates by the authors
are in Eur. Phys. J. C45, 701 (2006).
[34] T.Goto, Y.Okada, and Y.Shimizu, Phys. Rev. D58, 094006 (1998).
[35] T.Goto, T.Nihei, and Y.Okada, Phys. Rev. D54, 5904 (1996); ibid.
D53, 5233 (1996).
[36] CKMﬁtter Group, J.Charles et al., hep-ph/0406184, Eur. Phys.
J. C41, 1 (2005), updated results and plots available at
http://ckmfitter.in2p3.fr/ .

99

[37] UTﬁt Collboration, M.Ciuchini et al., hep-ph/0012308, JHEP
0107, 013 (2001), updated results and plots available at
http://utfit.roma1.infn.it/ .
[38] SuperKEKB Task Force, “Letter of Intent for KEK Super B Factory”,
KEK Report 2004-4 (2004).
[39] U.Haisch, hep-ph/0512007 .
[40] C-W.Chiang and F.J.Gilman, Phys. Rev. D62, 094026 (2000).
[41] D.S.Gorbunov and V.A.Rubakov, Phys. Rev. D64, 054008 (2001).
[42] A.Brignole and A.Rossi, Nucl. Phys. B587, 3 (2000).
[43] H.Park et al., Phys. Rev. Lett. 94, 021801 (2005).
[44] X-G.He, J.Tandean, and G.Valencia, Phys. Lett. B631, 100 (2005).
[45] N.G.Deshpande, G.Eilam, and J.Jiang, Phys. Lett. B632, 212 (2006).
[46] D.S.Gorbunov and V.A.Rubakov, Phys. Rev. D73, 035002 (2006).
[47] C.Q.Geng and Y.K. Hsiao, Phys. Lett. B632, 215 (2006).
[48] T.Sasaki, Master thesis (in Japanese), Yamagata University (2006).
[49] A.Alavi-Harati et al., Phys. Rev. Lett. 83, 917 (1999).
[50] A.Lai et al., Phys. Lett. B536, 229 (2005).
[51] G.D.Barr et al., Phys. Lett. B328, 528 (1994).
[52] J-H.Jiang, D-N.Gao, and M-L.Yan, hep-ph/0304111, Mod. Phys. Lett.
A18, 977 (2003).
[53] C.Q.Geng, C.C.Lih, and C.C.Liu, Phys. Rev. D62, 034019 (2000).
[54] S.Richardson and C.Picciotto, Phys. Rev. D52, 6342 (1995).
[55] P.Heiliger, B.McKellar, and L.M.Sehgal, Phys. Lett. B327, 145 (1994).
[56] G.D.Barr et al., Phys. Lett. B358, 399 (1995).
[57] H.Watanabe et. al., Nucl. Instrum. MethodsA545, 542 (2005).
[58] Valmiki Prasad, Ph.D Thesis, University of Chicago, June 2002100

[59] M.Doroshenko et. al., Nucl. Instrum. Method A545, 278 (2005).
[60] M.Itaya et. al., Nucl. Instrum. Methods A522, 477 (2005).
[61] Y.Akune, Master Thesis (in Japanes), Saga University (2003).
[62] Some informations of CopperII system
http://www-online.kek.jp/~daqplatform .

can[63] Some
detailsof
thismodulecan
http://hep.uchicago.edu/cpv/ce1337.html .

be

be

found

at

found

at

[64] S.Takita, Master Thesis (in Japanes), Yamagata University (2006).
[65] Particle
Data
Group,
Particle
Listings
2005
http://pdg.lbl.gov/2005/listings/contents listings.html[66] T. Alexopoulos et al., ”A Proposal for a Precision Measurement of
the Decay KL → π 0 νν and Other Rare Processes at Fermilab Using
the Main Injector - KAMI” (2001), available from Fermilab Library byrequest.
[67] H.Watanabe, Ph.D thesis, Saga University (2002).
[68] Talk at KEK seminar by P. Shagin, Jan. 1998, and more improved results of photon yield as a private communication from M. Korzhik (Institute of Nuclear Problems of Berarussian State University) at Minsk,
Aug. 2005.
[69] H. Takahashi, JPS talk, Kouchi, Sept. 2004.
[70] S. Ajimura et al., Nucl. Inst. Meth. A 552, 263 (2005).
[71] K. Sakashita, ”Measurement of the Photon Detection Ineﬃciency due to
Photo-nuclear Interaction”, Masters Thesis, Osaka University (2002).
[72] T. Inagaki, H. Hirayama, T. Sato, T. Shinkawa and Y. Yoshimura,
Nucl. Instrum. Methods A359, 478 (1995).
[73] KOPIO Conceptual Design Report, 2005.

101