An indirect search for WIMPs in the Sun andthe Earth using upward-going muon events inSuper-Kamiokande
Takayuki Tanaka
Division of Particle and Astrophysical Science,
Nagoya University
February 10, 2011

Abstract
We present the result of an indirect search for high energy neutrinos from
WIMP annihilation in the Sun and in the Earth using upward-going muon
events at Super-Kamiokande. Datasets from SKI-SKIII (3109.6 days) wereused for the analysis. We looked for excesses of neutrino signal from theSun and the Earth as compared with the expected atmospheric neutrino
background in three types of upward-going muon categories: stopping, nonshowering, and showering. No significant excess was observed.
The 90% C.L. upper limits of upward-going muon flux induced by WIMPs
of 100 GeV/c2 which annihilate in the Sun were 2.1 ×103 km−2 y−1 and 1.3
×103 km−2 y−1 for the soft and hard annihilation channels, respectively.
Those of the Earth were 1.1 ×103 km−2 y−1 and 9.0 ×102 km−2 y−1 for thesoft and hard annihilation channels, respectively.
The flux limits from the Sun correspond to upper limits of 4.5 ×10−3
pb and 2.7 ×10−4 pb for spin-dependent WIMP-nucleon scattering crosssections in the soft and hard annihilation channels, respectively. Those fromthe Earth correspond to upper limits of 8.1×10−6 pb and 7.0 ×10−7 pb forspin-independent WIMP-nucleon scattering cross sections in the soft andhard annihilation channels, respectively.

Acknowledgements
First of all, I would like to express my gratitude to Prof. Y. Itow for givingme the excellent opportunity of studying about neutrino astronomy. I havelearnt a lot of things and gained invaluable experiences under his guidance.
I also would like to thank Prof. K. Masuda, Prof. Y. Matsubara, Prof.
F. Abe, T. Sako, and T. Sumi. They gave me many valuable advice and support since I joined in this laboratory. This thesis would never exist without
their support and encouragement.
I would also like to thank Prof. Y. Suzuki for giving me the opportunityof studying in Super-Kamiokande experiment. I am grateful for help frommembers of the atmospheric neutrino analysis group. Especially, I thankProf. E. Kearns, Prof. M. Shiozawa, Prof. K. Kaneyuki, C. Saji, andJ.L. Raaf for taking time to give me many comments and helps. I also would
like to thank the other members of the atmospheric neutrino analysis group,
Prof. S. Moriyama, Prof. Y. Hayato, K. Okumura, M. Miura, Y. Obayashi,
J. Kameda, S. Nakayama, I. Higuchi, N. Tanimoto, Y. Shimizu, H. Kaji,Y. Takenaga, G. Mitsuka, H. Nishino, Prof. C.W. Walter, Prof. K. Scholberg, Prof. J.G. Learned, S. Mine, F. Dufour, M. Litos, E .Thrane, S. Smith,
M. Dziomba, J. Albert, P. Mijakowski and R. Wendell.
I would like to extend my gratitude to the staffs in Kamioka observatory,
Prof. M. Nakahata, Prof. Y. Takeuchi, Prof. M. Yamashita, Y. Koshio,
K. Abe, A. Takeda, H. Sekiya, K. Abe, A. Takeda, H. Sekiya, S. Yamada,H. Ogawa, K. Kobayashi and K. Hiraide.
The analysis in this thesis has relied on the hard work by all membersof Super-Kamiokande and all the people supporting this experiment. This
thesis is greatly indebted to them.
Related to the dark matter simulations, I offer my appreciation to C. Rott,
Prof. J. Beacom, and Prof. J. Edsjo. The fantastic discussions with themwere very exciting and I could achieve greatness.
I would like to thank my friends and colleagues who encouraged me forall the time. Especially, A. Fukui and T. Mase enriched my experience of
not only the days in the laboratory, but also those apart from the university.
1

I also wish to thank K. Kamiya, H. Menjo, K. Nagaya, K. Taki, N. Miyake,
K. Furusawa, K. Choi, T. Iida, M. Ikeda, K. Ueshima, C. Ishihara, D. Motoki
T.F. McLachlan, K. Ueno, T. Yokozawa, and Maggie.
Finally, I would like to express my greatest appreciation and gratitude to
my family, relatives and all my friends.

2

Contents
1 Introduction
1.1 Dark matter in the universe . . . . . . . . . . . . . . . . . . .
1.2 Cold dark matter candidate . . . . . . . . . . . . . . . . . . .
1.2.1 Axions . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 LSP as a WIMP candidate . . . . . . . . . . . . . . . . . . . .
1.4 Methods to detect WIMPs . . . . . . . . . . . . . . . . . . . .
1.4.1 Interactions between WIMP neutralinos and targets . .
1.4.2 Direct detection . . . . . . . . . . . . . . . . . . . . . .
1.4.3 Indirect detection . . . . . . . . . . . . . . . . . . . . .
1.5 Recent results for limit on SI and SD cross sections . . . . . .

6
6
9
9
10
12
15
15
16
17
27

2 Atmospheric neutrinos and neutrinos from the Sun
2.1 Atmospheric neutrinos . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Production of atmospheric neutrinos . . . . . . . . . .
2.1.2 Interaction of atmospheric neutrinos . . . . . . . . . .
2.2 Neutrinos from the Sun . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Solar neutrinos . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Solar flare neutrinos . . . . . . . . . . . . . . . . . . .
2.2.3 Solar-atmospheric neutrinos . . . . . . . . . . . . . . .
2.3 Neutrino oscillation . . . . . . . . . . . . . . . . . . . . . . . .

31
31
31
34
35
35
38
38
42

3 Analysis method
3.1 Overview of the analysis . . . . . . . . . . . . . . . . . . . . .
3.2 DarkSUSY . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Overview of the DarkSUSY . . . . . . . . . . . . . . .
3.2.2 Simulations using DarkSUSY . . . . . . . . . . . . . .
3.3 WIMP annihilation rate . . . . . . . . . . . . . . . . . . . . .
3.3.1 Neutrino flux from WIMP annihilation in the Sun andthe Earth . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Detection at the detector as upward-going muons . . .

46
46
47
47
49
49

3

55
58

3.3.3

Conversion factor . . . . . . . . . . . . . . . . . . . . . 62

4 The Super-Kamiokande detector
4.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . .
4.2 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Inner detector and outer detector . . . . . . . . . . . .
4.2.2 Photomultiplier tubes . . . . . . . . . . . . . . . . . .
4.2.3 Overview of the history of detector . . . . . . . . . . .
4.3 Data Acquisition System and electronics . . . . . . . . . . . .
4.3.1 ID DAQ . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 OD DAQ . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 trigger system . . . . . . . . . . . . . . . . . . . . . . .
4.4 Water purification system . . . . . . . . . . . . . . . . . . . .
4.5 Air purification system and Radon hut . . . . . . . . . . . . .

66
68
70
70
72
76
78
78
80
83
85
87

5 Calibration
90
5.1 Gain calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.1.1 HV determination . . . . . . . . . . . . . . . . . . . . . 90
5.1.2 Absolute gain calibration . . . . . . . . . . . . . . . . . 95
5.1.3 Relative gain calibration . . . . . . . . . . . . . . . . . 98
5.2 Charge linearity calibration . . . . . . . . . . . . . . . . . . . 98
5.3 Timing calibration . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4 OD calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.5 Water transparency measurement . . . . . . . . . . . . . . . . 103
5.5.1 Light scattering measurement using a laser . . . . . . . 105
5.5.2 Water transparency measurement using cosmic ray muons106
5.6 Energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6 Analysis for the upward-going muon events112
6.1 Overview of event categories for atmospheric neutrinos . . . . 112
6.1.1 Contained events . . . . . . . . . . . . . . . . . . . . . 112
6.1.2 Upward going muon event . . . . . . . . . . . . . . . . 113
6.2 Upmu dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.2.1 Upmu fitters . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2.2 1st reduction . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.3 2nd reduction . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.4 Precise fitter . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2.5 3rd reduction (selection cuts) . . . . . . . . . . . . . . 124
6.2.6 Showering and non-showering separation . . . . . . . . 128
6.2.7 4th reduction . . . . . . . . . . . . . . . . . . . . . . . 129
6.2.8 Eye scanning . . . . . . . . . . . . . . . . . . . . . . . 132
4

6.3

6.4

6.2.9 Background subtraction . . . . . . . . . . . . . . . . . 137
Monte-Carlo simulation for upmu . . . . . . . . . . . . . . . . 139
6.3.1 Atmospheric neutrino flux . . . . . . . . . . . . . . . . 139
6.3.2 Neutrino interactions . . . . . . . . . . . . . . . . . . . 140
6.3.3 Detector simulation . . . . . . . . . . . . . . . . . . . . 146
Summary of upmu dataset used for analysis . . . . . . . . . . 146

7 Result of Solar WIMP analysis
151
7.1 Event distributions . . . . . . . . . . . . . . . . . . . . . . . . 151
7.2 Limit on upmu flux . . . . . . . . . . . . . . . . . . . . . . . . 152
7.3 Limit on spin-dependent cross section . . . . . . . . . . . . . . 156
8 Result of Earth WIMP analysis
161
8.1 Event distributions . . . . . . . . . . . . . . . . . . . . . . . . 161
8.2 Limit on upmu flux . . . . . . . . . . . . . . . . . . . . . . . . 162
8.3 Limit on spin-independent cross section . . . . . . . . . . . . . 164
9 Discussions of uncertainties
170
9.1 Uncertainties from astrophysical models . . . . . . . . . . . . 170
9.2 Uncertainties in neutrino propagation . . . . . . . . . . . . . . 172
9.3 Detector uncertainties . . . . . . . . . . . . . . . . . . . . . . 172
10 Conclusion

173

5

Chapter 1
Introduction
1.1

Dark matter in the universe

The dark matter composes an important part of the universe. The dark
matter does not emit or absorb electromagnetic radiation at any wavelength.
Thus, it’s very difficult to be detected. It interacts gravitationally, though its
interaction becomes dominant only at the very large scales such as clustersof galaxies.
Existence of dark matter was originally suggested by F. Zwicky in Reference [1]. He observed Coma Clusters, and claimed the large structuresuch as Clusters can become stable in the presence of the unknown source ofgravity to bind each galaxy.
In 1959, L. Volders demonstrated that spiral galaxy M33 doesn’t circulate as expected according to Keplerian dynamics. Also the telescopic observations of many galaxies in 1970s showed that the circular velocities of allcelestial bodies are in the steady range (150 - 300 km/s ) with no dependence
on their distance from the galactic center [2]. This inplies the existence of aspherical-shaped distribution of the mass of the unobserved matter aroundthe spiral galaxies. The observed and estimated rotation curve of our galaxy
is shown in Figure 1.1 as an example [3].
In addition, the condition for a spiral galaxy to be stable was evaluatedusing a multi-body simulation to understand the process of galaxy formation.
From their calculation, much a smaller circular velocity than that of ourgalaxy is estimated (¿ 220 km/s), and this result also supports the existenceof dark matter [4].
In the past years, remarkable progress has been made in cosmology, bothin observation and theory. Recent analyses combining high-redshift supernova luminosity distances and cosmic microwave background fluctuations

6







)+*,% -     !"/.0# $ % &('  !"# $ % &('




Figure 1.1: Rotation curve of our galaxy [3]. The symbols show observational
data from HI measurements. The estimated rotation curve from visible matter (disk and bulge) is also shown. The halo dark matter contribution isneeded to explain the results from the observations of galaxy rotation.

7

reveal the features of our universe.
The present mass density of matter in the universe can be written as
ΩM =

ρM
,
ρcrit

(1.1)

where ρM is the observed mass density, and ρcrit is the critical density,
which is the average density of matter required for a flat universe. The ρcritis written as
3H02
ρcrit =
8πGN
= h2 × 1.9 × 10−29 g · cm−3 .

(1.2)
(1.3)

From observations of the clusters of galaxies, the mass and mass-to-lightratio of the clusters are estimated. From these results, the mass density isobserved to be [5]ρM ∼ 0.4 × 10−29 h2 gcm−3(1.4)

where, h ∼ 0.7 ± 0.15 is the present value of the Hubble constant in theunits of 100 km s−1 Mpc−1 .
The obtained range of the mass density is [5]0.1 . ΩM . 0.3.

(1.5)

Recent cosmic microwave background observations by WMAP imposes
more restrictive constraints on the densities of the components of the universe. They reported [6]ΩB h2 = 0.0224 ± 0.009,(1.6)ΩM h2 = 0.135 ± 0.009,(1.7)ΩΛ = 0.73 ± 0.04,(1.8)

where ΩΛ is the density of the dark energy taking a role described as thecosmological constant.
Subtracting the baryonic contribution ΩB h2 from the matter density,ΩM h2 , leaves a non-baryonic dark matter density ΩDM h2 ofΩDM = 0.113 ± 0.009.
8

(1.9)

From this result, the ratio of each component in the current universe is,ΩB : ΩM : ΩΛ = 4 : 23 : 73.

(1.10)

This result supports the scenario of a wealth of existence of non-baryonicdark matter.
Also from the point of view of structure formation, non-baryonic dark
matter seems to be necessary, and the main part of it should consist ofparticles that were non-relativistic at the time when structure formed (colddark matter, CDM). If the majority of the non-baryonic dark matter consistsof the particles that were relativistic enough at the time when structure
formed (hot dark matter, HDM), the small sub-structures in the large scale
galaxy are expected to be flattened, which is inconsistent with observation.
Thus, hot dark matter, such as light neutrinos are excluded from the dark
matter candidates. Together with galaxy surveys and Ly-α forest data underreasonable assumptions, the WMAP collaboration limits the contribution ofneutrinos to [6]Ων h2 < 0.0076 (95%C.L.).

(1.11)

As for the density of the local halo, it is calculated assuming a halo modeland a rotation velocity. For the usual calculation, the simplest reasonablemodel, the isothermal halo model, is used. The rotation velocity of our galaxy
increases linearly from zero at the center to roughly vc = 220 km/s in thesolar neighborhood, and remains roughly flat all the way out to ∼ 25 kpc[7]. Under those assumptions, the shape of the rotational curve is explainedby assuming that the density distribution of the dark matter in the dark haloisρ(r) =

ρ0,
1 + r2 /r02

(1.12)

where ρ0 is local halo density, and r0 is the local radius. From the Eq.
1.12, the local density of the halo dark matter is estimated to beρ0 ∼ 0.3 GeV c−2 cm−3 .

1.2

Cold dark matter candidate

1.2.1

Axions(1.13)

One of the well-motivated candidates of cold dark matter is the axions [8, 9].
The Quantum Chromo Dynamics (QCD) Lagrangian is written as
9

g2
GG̃,
(1.14)
32π 2
where the first term, Lpert is the perturbative Lagrangian responsible forthe numerous phenomenological successes of QCD. The second term is aconsequence of nonperturbative effects, and violates CP. In this term, θ isthe θ-vacuum introduced in the solution of the U(1) problem, G is the gluon
field-strength tensor, and G̃ is its dual. However, from the constraints of theneutron electric-dipole moment, the tiny value of θ is inferred to be θ < 10−10 .
In addition, experimentally, CP is not violated in strong interactions, or if
it is, the level of strong-CP violation is tiny. This inconsistency between
experiment and Eq. 1.14 is called ”the strong CP problem”. The axion
arises in the Peccei-Quinn solution to the strong CP problem as the pseudoNambu-Goldstone boson [10] and it can drive θ → 0 at the temperatures
below the QCD phase transition. Its mass is ma ∼ eV (107 /fa ) where fa isthe axion mass scale as a theoretical free parameter. The axion strength ofcoupling to ordinary matter is ∝ f−1
a . If the axion mass is in the relatively
small viable range, the relic density is Ωa ∼ 1 and may therefore account for
the halo dark matter. Such axions would be produced with zero momentum
in the early universe by a misalignment mechanism arised from the PecceiQuinn solution and can act as cold dark matter.
Axions can interact with magnetic fields and decay into microwave photons with a frequency proportional to the axion mass. The directional detection of axion experiments are based on using this interaction at the mass
range of ma = µeV - meV, which is a favored range from the theoretical axion
models of cold dark matter [11]. The recent SQUID-based microwave cavity
searching group excluded the range of ma = 1.9 µeV to 3.53 µeV, where oneof the realistic axion models predicted dark matter [12].
LÃ QCD = Lpert + θ

1.2.2

WIMPs

Suppose that in addition to the known particles of the Standard Model,
there exist new, yet undiscovered, stable or long-lived weakly-interacting
massive particles (WIMPs) χ [9, 13]. Weakly interacting means that theseparticles interact only via the weak interaction and gravity. Massive means
sufficiently massive to solve the structure-formation problem brought on by abaryons-only universe. At temperatures greater than the mass of the particle,
T À mχ , the equilibrium number density of such particles is nχ ∝ T 3 , but
for lower temperatures, T ¿ mχ , the equilibrium abundance is exponentiallysuppressed, nχ ∝ e−mχ /T . If the expansion of the universe was so slow that
thermal equilibrium was always maintained, the number of WIMPs today10Figure 1.2: Co-moving number density of a WIMP in the early universe[13]. The dashed curves are the actual abundance, and solid curve is theequilibrium abundance. The larger the annihilation cross section is, thelonger the particles remain in equilibrium and the smaller will be the relicabundance.
would be infinitesimal. However, the universe is not static, so equilibrium
thermodynamics is not the entire story. At high temperatures, T À mχ , χ’s
are abundant and rapidly converting to lighter particles and vice versa:χχ̄ ↔ l¯l,

(1.15)

where l¯l are quark-antiquark and lepton-antilepton pairs, and if mχ isgreater than the mass of the gauge and/or Higgs bosons, l¯l could be gaugeand/or Higgs-boson pairs as well. Shortly after T drops below mχ the number
density of χ’s drops exponentially, and the rate for annihilation of χ’s isΓ = hσvinχ ,(1.16)

where hσvi is the thermally averaged total cross section for annihilationof χχ̄ into lighter particles times relative velocity v. After that, Γ drops
below the expansion rate. At this point, the χ’s cease to annihilate, they fallout of equilibrium, and a relic cosmological abundance remains.

11Figure 1.2 shows numerical solutions to the Boltzmann equation which
determines the WIMP abundance. The equilibrium (solid line) and actual(dashed lines) abundances per co-moving volume are plotted as a function ofx ≡ mχ /T . As the annihilation cross section is increased, the WIMPs stayin equilibrium longer, and they are left with a smaller relic abundance.
An approximate solution to the Boltzmann equation yields the following
estimate for the current cosmological abundance of WIMPs,µ¶
3 × 20−27 cm3 sec−1mχ nχ2Ωχ h =∼,(1.17)ρc
σA v
where h is the Hubble constant in units of 100 km sec−1 .
The mass range of WIMPs depends on the candidates. Generally, GeV TeV ranges of WIMP mass are required from both cosmological and particle
physical points of view [14].

1.3

LSP as a WIMP candidate

The Standard Model (SM) provides a very good description for almost all
experimental data [15]. However, it does not pretend to answer unsolved
problems of key physics such as the origin of mass, the origin of the matter anitimatter asymmetry, the responsibility and the variant of the Higgs mechanism, and the probability of the unification of all forces including gravity.
All of these problems seem to point to new phenomena to be expected atlarger than TeV scale.
Supersymmetry (SUSY) is responsible for all of those problems [16].
Originally, SUSY was introduced to solve some of the outstanding problemsof the SM such as the hierarchy problem, gauge coupling unification, andradiative electroweak symmetry breaking. Also SUSY predicts new ideas formatter-antimatter asymmetry of the universe. Moreover, the unique mathematical nature of SUSY provides us with a prospect for the GUT/Planckscale where all forces unified.
In the SUSY mechanism, fermions (bosons) as a partners of the SM particles are introduced. In Table 1.1, the SM particles and corresponding SUSY
partners are shown. Particles with spin j in the SM have supersymmetricpartners with spin | j - 1/2 |.
A new symmetry, R-parity is introduced for particles in the SUSY theory.
R parity is defined as
R = (−1)2j+3B+L ,12(1.18)

SM particle
e, µ, τName
Charged leptons(electron,muon,
tau)

Spin
1/2

Feel theseforcesEM,WMediatesthese forces-νe , νµ , ντ

neutrinos

1/2Wu, c, tup, charm, top
quarks1/2d, s, bdown, strange,
bottom quarks

γSuperpartner
sleptonsẽ, µ̃, τ̃(selectron,
smuon,stau)

Spin
0

-

sneutrinos
ν˜e , ν˜µ , ν˜τ

0EM,W,S-squarksũ, c̃, t̃

01/2

EM,W,S-squarks
˜ s̃, b̃d,0photon1-EMphotino γ̃

1/2

W±

weak boson

1

EM,W

W

Wino W˜±

1/2Z

weak boson

1

W

W

Zino Z̃

1/2

g

gluon

1

S

S

gluino g̃

1/2Ggraviton

2-

GR

gravitino G̃

3/2

hHiggs boson

0W

generates
mass

higgsino h̃

1/2

Table 1.1: Table of the SM particles and corresponding SUSY partners. The
forces which particles feel, except for the gravitational force, are shown in
4th column, since all particles feel gravitational force. Characters in the 4th
and 5th column are: EM = electromagnetic force, W = weak force, S =strong force, GR = gravitational force. Particles with spin j in the SM havesupersymmetric partners with spin | j - 1/2 |.

13

where j is spin, B is the baryon number, and L is the lepton number.
All SM particles have R=1, while SUSY partners have R= −1. If R-parity
is conserved, all heavier SUSY particles decay into lightest SUSY particle(LSP), and this LSP is considered stable. In the minimal supersymmetricextension of the standard model (MSSM), the LSP is usually the neutralino,a linear combination of the SUSY partner of the photon, Z and Higgs bosons.
Neutralinos are considered to mix after electroweak-symmetry breaking, andexist in the present universe. Another possibility is the sneutrino, but theseparticles interact like neutrinos and have been ruled out over most of theavailable mass range [17]. Thus, neutralinos as the LSP are the one of thebest motivated candidates for cold dark matter [13, 18, 19].
The photino γ̃ and Zino Z̃ are expressed with the superpartners of gauge
fields, B̃ and W̃3 . B̃ is the superpartner of U(1) gauge field, and W̃3 is thesuperpartner of SU(2) gauge field. They are written asγ̃ = cosθW B̃ + sinθW W̃3(1.19)

Z̃ = −sinθW B̃ + cosθW W̃3(1.20)

Thus the mass matrix of the neutralino is written with basis vectors of
B̃, W̃3 , and two Higgsinos which are the partners of the Higgs particles (H̃u0 ,H̃d0 ) asM10−mz cosβsinθw mz sinβsinθw

0M2
mz cosβcosθw −mz sinβcosθw M = −mz cosβsinθw mz cosβcosθw
0−µmz sinβsinθw −mz sinβcosθw−µ
0(1.21)
where M1 and M2 are the respective mass parameters of U(1) and SU(2)gaugino, µ is the higgsino mass parameter, sin2 θW is the weak mixing angle,
mz is the Z boson mass, and tanβ = v2 /v1 , where v1 and v2 are the vacuum
expectation values of the two Higgses.
Using an orthonormal matrix, Eq. 1.21 can be diagonalized as
f0 = N1 B̃ + N2 W̃3 + N3 H̃ 0 + N4 H̃ 0 .
χ
u1
n
d2

(1.22)The lightest neutralino, χ01 (to be called χ for simplicity), can act as
LSP, and can become a candidate for the particles of cold dark matter. The
features of the lightest neutralino depend on the mass parameters M1 , M2 ,and µ in Eq. 1.21. For example, if M1 ¿ M2 , µ, the lightest neutralino, isprimarily B̃. The composition of the lightest neutralino affects such things as

14

the annihilation cross section, the primary particles from their annihilation,and the neutralino-nucleon cross section.
From the SUSY breaking mechanism, constraints from accelerator experiments, and astronomical observations, the neutralino mass is expected to bein the range from several tens of GeV to 10 TeV, depending on the SUSY
parameters [20, 21].

1.4

Methods to detect WIMPs

1.4.1

Interactions between WIMP neutralinos and targets

The several effective interactions between WIMPs and nucleons can be considered. If we take into account the Majorana neutralino, and interactions
under non-relativistic conditions, the effective interaction may be one of two
interactions: spin-dependent (SD) or spin-independent (SI).
A. Spin-dependent (axial-vector) interaction
In the spin-dependent (axial-vector) interaction, WIMP neutralinos couple
to the spin of the target nucleus.
The Feynman diagrams of this interaction are shown in Figure 1.3.

Figure 1.3: The Feynman diagrams of spin-dependent interactions. χ is the
WIMP neutralino, q is the quark, Z is the weak boson, and q̃ is the squark.
The WIMP-nucleon scattering cross section in this interaction is writtenas
J +1
G2F µ2(ap {Sp(N ) } + an {Sn(N ) })2,(1.23)
πJ
where GF is the Fermi constant, µ = Mχ MN / Mχ + MN with Mχ isthe mass of neutralino, and MN is the mass of target nucleus, ap and an
σSD = 32

15

are the coupling constants for proton and neutron, respectively, {Sp(N ) },{Sn(N ) } are the spin of the proton and neutron in the nucleus N, and J
is the coupled angular momentum of the nucleus. From Eq. 1.23, the SD
interaction is effective when WIMPs interact with a nucleus in which thenumber of unpaired protons and neutrons is large.
B. Spin-independent (scalar) interaction
In the spin-independent (scalar) interaction, WIMP neutralinos coherently
scatter with a nucleus.
The Feynman diagram of this interaction is shown in Figure 1.4.

Figure 1.4: The Feynman diagrams of spin-independent interactions. χ isthe WIMP neutralino, q is the quark, H and h are the Higgs bosons, and q̃
is the squark.
The WIMP-nucleon scattering cross section in this interaction is written
as4µ2(Zfp + (A − Z)fn )2 F 2 (q)(1.24)
π
where fp and fn are the coupling constants for protons and neutrons,
respectively, A is the mass number of the target nucleus, Z is the atomic
number of the target nucleus, and F (q) is the form factor of target nucleus N.
This interaction is coherent, and the scattering cross section is proportional
to the square of mass number of the target nucleus A. Thus, this interaction
becomes effective when the WIMP interacts with a nucleus in which the mass
number is large.
σSI =

1.4.2

Direct detection

As our solar system moves in the galaxy, the earth encounters the dark matter
halo with a relative speed. The WIMPs from the halo can elastically scatter16

Figure 1.5: Schematic view of the direct detection. In the direct detection,
the recoil energy from WIMP-nucleon scattering shown by red arrow is to be
detected.
off the target nucleus of a terrestrial detector, and transfer a small amountof energy, which is typically less than 100 keV, to the recoil. Detecting thissmall amount of energy from the recoil nucleus will give strong support for
direct detection of WIMPs. A schematic view of the direct detection is shownin Figure 1.5.
The main challenge of direct detection of WIMPs is the discriminationof WIMP recoil events from background events. Gamma rays and neutrons
will make background events with energies similar to those of WIMPs. Also,
the very low expected event rate is estimated from theoretical calculation tobe ∼ 1 count/day/kg for the most effective target nucleus [13]. To pick out
the event candidate from enormous backgrounds, these experiments requirea very low background environment, thus they are usually located in deep
underground laboratories. The techniques to detect the recoil energy arefollowing: the detection of the scintillation light from the recoiled nucleus, thedetection of the ionization caused by the recoiled nucleus, and the detectionof pyretic action by the recoiled nucleus. Many detectors use one or moreof these techniques. Usually, the heavy nucleus is used as the target toenhance the SI cross section. Also, some detectors have a sensitivity for
SD interactions as well. They use a target nucleus which has a natural
isotope, therefore they have some unpaired protons/neutrons in their target.
In Figure 1.6, major experiments and their detection techniques are shown.

1.4.3

Indirect detection

In indirect searches, people try to detect the signal from WIMP annihilation.
One method of searching for this signal is an indirect search where decay or
annihilation products from WIMPs are observed as originating from the cen17

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Figure 1.6: The major experiments and their detection techniques areshown [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]. The major experiments are shown in purple frames, and the techniques they use areshown. They choose one or two of following three techniques: ionization,
scintillation light, the pyretic action (heat). Also the typical target nucleus
for each technique is shown in the green frame.

18

Figure 1.7: Schematic view of indirect detection. The brown region meansa gravitational field such as a celestial body. In the indirect detection, thesecondary particles from WIMP annihilation as shown by the red arrow are
to be detected.
ter of a gravitational potential well such as a celestial body, or the part in
the halo where matter is dense. WIMPs have a small but finite probability ofelastic scattering with a nucleus. As matter is concentrated in deep gravitational potential wells, this scattering is more likely to occur near the centersof such wells; if their final velocities after the scattering are less than theescape velocity, they are trapped gravitationally and eventually accumulated
in the center of the gravitational potential. WIMP neutralinos, being Majorana particles, can annihilate in pairs and produce various kinds of primaryparticles, depending upon their masses and compositions. A schematic viewof indirect detection is shown in Figure 1.7.
The main channels of the primary annihilations are written in the following equations:

19

χ

f f¯
W +W −
Z 0Z 0gg−→ γγ
W +H −, W −H +Z 0 A0Z 0 H 0 , Z 0 h0
A0 A0 , H 0 H 0 , h0 h0 , H 0 h0
A 0 H 0 , A 0 h0
H +H −(1.25)(1.26)(1.27)(1.28)(1.29)(1.30)(1.31)(1.32)(1.33)(1.34)(1.35)

where, f = νl νl , ll qq, for l = e, µ, τ and q = u, d, s, c, b, t, W ± , Z 0 is the
weak boson. g is gluon, and γ is gamma ray. Also, the five types of Higgs
bosons appearing in Eq. 1.30 - 1.35 as, scalar Higgs (h0 , H 0 ), pseudo-scalar
Higgs (A0 ), and charged Higgs (H + , H − ), are required by SUSY theory.
SUSY theory needs at least two Higgs doublets in complex form and after
the spontaneous breaking of symmetry, the remaining degrees of freedom areffive. Note that the effective annihilation cross section into fermions (σeff ) isproportional to the fermion mass, and annihilation into light fermions suchas neutrinos is practically impossible. In the later sections, we will mainly
consider annihilation into fermions or weak bosons. The Feynman diagramsof these are shown in Figure 1.8 and Figure 1.9 for annihilation into fermionsand weak bosons, respectively.
At the final step, these primary particles may produce gamma rays andmany kinds of particles such as neutrinos, positrons, antiprotons, antideuterons,
etc., via their decay.
As for the gamma rays from WIMP annihilation, 3 components as: continuum emission from quark jets and π 0 , line emission from the annihilation
channel into γγ (Eq. 1.29) and internal bremsstrahlung which is produced
from the charged particles from the WIMP annihilation may be produced[37]. The advantages of an indirect search using gamma rays are that a
relatively large flux is predicted, no attenuation is expected except fromvery dense sources, and there are no diffusion model uncertainties as for the
charged particles. In the indirect search using gamma rays, the WIMP induced gamma rays from the halo are searched for since the celestial bodies
emit background gamma rays. The expected gamma ray flux from WIMP
20

Figure 1.8: The Feynman diagrams of neutralino annihilation into fermion
pairs. χ is the WIMP neutralino, f is the fermion, f¯ is the anti-fermion, Z
is the weak boson, f˜ is the sfermion, and A is the Higgs boson.
annihilation is shown in Figure 1.10 [38]. The Fermi satellite is searching for
WIMP-induced gamma rays from the halo and the galactic center, to try toobtain a limit on the WIMP self-annihilation cross section for the estimated
WIMP mass [39] .
As for an indirect search using antiprotons, several satellites and balloon
experiments are trying to measure its flux from the halo. In this search, thebackground antiprotons in the cosmic ray are important. Those backgrounds
are affected by its emission mechanism and the electro-magnetic fields in theuniverse in their propagation. Thus, concrete knowledge of them is needed forthis search. Recently the PAMELA satellite observed the flux of antiprotons.
The result is shown in Figure 1.11 [40]. The results from PAMELA and otherpast experiments are shown. Also the theoretically calculated background
fluxes with different assumption for the halo and emission models are shown[41, 42]. The significant excess that may come from WIMP annihilation is
not observed, though they are trying to obtain a limit on SUSY parameter
space with better knowledge of the background.
A search using antideuterons has similar features as that of antiprotons.
Compared to antiprotons, the background of antideuterons is essentially zeroat low energies around the few hundred MeV range. Currently, no experi21

Figure 1.9: The Feynman diagrams of neutralino annihilation into the weakboson pairs. χ is the WIMP neutralino, Z and W are the weak bosons,h and H are the Higgs bosons, χn is the 4 types of neutralino, and χ+
n is
the chargino which is a linear combination of the charged wino and charged
higgsinos.

22

Figure 1.10: The differential flux distribution of gamma rays from typical
WIMP annihilations (solid line). The contributions from continuum emission(dotted line) and internal bremsstrahlung (dashed line) are also shown. The
spike between 1 and 2 TeV is from the line emission [38].
ments search for an antideuteron signal, but AMS, or Gaseous AntiParticle
Spectrometer (GAPS) group will try to search for them [43].
As for the search using positrons, it has similar features as the antiproton
search as well. Compared to antiprotons, higher energies are expected since
the prompt annihilation channel from weak bosons is effective to produce
positrons. Though, the larger uncertainties in the propagation exist, suchas energy loss and the effect of solar modulation. The PAMELA and theHEAT satellites observed the flux of positrons. They measured the ratio
between the positron and the sum of positron plus electron flux [44, 45].
They observed significant excesses of the positron flux compared with thebackground. In Figure 1.12, their results are compared with the expected
flux from dark matter annihilation [46]. The benchmark models BM3 (green
lines) and BM5 (red lines) are shown with (dashed lines) and without (dottedlines) radiative corrections. A large (3 × 104 ) boost factor is applied tothe expected signals from BM3 and BM5. If we explain this by WIMP
annihilation, understanding of the mechanism to give such a large boost
factor is needed. Another possible source of this excess could be the effect of
unknown pulsars.
The indirect search for WIMP-induced neutrinos aims to detect the signal
from the Sun/Earth or diffuse neutrinos in the halo. Thanks to the low back23

Figure 1.11: Results from PAMELA (red points) and other past telescopes(other symbols) are shown [40]. Also the theoretically calculated background
fluxes with different assumptions for the halo and emission models are shown.
The dotted and dashed lines are calculated in Reference [41], and solid line
is calculated in Reference [42].

24Figure 1.12: The ratio between the positron flux and the sum of the positronplus electron flux. The results from PAMELA [44] and HEAT [45] arecompared with the expected flux from dark matter annihilation [46]. The
benchmark models BM3 (green lines) and BM5 (red lines) are shown with(dashed lines) and without (dotted lines) radiative corrections. A large (3 ×104 ) boost factor is applied to the expected signals from BM3 and BM5.

25

ground from the Sun/Earth in the energy region of expected WIMP-induced
neutrinos, neutrins are a good probe to search for WIMP annihilation in the
Sun/Earth. The details of the features of expected fluxes and uncertainties
are described in Chapter 3 and Chapter 9. Also we describe the possible
background sources in Chapter 2. In the search for neutrinos from WIMP
annihilations in the Sun or the Earth, we can set a limit on WIMP-nucleon
scattering cross sections, the same as direct searches. For the search for
WIMPs in the Sun, WIMPs are most likely to scatter on the dominant component, hydrogen, either via spin-dependent or spin-independent coupling.
On the other hand, for the search in the Earth, WIMPs mostly scatter on
the heavy materials in the earth via spin-independent coupling. Generally
direct detection searches turn out to have a sensitivity advantage for spinindependent interactions. For the analysis of the SI cross section, the event
rate of a 1 kg germanium detector for direct detection is comparable withthe event rate from the solar plus Earth WIMPs at the 104 m2 - 106 m2
neutrino telescopes. For the analysis of the SD cross section, the event rateof a 50 kg Hydrogen detector for direct detection is comparable with theevent rate from solar WIMPs at 10 m2 - 500 m2 neutrino telescopes [47].
Thus, this method has an advantage especially in the search for SD interactions. Several neutrino telescopes are taking high energy neutrino event[48]. At the current detectors, they are detecting the Cherenkov light fromthe neutrino induced charged particles, which are produced when the particles pass through the detector. IceCube detector is constructed at the South
Pole and it consist of 80 strings [49]. Each string contain 60 optical modules uniformly distributed between 1450m and 2450m under the ice surface.
The optical modules contain 25 cm PMTs. They also have anothor 6 strings
on which the optical modules are located between 1760 and 2450 m, thus
providing a denser distribution to yield a lower energy threshold. Those 6
strings are called Deep Core. In addition, the observatory also contains asurface detector consisting in 80 pairs of tanks on top of the strings. The
full effective volume of this detector is ∼ 1 km3 and its energy threshold forneutrino event is around 100 GeV without Deep Core and a few tens of GeV
with Deep Core. They started the data taking from 2008 using partially constructed detector, and full construction is finished in the end of 2010. The
forerunner of the IceCube was AMANDA detector [50]. AMANDA used 19
strings and optical module ranged from 1500 to 2000m. the total numberof the optical module was 677. The volume was ∼ 10−3 km3 . They started
data taking on 1997. The construction work for the IceCube was started
from 2005, and AMANDA detector was merged into the IceCube detector .
BAIKAL neutrino telescope [51] is deployed in Lake Baikal, Russia, 2.6 km
from shore at a depth of 1.1 km. It consists of 8 strings, 72m long, each with26

24 pair of optical modules and is running since 1998. The volume is ∼ 10−3
km3 . The energy threshold of the neutrino is ∼ 10 GeV. ANTARES detector [52] is located in the Mediterranean sea, 40 km off the French coast near
Toulon. ANTARES consist of 12 lines anchored to the sea bed. Each line
contains 25 storeys. The lowest storey is 100 m above the sea bed and thevertical distance between consecutive storeys is 14.5 m. The total line lengthis 480 m. The first line was deployed in 2006, the detector was operated with
5-lines during several months in 2007 and was fully deployed in 2008. The
total effective area is ∼ 1 km3 , with the neutrino energy threshold is ∼ 100
GeV. As for the WIMP search, Super-Kamiokande (Super-K), AMANDA,
IceCube, and BAIKAL have reported the indirect searches [53, 54, 55, 56],
and their results are shown in latter Chapters. Also, the detail of the Super-K
detector is written in Chapter 4.

1.5

Recent results for limit on SI and SD
cross sections

The results from recent observations are shown in Figure 1.13 and Figure
1.14 for the limit on SI and SD WIMP-nucleon cross sections, respectively.
All the results shown in Figure 1.13 are from direct detection experiments(lines) [57, 58, 59, 60, 61, 62, 63]. On the other hand, the results fromboth direct detection experiments (KIMS, PICASSO) and indirect detection
experiments (IceCube, Super-K) are shown in Figure 1.14 [57, 64, 65, 55, 53].
Also the expected regions from theoretical predictions are shown in both
figures (shaded region) [57, 66, 67].
Clear evidence for a WIMP signal has not been detected so far. However,each experiment sets a good limit and cuts into the expected region fromtheoretical predictions.
Recently, the some direct detection experiments suggest the existence ofa low mass WIMP (< 100 GeV) [68]. Super-K is better equipped for the
search of lower mass WIMPs (< 100 GeV) due to its lower energy thresholdfor neutrino signals, while other neutrino detectors such as IceCube havelarger acceptances for higher mass WIMPs.
In this thesis, we’ve carried out the WIMP indirect search using neutrinos
in Super-K. A previous WIMP search in Super-K was done in 2004 using
a dataset of 1679.6 days of upward through-going muon events [53]. Now
we have nearly doubled the size of the dataset (3109.6 days). In addition,
we introduced a new event categorization to take into account the neutrinoenergy dependence, in order to improve the limits on WIMP-induced upward27            ! &('.

/ 

0*21354"# $%&(') #*$ +*, - 
"# $%&(') #*$ +*, - 
6$ +*7 7 897%-8 : 8 7%;< 7%-8

! 
=

Figure 1.13: The limit on WIMP-nucleon SI cross section from recent experiments [57, 58, 59, 60, 61, 62, 63]. The expected region from the theoreticalpredictions are shown by shaded regions [66, 67]. The upper limit of recent direct detection experiments are shown by solid lines. The expected
sensitivities for the projected experiments are shown by dashed lines.

28         "!$#    % &'( )$ * !+ ," . "/ )$01 )$2""/ 


-

-

Figure 1.14: The limit on WIMP-nucleon SD cross section from recent experiments [57, 64, 65, 55, 53]. The expected region from the theoreticalprediction is shown by the shaded region [57]. The upper limit on the recent direct and indirect detection experiments are also shown. The expected
sensitivities for the projected experiments are shown by dashed lines .

29

going muon flux and WIMP-nucleon cross section, especially for lower mass
WIMP.

30

Chapter 2
Atmospheric neutrinos andneutrinos from the Sun
2.1

Atmospheric neutrinos

2.1.1

Production of atmospheric neutrinos

Primary cosmic rays consist of protons and nuclei. They interact with theatmosphere around an altitude of 10000 - 30000 m, and various kinds ofmesons are produced. The neutrinos are produced from the decay of thosemesons. Those neutrinos are called atmospheric neutrinos. In Eq. 2.1 - 2.7,
the effective reactions which play an important role for the production of
atmospheric neutrinos are listed.
π ± → µ± + νµ (ν¯µ )µ± → e± + νe (ν¯e ) + ν¯µ (νµ )K ± → µ± + νµ (ν¯µ )→ π 0 + µ± + νµ (ν¯µ )→ π 0 + e± + νe (ν¯e )KL0 → π ± + µ± + νµ (ν¯µ )→ π ± + e± + νe (ν¯e )

(2.1)
(2.2)
(2.3)
(2.4)
(2.5)
(2.6)
(2.7)

Also, a schematic view of the production of atmospheric neutrinos isshown in Figure 2.1, and the expected atmospheric neutrino flux is shown in
Figure 2.2.
From Eq. 2.1 - 2.7, the expected ratio between muon neutrinos (νµ ) and31     

Figure 2.1: The production of atmospheric neutrinos

32
  

Figure 2.2: The atmospheric neutrino flux from the Honda(HKKM) [69],[70],Bartol [71], and Fluka [72] models. In the simulation of atmospheric neutrino for this analysis, the HKKM06(Honda06) model is used, as discussed
in Chapter 6.

33

electron neutrinos (νe ) becomesνµ : νe ∼ 2 : 1 .

(2.8)

However, the observed ratio in Super-K was [73]
νµ : νe ∼ 1 : 0.7 .

(2.9)

Compare the Eq. 2.8 with 2.9, an obvious lack of νµ or excess of νe areinferred from the observation (atmospheric neutrino problem). This problem
is explained by neutrino oscillation, as discussed in Chapter 2.3.

2.1.2

Interaction of atmospheric neutrinos

Since neutrinos don’t have charge, and they interact via the weak interaction
only, the cross section of the interaction is very small. However they interact with nuclei and electrons inside the detector in the small probability.
Neutrino telescopes try to detect the products from these neutrino interactions. There are two types of interaction of neutrino: charged current (CC)and neutral current (NC). The Feynman diagrams of these interactions areshown in Figure 2.3 and 2.4 for the CC interaction and the NC interaction,
respectively.

Figure 2.3: Feynman diagram of neutrino-nucleon CC interaction. l means
the leptons (e,µ, τ )In CC interactions, neutrinos interact via W ± , and exchange charge withthe target nucleon. Thus, a charged lepton is generated from the CC interaction. The produced lepton’s flavor conserves the original neutrino’s flavor,
and the identification of the flavor of the original neutrino in the detector is34

Figure 2.4: Feynman diagram of neutrino-nucleon NC interaction. l means
the leptons (e,µ, tau)possible if the neutrino interacts via CC. On the other hand, neutrinos interact via Z 0 in NC interactions, and do not exchange charge with the target
nucleon. Thus, the identification of the flavor of the original neutrino in thedetector is impossible if the neutrino interacts via NC.

2.2

Neutrinos from the Sun

2.2.1

Solar neutrinos

At the core of the Sun, numerous neutrinos are produced via nuclear fusion.
Especially, the two processes of nuclear fusion play an important role in the
production. First is the reaction called the pp-chain, in which the fusion of
protons triggers a chain reaction and produces up to Boron. Second is thereaction called the CNO cycle, which is the cycle reaction among Carbon,
Nitrogen, and Oxygen. In Figure 2.5 and Figure 2.6, an overview of the
pp-chain and CNO cycle are shown, respectively. Also the expected energy
spectrum of solar neutrinos is shown in Figure 2.7 with the spectrum of theother neutrinos.
The precise observation of neutrino fluxes from those reactions gives aprediction for the features of the nuclear reaction inside the Sun. The energy
threshold of typical water Cherenkov detectors such as Super-K is around
5 MeV. Thus, the neutrinos from the boron decays (8 B neutrinos) can beobserved since their energy is relatively higher among the neutrino-emitting
reactions. The observation of solar neutrino was started by the experimentusing the carbon tetrachloride in the 1970s, and they found the observed35  

   ** + $,- 

. +  ,-      
/10 -  "!) -# "! "! $%'& 

)("!

(!
(!  

Figure 2.5: pp-chain reaction. The percentage below the equations is thebranching ratios. Reactions which produce neutrinos are in boxed text. The
neutrinos emitted from each reaction are called 1: pp neutrino, 2: pep neutrino, 3: 7 Be neutrino, 4: 8 B neutrino.

36

Figure 2.6: The CNO cycle [74]. The neutrinos produced after the reactionof 13 N, 15 O, and 17 F is called 13 N neutrino, 15 O neutrino, and 17 F neutrino,
respectively.

37

flux was smaller than the expected flux by 30∼50% (solar neutrino problem)[75]. The precise observation of solar neutrino was done in Super-K, and theyclaim that neutrino oscillation (see Chapter 2.3) caused the smaller flux [76].
Also the result from the SNO experiment support the oscillation hypothesis[77]. Therefore, the smaller flux was concluded to be a result of the neutrino
oscillation.
The energies of solar neutrinos extend up to several tens of MeV as shownin Figure 2.7, while that of WIMP induced neutrinos are more than GeV
order. Thus we can discriminate the solar neutrinos from the neutrinos from
WIMP annihilation in the Sun using the difference of energy ranges.

2.2.2

Solar flare neutrinos

On the solar surface, sunspots where the temperature is relatively low and themagnetic field is extremely high exist. They are generated at the convective
layer inside the Sun, and pushed up to the surface, enhancing the magnetic
field. The sunspots come in huge waves over the 11-year cycle, occurring
regularly. When the number of sunspots is large, increased solar activity
is observed. In such periods, a lot of bursts occur around the sunspots torelease the accumulated magnetic energy. These bursts are called solar flares.
In a solar flare, an energy of 1029 - 1033 ergs are emitted, and electromagnetic
waves of wide range of wavelength and cosmic rays are emitted. The highenergy cosmic rays generated from solar flares produce a large number ofpions. As a result, neutrinos are emitted. The order of the timescale ofa solar flare is a few to a few tens of minutes. In this period, solar flare
neutrinos are expected to have 4-5 times larger flux than the atmospheric
neutrinos [78]. In Figure 2.7, the expected flux of this period is shown. In
Super-K, solar flare neutrinos are searched for in a wide energy range, but
no significant events of solar flare neutrinos are observed.
The typical energy of the solar flare neutrinos are around 100 MeV. Thus
solar flare neutrinos don’t affect the analysis for neutrinos from the WIMP
annihilation in the Sun because of the difference of their energy range.

2.2.3

Solar-atmospheric neutrinos

The solar-atmospheric neutrinos are generated by high energy cosmic rays
interacting inside the Sun when they pass through it. A schematic view of
their production is shown in Figure 2.8.
Solar-atmospheric neutrinos are discussed in Reference [79], and the expected amount of produced neutrinos is calculated. Using the results from
Reference [79], the expected flux in the Earth is calculated [80] and shown
38

Figure 2.7: Spectrum of the neutrinos from many kinds of source. Atm
is atmospheric neutrinos, SRNrelic is the supernovae relic neutrino. SF is
the solar flare neutrinos with two types of neutrino emitting scenario. The
remains are the solar neutrinos from each reaction [78].

39   

Figure 2.8: A schematic view of the production of solar-atmospheric neutrinos.

40

105*E3 (E)(GeV-2cm-2s-1)

in Figure 2.9. To obtain the flux as in Figure 2.9, the assumption is that theratio of each flavor of solar-atmospheric neutrinos is νe :νµ :ντ = 1:1:1 when
they reach the Earth due to the effect of oscillation, though the ratio at thecreation point is νe :νµ :ντ = 1:2:0. Also matter effects for the oscillation when
they pass through the inside of the Sun are considered.



1

10-



10-2
10

100
E(GeV)

1000

Figure 2.9: The flux of solar-atmospheric neutrinos from the Sun. This is
the flux of the muon-neutrinos and the anti muon-neutrinos observed in the
Earth. The shaded region indicates the uncertainty of the propagation
The search for solar-atmospheric neutrinos has just started experimentally, and this holds great potential for the understanding of neutrino oscillation at very high energy, the matter effects, the composition of the solar
atmosphere, and so on.
The expected flux of solar-atmospheric neutrinos from the Sun is smaller
than the flux of atmospheric neutrinos by the order of 105 ∼ 106 at 10 ∼1000 GeV [80], and it does not become an important background source forthe search for WIMP annihilation in the sun.

41

2.3

Neutrino oscillation

If the neutrinos have a non-zero, but small amount of mass, oscillation between each flavor of neutrino may occur.
In this section, the oscillation between two flavors is described for simplicify. The relationship between the flavor eigenstate of an observed neutrino|νµ i,|ντ i, and its mass eigenstate |ν1 i,|ν2 i is written using the transfer matrix Uln as,
µ
¶
µ
¶ µ
¶µ
¶
νe
ν1
cosθ sinθν1≡ (Uln )=(2.10)
νµν2−sinθ cosθ
ν2
where, l is the flavor of the neutrino (e,µ), and n is the index of the mass
eigenstate (1,2). When a neutrino νl propagates as a free particle, the wave
function at time t seconds is written by adding the term for time evolutionas|νl (t)i = e−iHt |νl (0)i

(2.11)

where, H is the Hamiltonian. This H is diagonalized for ν1 and ν2 , andits characteristic root is,p

m2n(2.12)
2E
where, E is the energy, p is the momentum, and mn is the neutrino mass.
Here, the approximation as mn << p is used since the neutrino mass isextremely small. Eq. 2.11 is written using Eq. 2.12 as
Hn = En =|νl (t)i =X

p2 + m2n ∼ E +Uln exp(−iEn t)|νn i(2.13)Uln Ul0 n exp(−iEn t)|νl0 i.

(2.14)

n

=

X
n,l0

is,

Thus, the probability of mixing with another flavor νl0 during the time t

P (l → l0 ) = |hνl0 |νl (t)i|2
X=
Uln Ul0 n Uln0 Ul0 n0 cos[(En − En0 )t].

(2.15)(2.16)

n,n0

When neutrinos travel distance L during time t, the Eq. is written as,
42

µ

¶
∆m2
P (νµ → νe ) = (νe → νµ ) = sin (2θ)sin
L
4E
µ
¶
∆m2
2
2
P (νµ → νµ ) = (νe → νe ) = 1 − sin (2θ)sin
L
4E
2

2

(2.17)(2.18)

where, ∆m2 is the amount of the difference between the square of themass characteristic roots,∆m2 = m22 − m21(2.19)

Using the unit eV2 for ∆m2 ,MeV for E, and m for L, the value (∆m2 /4E)·
L appearing in Eq. 2.18 is,∆m2∆m2 [eV 2 ]L = 1.27
L[m]4E
E[M eV ](2.20)

From Eq. 2.20, the transition probability into another flavor when theneutrino has energy E and travels a distance L depends on ∆m2 and θ.
The atmospheric and solar neutrino problems are interpreted to be theresult of neutrino oscillations. For atmospheric neutrinos, νµ can change toντ when they propagate in the atmosphere, and for the solar neutrino, νe ischanged to νµ when they propagate in the space from the Sun to the Earth.
This oscillation effect is precisely checked using solar neutrinos, atmospheric neutrinos, the neutrinos from reactors, and neutrinos from accelerators [81, 82, 83, 84, 85].
The allowed region of oscillation parameters for the ∆m223 and sin2 2θ23 ,which corresponds to the oscillation between νµ and ντ and for the ∆m212 andtan2 2θ12 , which corresponds to the oscillation between νµ and νe is shown in
Figure 2.10 and 2.11, respectively.
As for the ∆m213 , sin2θ13 , several experiments are now trying to search
for these [88, 89, 90].

43

Figure 2.10: The allowed regions of oscillation parameters for νµ ↔ ντ . The
horizontal axis shows sin2 2θ23 and the vertical axis shows ∆m223 . The results
are taken from Super-K of the zenith and L/E analysis [86], K2K [85] andMINOS [87].

44     !#"

 

Figure 2.11: The allowed regions of oscillation parameters for νe ↔ νµ at 95% C.L.. The horizontal axis shows tan2 2θ12 and the vertical axis shows ∆m212 .
The results shown here are Super-K analysis [86], and combined Super-K plus
KamLAND [84].

45Chapter 3
Analysis method
3.1

Overview of the analysis

We search for the upward-going muon (upmu) events from the Sun or the
Earth in order to perform the indirect WIMP search from those targets.
Upmu events are those where a penetrating muon traveling in the upward
direction enters and either stops in or passes through the detector, and are
attributed to muons produced by neutrino interactions in the surroundingrock. The energy of WIMP-induced neutrinos are estimated to be in the
GeV - few TeV region. In this energy range, neutrino cross section (σν )and effective volume (Vef f ), and detected event rate (Ndetect ) are related toneutrino energy as,σν ∝ Eν(3.1)

Vef f ∝ Eν

(3.2)

Ndetect ∝ Eν2(3.3)

Thus, for the search for high energy neutrinos such as WIMP-induced
neutrinos, upmu events are a good probe. To know the WIMP features suchas WIMP mass and WIMP-nucleon cross sections, we consider the processof WIMP capturing in the targets, annihilation rate, and propagation of
WIMP-induced neutrinos. We used the DarkSUSY simulator [91] to consider
those processes. In this section, we explain about the DarkSUSY simulator
and describe each process. Finally, the conversion factor from upmu flux to
WIMP-nucleon cross section is obtained.

46

3.2

DarkSUSY

3.2.1

Overview of the DarkSUSY

DarkSUSY is a publicly-available advanced numerical package for neutralino
dark matter calculations [91]. The dark matter relic density, the direct
detection rate with various nuclei, and indirect detection rates for neutrinos, gamma rays, and charged particles can be computed by DarkSUSY.
The SUSY parameter sets are used for input. The minimal supersymmetric enlargement of the Standard Model (MSSM) is considered for the SUSY
benchmark model in DarkSUSY [92, 91]. The usual MSSM model has 124
parameters. To reduce the number of parameters, some of the constrained
MSSM models such as MSSM-n models are developed. In the MSSM-n models, the parameters are specified at the electroweak scale. Also, the minimal
supergravity (mSUGRA) model [93, 94] is another approach to reduce thenumber of parameters, in which the SUSY parameters at the SUSY breaking
scale are considered. DarkSUSY can be used under the assumption of either
the MSSM-n or the mSUGRA model.
There are two important packages for our indirect search used in the
DarkSUSY: Supersymmetry Les Houches Accord (SLHA) [95] and WIMPsim [96]. SLHA is used for the calculation to define the SUSY model fromthe input parameters. WIMPsim can simulate annihilations in the Sun or
the Earth, collects all the neutrinos that emerge and lets these propagate
out of the Sun/Earth to the detector, including neutrino interactions andoscillations.
The indirect detection signal of neutrinos with which we concerned, istreated in a realistic way in DarkSUSY as follows. The halo model can bechosen from several models, and the Navarro-Frenk-White (NFW) profile[97] is used as a default. For the velocity of the circulation of the solar
system (vc ), vc = 220 km/s is used as discussed in Chapter 1.1. The massconstraints on the SUSY particles from accelerator experiments are taken
into account. Neutrino oscillation is considered for the neutrino propagation.
For the evolution of the neutrino state in the propagation inside the Sun
and the Earth, the matter effects of the neutrino oscillation as described by
the Mikheyev-Smirnov-Wolfenstein(MSW) effect are considered. For solar
WIMPs, standard vacuum oscillation is considered [98] for the propagation
between the Sun and the Earth. Also, the re-generation and absorption ofneutrinos when they travel inside the Sun or the Earth [98] are taken into
account. Some neutrinos interact with a nucleus in the Sun (Earth) via CCor NC interaction. The charged lepton products from the CC interaction
will decay, and secondary neutrinos will be generated from the decay. These
47



































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



"


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&


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

#

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

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



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







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











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

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

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

Figure 3.1: The schematic view of the DarkSUSY simulation.

48

















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

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

















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secondary neutrinos are mainly produced from the τ leptons come from CCinteraction of τ neutrinos, since τ leptons can decay before they are stopped
or absorbed. In addition, the effect of NC interactions is considered. The
main effect of NC interaction is to change the energy of neutrino. Moreover,the suppression of capture rate due to the gravitational effect from otherplanets, especially Jupiter, during the capture process [99, 100] is taken into
account. After the first scattering, if the WIMP reaches Jupiter, Jupiter candisturb the orbit so that it no longer passes through the Sun and eventuallygets thrown out of the solar system. This effect is not relevant to the WIMP
capturing in Earth because the gravitational sphere of the Earth is verysmall. This effect becomes relevant for WIMPs with masses in the TeV
range. Assuming capturing via SD scattering, the suppression factor for thecapture rate is 0.9 at 1 TeV and 0.1 at 10 TeV.
For the solar model, BS2005-AGS [101] is used. For the Earth, the density
profile of [102] with the compositions given in [103] are used. Also, detector
responses such as energy threshold are considered when the upmu event rateis calculated. The degrees of those effects are discussed in Chapter 9.
The schematic view of the DarkSUSY simulation is shown in Figure 3.1.

3.2.2

Simulations using DarkSUSY

For the calculations to apply the simulation result from DarkSUSY to ouranalysis, we used the special settings as following.
We used the MSSM-7 model which is one of the constrained MSSM models
for this analysis. The MSSM-7 model has 7 free SUSY parameters as shownin Table 3.1. In Table 3.1, the range of MSSM-7 parameters used whenrunning the DarkSUSY scan are also shown.

Higgsino mass parameter
Gausino mass parameter
Mass of CP-odd Higgs boson
Ratio of Higgs vacuum expectation values
Common mass scale factor
Squark mass parameter 1
Squark mass parameter 2

symbolrangeµ[10,30000]
M2[10,30000]
Ma[10,30000]
tanβ[1,60]
m[10,30000]
At /m[-3,3]
Ab /m[-3,3]

Table 3.1: Seven free SUSY parameters of the MSSM-7 model. The range of
MSSM-7 parameters used as the default setting when running the DarkSUSY
scan are also shown.
As for the accelerator mass bound, if we apply the bound in Reference[104], neutralino masses below ∼ 40 GeV/c2 are not allowed when the MSSM7 model is assumed. However, we can set the limit for much lower mass
WIMPs from our experiment. Also, the search for low mass WIMPs is wellmotivated since the DAMA/LIBRA experiment claims evidence for low mass
WIMPs in the range from a few to 90 GeV/c2 [68]. Thus, we have removed
the accelerator bound for our calculation.
The examples of scanning results using the parameter space in Table 3.1
are shown in Figure 3.2 and Figure 3.3. The WIMP-induced upmu flux asa function of the WIMP mass from the Sun and the Earth are shown in
Figure 3.2 and Figure 3.3, respectively. The models which are in the allowed
region of relic density of the dark matter in the universe today, 0.094 <ΩCDM h2 < 0.135 [105] are shown as red points in Figure 3.2 and Figure 3.3.
See Chapter 1.1 for the relic density of the dark matter.

3.3

WIMP annihilation rate

The number of neutralinos in the Sun or Earth, N, is described as
49

-2

-1

Φv(km y )

10

6

10

3

1
-3

10
-6

10
-9

10
-12

10
-15

10
-18

10
-21

10
-24

10
10

2

10

3

10
2

4

WIMP mass(GeV/c )Figure 3.2: The example of scanning result using the parameter space inTable 3.1. The WIMP-induced upmu flux as a function of the WIMP massfrom the Sun are shown. The models which are in the allowed region ofdensity of the dark matter in the universe today, 0.094 < ΩCDM h2 < 0.135[105] are shown as red points.

50

-2

-1

Φv(km y )

6

10
4
10
10
-2

10
-5

10
-8

10
-11

10
-14

10
-17

10
-20

10
-23

10
-26

10
-29

10
10

2

10

3

10
2

4

WIMP mass(GeV/c )Figure 3.3: The example of scanning result using the parameter space inTable 3.1. The WIMP-induced upmu flux as a function of the WIMP massfrom the Earth are shown. The models which are in the allowed region ofdensity of the dark matter in the universe today, 0.094 < ΩCDM h2 < 0.135[105] are shown as red points.

51

dN= Cc − CA N 2 − CE N,(3.4)
dt
where the three constants describe WIMP capture(CC ), annihilation(CA ),and evaporation(CE ). We neglect CE since the effect of evaporation becomesdominant only below a few GeV, and it’s enough smaller than the masses withwhich we are concerned here [106]. We consider only the SD (SI) interaction
for the WIMP capturing in the Sun (Earth), as discussed in Chapter 1.4.3.
The neutralino annihilation rate ΓA is1
ΓA = Cc tanh2 (t/τ ),
2

(3.5)

p
τ = 1/ CC CA .

(3.6)

where

We can calculate the present rate using t = t¯ ∼ 4.7 × 109 years. Whent¯ /τ À 1 annihilation and capture are in equilibrium, dN/dt = 0. In thiscase, ΓA is considered as only depending on the capture rate CC as1
ΓA = CC .
(3.7)
2
The equilibrium time scale τ is determined by the WIMP-nucleon scattering cross section, the WIMP self-annihilation cross section, and the WIMP
mass. In the Figure 3.4, we show the ratio between the age of solar system andequilibration time scale of Sun (t¯ /τ ), as a function of the self-annihilation
cross section (hσA vi) and the WIMP-nucleon spin dependent scattering crosssection (σ SD ). They are evaluated from DarkSUSY, scanning for mχ = 10
GeV/c2 , 100 GeV/c2 ,and 1000 GeV/c2 . The corresponding fractions of neutrino flux compared to the maximal flux reached in equilibrium are shown in
Figure 3.5. From Figure 3.4 and Figure 3.5, we can assume at the SD crosssection where recent observations described in Chapter 1.5 can reach, and at
the WIMP self-annihilation cross section from recent predictions as discussed
in Reference [107, 108], the condition t¯ /τ À 1 is guaranteed for almost allmodels. Thus, we can consider the equilibrium condition between annihilation and capture is guaranteed in almost all models for the solar WIMP and
can use Eq. 3.7 when calculating the annihilation rate.
On the other hand, the volume of the target for the WIMP-nucleon scattering in the Earth, and the gravitational field of the Earth is much smaller
than the Sun. Thus, the capture rate is smaller than the WIMP capturingin the Earth, and the degree of equilibrium t¯ /τ in Eq. 3.5 doesn’t exceed
1 for almost all models. In Figure 3.6, the ratio between age of the solar52 
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 "!#%$'&  () %* 

Figure 3.4: The ratio between the age of solar system and the equilibration time scale of the Sun, as a function of the self-annihilation cross section (hσA vi) and the WIMP nucleon spin dependent scattering cross section(σ SD ). They are evaluated from DarkSUSY scanning for mχ = 10 GeV/c2 ,100 GeV/c2 ,and 1000 GeV/c2 .

53

&('*),+- ./),+0 ' 132 4/5






 

  

   

 

&('*),+- ./),+0 ' 132 4/5
&('*),+- ./),+0 ' 132 4/5

"$#% 
    !

 

"$#%   

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 

 
    !

 

"$# %   

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 

 
    !

 

Figure 3.5: The fraction of neutrino flux compared to the maximal flux
reached in equilibrium for solar WIMPs. They are plotted as a function of
the self-annihilation cross section (hσA vi) and the WIMP nucleon spin dependent scattering cross section (σ SD ) . They are evaluated from DarkSUSY,
scanning for mχ = 10 GeV/c2 , 100 GeV/c2 , and 1000 GeV/c2 .

54system and the equilibration time scale of Earth, as a function of the selfannihilation cross section (hσA vi) and the WIMP nucleon spin independent
scattering cross section (σ SI ) is shown. They are evaluated from DarkSUSY
scanning for mχ = 10 GeV/c2 , 100 GeV/c2 , and 1000 GeV/c2 . In Figure
3.7, the fraction of the neutrino flux compared to the maximal flux reachedin equilibrium, as a function of the self-annihilation cross section (hσA vi)
and the WIMP nucleon spin independent scattering cross section (σ SI ) isshown. Thus, we must consider the degree of equilibrium when calculating
the WIMP annihilation rate in the Earth as Eq. 3.5.

3.3.1

Neutrino flux from WIMP annihilation in the
Sun and the Earth

To calculate the fluxes, we follow earlier approaches [109, 110] as implemented in DarkSUSY for the calculation of the capture rate. For the velocityof the WIMPs, we assume it follows a Maxwellian distribution:rf (u)/u =³ 3(u + v )2 ´´³ 3(u − v )2 ´
3 nχ ³
¯
¯
−
exp
,
exp −
2
2
2π vd v¯
2vd
2vd

(3.8)

where u is the velocity of the WIMP away from the gravitational field,v¯ = 220 km/s is the velocity of the Sun relative to the halo, vd = 270 km/s
is the WIMP velocity dispersion, and nχ is the WIMP number density. We
assume that the local WIMP density is 0.3 GeV/cm3 . Using this assumption
on the velocity, the total capture rate is written as
Z R¯
X dCi (r)CC =4πr2 dr
,
(3.9)
dV
0
i
where R¯ is the radius of the Sun or Earth, Ci is the WIMP capture
rate per unit shell volume of given composition [101] from element “i” in
the Sun or Earth. In the Sun, WIMPs are most likely to scatter on thedominant component, hydrogen, either via SD or SI interactions. To set thelimit on the WIMP-proton SD cross section, we put the assumption that
σSI = 0 for the calculations of solar WIMPs. Since the SI scattering isstrongly constrained, this assumption is safe enough. On the other hand, in
the Earth, the WIMP-nucleon scattering is mainly via SI interaction, since
the Earth consists of atoms with relatively high mass number. Thus the
SD interaction for the calculations of Earth WIMP can be neglected. The
neutrino and anti-neutrino fluxes of flavour m at the detector (Φνm ) arecalculated from the WIMP annihilation rate in the Sun as55 
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 
"!$#&%' (*)  "+,  - .
    

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"!$#&%' (*)  "+,  -/10*2

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 .

    

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 
"!$#&%' (*)  "+,  -Figure 3.6: The ratio between the age of the solar system and the equilibration time scale of Earth, as a function of the self-annihilation cross section(hσA vi) and the WIMP nucleon spin independent scattering cross section(σ SI ). They are evaluated from DarkSUSY, scanning for mχ = 10 GeV/c2 ,100 GeV/c2 , and 1000 GeV/c2 .

56

&('*),+!- ./),+!0 '  132 4/5


 


&('*),+!- ./),+!0 '  132 4/5

687!9   687!9      

   

 
 %

 %
    

 
 

&('*),+!- ./),+!0 '  132 4/5


 


 
 !  "#  $    

 
 

 
 !  "#  $687#9

     

 
 %

    

 
 

 
 !  "#  $Figure 3.7: The fraction of neutrino flux compared to the maximal flux
reached in equilibrium for Earth WIMPs. They are plotted as a function of
the self-annihilation cross section (hσA vi) and the WIMP nucleon spin independent scattering cross section (σ SI ). They are evaluated from DarkSUSY,
scanning for mχ = 10 GeV/c2 , 100 GeV/c2 , and 1000 GeV/c2 .

57

ΓA nt
Φνm =
2
4πD¯

Z ∞
dEνm
0

X
i

P (m, i)

X
f

dNif
Bf
,
dEνm

(3.10)

where D¯ is the distance from the center of the Sun, nt is the target number density, P (m, i) is the probability that a produced neutrino of flavour ioscillates to flavour m when it propagates to the detector, Bf is the branchingratio for annihilation channel f , and dNif /dEνm is the differential number ofneutrinos of flavour i produced per annihilation in channel f . For neutrino
oscillation, we use the parameters described in Reference [111]: θ12 = 33.2◦ ,θ13 = 0◦ , θ23 = 45◦ , δ = 0, ∆m221 = 8.1×10−5 eV 2 and |δm231 | = 2.2×10−3 eV 2 .
The neutrino fluxes from WIMP annihilation for mχ = 100 GeV/c2 at various distances from the Sun are shown in Figure 3.8 and Figure 3.9 for solar
WIMPs, and Figure 3.10 and Figure 3.11 for Earth WIMP [96]. The annihilation channels: χχ → bb̄ (Figure 3.8) and χχ → W + W − (Figure 3.9)
are assumed. In Figure 3.8 and Figure 3.9, the neutrino fluxes for 3 flavour
neutrinos at the neutrino creation or the center of the Sun, at the surface of
the Sun, at the 1 AU distance, and at the detector are shown, respectively.
In Figure 3.10 and Figure 3.11, the neutrino fluxes for 3 flavour neutrinos atthe neutrino creation or center of the Earth, and at the detector are shown.

3.3.2

Detection at the detector as upward-going muons

The WIMP-induced upmu flux, Φµ , which is the sum of the µ− and µ+ fluxes,
is calculated from the neutrino flux (Eq. 3.10) as
Z ∞Z ∞Z ∞ Z Eν
ΓA n
Φµ =
dEµ
dEν
dλ
dEµ0 P (Eµ , Eµ0 , λ)
2
4πD¯
th
th
th
Eµ
Eν (Eµ )0Eµ
0 X
X dN fdσν (Eν , Eµ )i
P (µ, i)Bf
, (3.11)
0
dEµ
dEν
i
f
where Eµth is the detector’s energy threshold for the upmus, Eνth (Eµth ) is theenergy threshold for the parent neutrino for the detector which has the energy
threshold for the upmu events of Eµth , λ is the muon range, P (Eµ , Eµ0 , λ) is
the probability for a muon of energy Eµ0 to have a final energy Eµ after apath-length λ in the detector material, dσν (Eν , Eµ0 )/dEµ0 is the differential
neutrino cross-section for production of a muon with energy Eµ0 from a muon
neutrino of energy Eν . The calculated upmu spectrum from annihilationof 100 GeV/c2 WIMPs is shown in Figure 3.12 for the solar WIMPs, andFigure 3.13 for the Earth WIMPs. Two cases of annihilation channel: χχ →bb̄ (left) and χχ → W + W − (right) are assumed.
58    ! #"%$&(')*+#+
,.,./
,0

    "!$#%'&)(+*,-.$.
/021  3 4/51  3 4/6'1  3 4/021 2!78%:9;4/51 2!78%:9;4/ 6 1 2!78%:9;4     !#"$&%('*)+$-,#,./0  1 2.30  1 2.4&0  1 2./0 -568792.30 -568792. 4 0 -568792

        ! "# $%!'&(*)+!,-.!/.0.1Figure 3.8: The neutrino fluxes from 100 GeV/c2 WIMP annihilations in theSun. We show the flux for the 3 flavour neutrinos at the neutrino production(upper left), at the surface of the Sun (upper right), at the 1 AU distance(lower left), and at the detector (lower right). The horizontal axis z is definedas Eµ /mχ . The first three panels show the flux per one annihilation, and last
panel shows that per one annihilation per unit area. Annihilation into bb̄ isassumed here. The component of secondary neutrinos are also shown in thesecond and third figures by the dashed lines.

59    !#"%$%&'  (*),+   -/.102 34,4    )5( 76
     )5( 76 
#  )5( 76     !"#!$ %&'$!)(*,+-.//
01
02
0$3

     !#"$&%'  (*),+   .- /01 "2,2    )3( 54.
     )3( 54.
 
6  )3( 54.

    ! " #$" %'&)(*+,"-.'.
/0
/1
/"2

Figure 3.9: The neutrino fluxes from 100 GeV/c2 WIMP annihilations in
the Sun. We show the flux for 3 flavour neutrinos at the neutrino production(upper left), at the surface of the Sun(upper right), at the 1 AU distance(lower left), and at the detector(lower right). The horizontal axis z isdefined as Eµ /mχ . The first three panels show the flux per one annihilation,and last panel shows that per one annihilation per unit area. Annihilation
into W + W − is assumed here. The component of secondary neutrinos arealso shown in the second and third figures by the dashed lines.

60     !
" #$#&%')(*+-,,
./
.0
.1

       !
" #$&%')(*+-,,
./
.0
.1

Figure 3.10: The neutrino fluxes from 100 GeV/c2 WIMP annihilations in the
Earth. We show the flux for 3 flavour neutrinos at the neutrino creation(left),and at the detector(right). The horizontal axis z is defined as Eµ /mχ . The
left panel shows the flux per one annihilation, and the right panel shows that
per one annihilation per unit area. Annihilation into bb̄ is assumed.

     !
"# $%&')(*,+-.0//
12
13
14

      !
" #$%'&(*)+,-$./.0.1

Figure 3.11: The neutrino fluxes from 100 GeV/c2 WIMP annihilations in the
Earth. We show the flux for 3 flavour neutrinos at the neutrino creation(left),and at the detector(right). The horizontal axis z is defined as Eµ /mχ . The
left panel shows the flux per one annihilation, and the right panel shows that
per one annihilation per unit area. Annihilation into W + W − is assumed.

61      
!"$#%'&(*)+%,.-$/%0/%1     "!
#$ %'&(*)+-,./1002(32(4Figure 3.12: The calculated upmu flux from WIMP annihilation in the Sun(using Eq. 3.11). The horizontal axis z is defined as Eµ /mχ . 100 GeV/c2
is assumed for the WIMP mass, and the annihilation channels into bb̄ (left)
and W + W − (right) are considered.

3.3.3

Conversion factor

From the estimated muon flux as described in Chapter 3.3.2, we calculated
the conversion factors from the muon flux limits to a WIMP-nucleon scattering cross section. For a specific SUSY model, we typically know the branchingratio Bf for some allowed annihilation channels. To do a model-independent
approach, we consider the extreme cases in which one annihilation channel
dominates (i.e., assuming Bf =1 for some annihilation channel f in Eq. 3.10
and Eq. 3.11). If we assume Bf =1, we can relate the observed muon flux,
Φobsµ , to annihilation rate byffΦobsµ = Φµ = η (mχ )ΓA ,(3.12)

where η f (mχ ) is a function depending on WIMP mass mχ. The WIMPproton SD cross section, σ SD , for solar WIMPs and the WIMP-nucleon SI
cross section, σ SI , for Earth WIMPs as a function of annihilation rate ΓA are
written as
σ SD = λSD (mχ )ΓA(3.13)σ SI = λSI (mχ )ΓA ,(3.14)

using λSD (mχ ) or λSI (mχ ) which are functions of the WIMP mass mχ.
For the solar WIMPs, we finally obtain the relationship between muon flux,62     !"# $% &('*)+-,.(/0&0
1(21(3    !
"# $%'&)(*,+-.//
0'1
0'2

Figure 3.13: The calculated upmu flux from WIMP annihilation in the Earth(using Eq. 3.11). The horizontal axis z is defined as Eµ /mχ . 100 GeV/c2
is assumed for the WIMP mass, and the annihilation channels into bb̄ (left)
and W + W − (right) are considered.
Φfµ , and SD cross section, σ SD , from Eq. 3.12 and Eq. 3.16 asσSD

λSD (mχ ) ff
Φµ = κSD= ff (mχ )Φµ ,η (mχ )

(3.15)For the Earth WIMPs, we also obtain the relationship between muon
flux, Φfµ , and SI cross section, σ SI , from Eq. 3.12 and Eq. 3.14 as
σ SI =λSI (mχ ) f
f
Φ = κSIf (mχ )Φµ ,η f (mχ ) µ(3.16)

To calculate the conversion factor κSD
or κSIff , we scanned MSSM-7 models [91, 92] using DarkSUSY and obtained the ratio between σ SD and Φfµ atmany WIMP masses. The parameter space as shown in Table 3.1 is used.
In this calculation, we put the following assumptions: local halo density is
0.3 GeV/cm3 , WIMP velocity distribution is simple Maxwellian form withvelocity dispersion of 270 km/s, and circular velocity at the solar system’s
location is 220 km/s for both solar and Earth WIMPs. In addition, for thesolar WIMPs, we put the assumptions that the full equilibrium conditionis achieved, and the SI cross section is zero. The uncertainties on thoseassumptions are described in Chapter 9.1.
For the solar WIMPs, we assumed 4 annihilation channels: χχ → bb̄, W + W − ,tt̄, and tau+ τ − . The obtained conversion factor as a function of WIMP mass
is shown in Figure 3.14. Typically, the conversion factor κSD(= σ SD /Φfµ ) isf
63

small for an annihilation channel in which neutrino flux is hard since many
upmus can reach the detector due to their long range.
In a later section, the channel χχ → bb̄ is nominated as a representative ofsofter channels, namely the “soft channel.” Also, χχ → W + W − is nominatedas a representative of harder channels, namely the “hard channel.” If weconsider the neutralinos to be WIMPs, these channels have relatively higher
branching ratios in many SUSY models [13].
σSD/Φµ(pb km2 y)

-2

10
-3

10

bb
tt
WW
ττ

-4

10
-5

10
-6

10
-7

10
-8

10
10

2

10

3

10
mχ(GeV/c2)

4

Figure 3.14: Ratio of spin-dependent cross section, σ SD , compared to upward
going muon flux above 1 GeV within 30◦ of the Sun under the assumptionof the equilibrium condition and standard halo parameters.
For the Earth WIMPs, the SI interaction dominates in the capturing
process. In the SI interaction with elements in the Earth, we must consider
kinematic and other enhancements, in particular if the mass of the neutralinoalmost matches one of the heavy elements in the Earth. This enhancement
is substantial in the WIMP mass range from 10 to 90 GeV and occurs by theresonance with 16 O, 24 M g, 28 Si, 32 S, 40 Ca, 56 F e, or 58 N i. The most effective
enhancement occurs by a resonance with iron (52.4 GeV) and in this case ∼20 times larger capture rate is expected [109]. In DarkSUSY, this effect isalso considered, and the calculated conversion factor is shown in Figure 3.15.
In Figure 3.15, we assume the degree of equilibrium, t/ τ = 1. From Eq. 3.5
and Eq. 3.12,641Φfµ = Cc η f (mχ )tanh2 (t/τ ).
(3.17)
2
We can obtain the conversion factor for smaller degrees of equilibrium by
scaling the conversion factor in Figure 3.14 using Eq. 3.17.
σSI/Φµ(pb km2 y)

-3

10
-4

10
bb
WW

-5

10
-6

10
-7

10
-8

10
-9

10
-10

10
10

2

10

3

10
2

4

mχ (GeV/c )Figure 3.15: Ratio of spin-independent cross section, σ SI , compared to
upward-going muon flux above 1 GeV within 30◦ of the Earth. We assumed
degree of equiblium as 1 in this plot.

65

Chapter 4
The Super-Kamiokande
detector
The Super-K experiment has been used to study various kinds of physics
and astronomy topics based on neutrinos such as solar neutrinos, neutrinos
from both current and relic supernovae, atmospheric neutrinos, and high energy neutrinos resulting from a variety of phenomena in the universe. Also,
Super-K has been used for the nucleon stability studies like proton decay
searches. Super-K also served as the far detector for the K2K experiment,
and is currently serving the same purpose for the T2K long-baseline neutrino oscillation experiment. The details of the experiment can be found in
Reference [86].
The Super-K detector is the world’s largest underground water Cherenkov
detector. The detector construction started in 1991 and was completed in
1995. It began operating in April, 1996. The shape of the detector is cylindrical, with a diameter of 39.3 m and a height of 41.4 m. It contains 50000
tons of ultra-pure water, and photo-multiplier tubes (PMTs) are installed on
the inner surface of the wall. The Super-K detector is located in Kamioka
mine in Hida-city, Gifu, Japan, with coordinates of 36◦ 25’N latitude and137◦ 18’E longitude. The detector is beneath 1000m of rock overburden.
Cosmic ray muons with energy less than about 1.3 TeV cannot reach theSuper-K detector due to energy loss in the rock. The cosmic ray muon rate
at the Super-K detector is around 2 Hz. The detector consists of two parts,
an inner and an outer detector which helps to identify the charged particles
coming from the outside. A schematic view of the detector is shown in Figure4.1. The details of the Super-K detector can be found in Reference [112].

66

LINAC roomelectronics hut

control room

20" PMTs

water system
Mt. IKENOYAMA

1000m

Figure 4.1: The Super-K detector.

67

4.1

Cherenkov Radiation

In Super-K, Cherenkov light is used to search for charged particles travelinginside the detector.
When a charged particle passes through a medium, charge polarization
occurs. The charged particle exchanges photons with the surrounding electricfield, but if the speed of the particle is greater than the speed of light in themedium, the photons cannot catch up with the traveling charged particle.
Those photons creates a shock wave as shown in Figure 4.2, and this is called
Cherenkov radiation.

         

!"$#&%'( ')*  +
Figure 4.2: Cherenkov radiation

The relationship between charged particles and emitted photons is written
as
1
,
(4.1)
nβ
where θ is the angle between the traveling direction of the charged particle
and the wavefront of the resulting radiation, n is the refractive index of themedium, β = v/c with the speed of the charged particle (v) and the speed oflight in vacuum (c). Given v ∼ c or β ∼ 1, θ ∼ 42◦ in pure water of n ∼ 1.34.
cos θ =

68

The criterion of the speed of a charged particle to emit Cherenkov light issolved as v ≥ c/n with 0 ≤ cos θ ≤ 1. The energy of the charged particle
when v = c/n is defined as the threshold energy Ethr , and it is written as
n
mc2
(4.2)
2
n −1
where m is the mass of the charged particle. When the medium is purewater, Eq. 4.2 becomes,
Ethr = √Ethr ∼ 1.5mc2 .

(4.3)

In Table 4.1, the Ethr for charged particles which are detected in the
Super-K detector are shown. A schematic view of the detection of Cherenkov
light by the PMTs is shown in Figure 4.3.
Particlee±µ±π±Rest mass(MeV/c2 )
0.511
105.7
139.7

Ethr (MeV)
0.767
157.4
207.9

Table 4.1: The value of Ethr for e± , µ± , and π ±The total number of emitted photons (Nphoton ) per unit wavelength (dλ)
and per unit length (dL) when a charged particle with charge Ze passes
through the medium isµ¶2παZ 21
d2 Nphoton=
1− 2 2
(4.4)
dλdL
λ2
nβ
where α is the fine structure constant (∼ 1/137). Eq. 4.4 can be integrated by λ using 4.1 asdNphoton= 2παZ 2 sin2 θ
dL

Z λ2

dλ
λ2

¶
µλ1
1
1
2
2
−
.
= 2παZ sin θ
λ1 λ2

(4.5)

As described in Section 4.2.2, the effective wavelength of Super-K’s PMTs
is 300 ∼ 600 nm. In this wavelength range, the number of photons emitted from Cherenkov radiation when a charged particle with charge e passes
through the pure water can be calculated from Eq. 4.5 as ∼ 370 photons
per cm.
69

Figure 4.3: A schematic view of the detection of Cherenkov light by the
PMTs.

4.2

Detector

4.2.1

Inner detector and outer detector

The Super-K detector is a cylindrical form as shown in Figure 4.1. The area
where the distance from the rock wall is more than 2.7m is called the innerdetector (ID), and the area within 2.7m of the rock wall is called the outerdetector (OD). The border between these regions is divided by an array ofsteel frames. Each array holds twelve 20-inch PMTs facing toward the ID sideand two 8-inch PMTs facing toward the OD side. This unit array is called asuper module (SM). There are 974 super SM’s in Super-K. A schematic viewof a SM is shown in Figure 4.4.
The walls of the ID are covered with black sheet made of Polyethylene
terephthalate (PET) to suppress unwanted low-energy events due to residual
radioactivity occurring behind the PMTs. The walls of the OD are covered
with reflective Tyvek sheet to enhance the total light collected. The reflectivity of the Tyvek is about 90% at 400 nm falling to about 80% at about
340 nm. The light is shielded between the ID and OD by the black sheet andthe Tyvek sheet.
Using the information of the detected photons in the ID and OD, we can70

$NCEMUJGGVFigure 4.4: A super module in the Super-K detector.

71identify particles coming from the outside, such as high energy cosmic raymuons and γ-rays from the environment.

4.2.2

Photomultiplier tubes

For the PMTs of the ID, type R3600-5 PMTs developed by Hamamatsu
photonics in cooperation with the Kamiokande collaboration, are used [113].
In Figure 4.5, a schematic view of the type R3600-5 PMT is shown.

Figure 4.5: A schematic view of the type R3600-5 PMT
The photocathode is approximately hemi-spherical in shape and consistsof a bialkali (Sb-K-Cs) photocathode with a peak quantum efficiency of about
22% at 360-400 nm, and with sensitivity ranging from 280-660 nm wavelength. The quantum efficiency as a function of the wavelength is shown in
Figure 4.6.
To use in the Super-K detector, these PMTs were designed to have highwater resistance and pressure resistance. The diameter of the PMT is 20inches. This large diameter was designed to achieve a wide light-receiving
section. It is difficult to achieve fine timing resolution in such a huge PMT
since the time of flight of the photoelectron isn’t uniform; it depends on thelocation of the photon hit. Thus, the size of the first dynode was precisely
optimized and the average transit-time spread for a 1 p.e. signal is 2.2 ns.
72

Figure 4.6: The quantum efficiency of the type R3600-5 PMT as a functionof the wavelength.

73

The distribution of the transit-time for the 1 photon signal is shown in Figure
4.7.

Figure 4.7: The distribution of the transit-time of the type R3600-5 PMT
for the 1 photon signal.
Also the structure and composition of the dynodes, as well as the applied
voltage among dynodes were optimized. This increased the probability ofcapturing secondary photoelectrons, and the photoelectron distribution when
one photon is injected is the ideal shape. This distribution is shown in Figure
4.8.
The threshold to discriminate between the photon signal and the darknoise of the PMT was set to 0.3 p.e., which corresponds to the valley shownin Figure 4.8. The dark noise rate at the 0.3 p.e. threshold is around 3.5
kHz.
Because of its huge size, the travel length of the photoelectrons in the
PMTs is long, and it is affected by the Earth’s magnetic field. To prevent
this effect, a Helmholtz-type coil is installed around the water tank. This
coil generates a magnetic field to negate the effect of the Earth’s magnetic
field, and the magnetic field in the Super-K detector is reduced by 50mG. A
summary of the features of the type R3600-5 PMT is shown in Table 4.2.
Each ID PMT is covered by acrylic covers and FRP cases as shown in
Figure 4.9 since the SK-II phase. The transparency of the acrylic case ishigher than 96% at 350 nm wavelength.
74

Figure 4.8: The one photoelectron distribution of type R3600-5 PMTs

Diameter of the photocathodeMaterial of photoelectric effectDynodeQuantum efficiency
Efficiency of the photoelectron capturing
Gain
Operating voltage
Dark current
Dark rate
Time resolution
Resistance to pressure
Transit time
Rise time
Fall time
Proper magnetic field

50 cm
Bialkali (Sb-K-Cs)
Venetian bind type 11 stages
22% @390 nm
70%
107 (∼ 2000 V supply voltage)+1500 ∼ 2500 V
200 nA(Gain∼107 )3.5kHz(Gain∼107 )2.2 ns (1σ) @1p.e.
6 kg/cm2∼100 ns(Gain∼107 )∼10 ns∼10 ns
100 mG

Table 4.2: Summary of the feature of the type R3600-5 PMTs

75

Figure 4.9: PMT case

For the OD, 8-inch PMTs are used. To enhance the light collection efficiency, wavelength shifter plates are attached to each PMT. The wavelength
shifter plates are square acrylic panels of length 60 cm and about 1.3 cm
thick and are doped with 50 mg/l of bis-MSB. These plates absorb light in awide range of wavelengths, and re-radiate the light at the wavelength where
the PMT sensitivity peaks. The wavelength shifter increases light collection
efficiency of the OD by about 60%. The time resolution of the OD PMTs is
15 ns with the wavelength shifter.

4.2.3

Overview of the history of detector

Since Super-K started operation in 1996, there have been four experimental
phases: SK-I, SK-II, SK-III and SK-IV. The main difference in each phaseis the number of PMTs and PMT cases. SK-I started in April, 1996 with
11146 ID PMTs and 1885 OD PMTs. The photocoverage of the ID was
40%. After 5 years of operation, an accident occurred in November, 2001
during maintenance work for the replacement of bad PMTs. One of thebottom PMTs broke first, and 6777 ID PMTs and 1100 OD PMTs were thenbroken by the chain reaction due to the resulting shock wave. To prevent a
recurrence, the acrylic covers as described in Section 4.2.2 were introduced
and installed for the ID PMTs. In October 2002, the SK-II phase was started
using the remaining PMTs for the ID, and remaining and newly-introduced
PMTs for the OD. In the SK-II, 5182 ID PMTs with acrylic covers and 1885
OD PMTs were used, and the photo coverage of ID was 20%. Thus, theenergy threshold was worse than that of SK-I. From July 2005, reconstruction76segmentation
Tyvek

Figure 4.10: Schematic showing the OD segmentation Tyvek layer to optically separate the endcap and barrel regions of the OD.
work was done to restore the lost PMTs. After that works, SK-III was started
in July 2006 with 11129 ID PMTs, and 1885 OD PMTs. The photocoverage
was recovered to 40%, and the energy threshold was also recovered to thesame level as SK-I.
The outer detector was completely rebuilt to its original configurationfor SK-II. For SK-III, dead photo-tubes were replaced and a vertical layer
of Tyvek to optically separate the barrel and end cap regions was installed
as shown in Figure 4.10. The optical segmentation was done in order tobetter separate background corner-clipping cosmic ray muons from neutrino
interactions with an exiting lepton.
From Sep. 2008, the SK-IV phase was started with newly introduced
electronics [114]. Thanks to the new electronics, we could reduce the deadtime of the data acquisition, expand the dynamic range, and achieve a lower
energy threshold. The features of each Super-K phase are shown in Table
4.3.
In this thesis, the datasets from SK-I to SK-III were used for the analysis.
The systems and analysis method described in later sections are based on
those for the SK-I to SK-III periods.

77

Start of data taking
End of data taking
PMT cases
Number of ID PMTs
Number of OD PMTs
Photo coverage
Energy threshold

SK-I
Apr. 1996
Jul. 2001
No
11146
1885
40%
5MeV

SK-II
Oct. 2002
Oct. 2005
Yes
5182
1885
19%
7MeV

SK-III
Jul. 2006
Aug. 2008
Yes
11129
1885
40%
4.5MeV

SK-IV
Sep. 2008
Yes
11129
1885
40%
4 MeV(target)

Table 4.3: The features of each Super-K phase

4.3

Data Acquisition System and electronics

In this section, we provide an overview of the Super-K Data Acquisition
System (DAQ) used for the SK-I to SK-III phases. For a more comprehensive
discussion, see Reference [112].
There is a central hut and 4 peripheral huts in the dome above the SuperK tank. The trigger system and control electronics are placed in the central
hut, and front-end electronics and high voltage systems are placed in peripheral huts.

4.3.1

ID DAQ

Data from ID PMTs is processed by analog timing modules (ATMs). ATMs
were developed based on the TKO (Tristan KEK online) standard for theSuper-K experiment [115, 116]. One ATM can process data from up to 12
PMTs, and 934 ATM boards were used in total. The overview of the ID
DAQ system is shown in Figure 4.11.
Upon entering an ATM, each analog PMT pulse was amplified 100 times
and split into multiple, identical signals.
One copy of the signal was sent to a discriminator, which fired a digital 15
mV, 200ns pulse for each analog pulse it received below a threshold of -1mV,
which corresponds to a charge of 0.3 p.e.. When a PMT pulse exceeded thediscriminator threshold, the PMT was treated as the hit PMT. The otherdigital PMT output pulses that were uniform in amplitude (15 mV) areadded. The accumulated signal were called as ID HITSUM signal, and took
on discrete values. They were proportional to the number of hit ID tubes.
The HITSUM signal played a key role in the triggering system as shown in
Section 4.3.3.

78

20-inch PMT
SCH
ATM
x 20
x 240

ATM
GONG

20-inch PMTSCHATMinterface
Ultra Sparc

x 20
x 240

SMP

ATM

SMP

GONG

online CPU(slave)

SMP
SMP
SMP
SMP

x6

Super Memory Partner

VME
20-inch PMT
SCHUltra Sparc

ATM

online CPU(slave)

x 20
x 240

Ultra Sparc

ATM
GONG

online CPU(host)

Analog Timing Module

online CPU(slave)
TKO

FDDI

Ultra Sparc

Ultra sparc

online CPU(slave)
Ultra Sparc

online CPU(slave)
Ultra Sparc

FDDI

online CPU(slave)
Ultra Sparc

online CPU(slave)

online CPU(slave)interface
Ultra Sparc
SMP
SMP

Ultra Sparc

online CPU(slave)

SMP
SMP
SMP
SMP

Super Memory Partnerinterface

VME
VME

interrupt reg.
TRG

20-inch PMT
SCH
TRIGGERATM

TRIGGER

x 20
x 240

PROCESSORHIT INFORMATION
ATM
GONG

Analog Timing ModuleTKO

PMT x 11200

ATM x ~1000

SMP x 48

online CPU(slave) x 9

Figure 4.11: Overview of the ID DAQ system

79

Another copy of the signal made the sum of the input signal for one ATM
board. This was called PMTSUM. This output signal went into a Flash ADC
that recorded the waveform information.
Other copies of the signal were sent to charge-to-analog converters (QAC)
and time-to-analog converters (TAC). When another discriminator output
pulse was received at the QAC/TAC, a calculation of PMT charge and firing
time was started. The QAC received as input one of the split PMT signals
and began integrating the signal for 400 ns. The TAC, on the other hand,
integrated a constant current. The duration of the TAC signal, therefore,
was proportional to the time since the PMT was hit.
If a global trigger (See Chapter 4.3.3) was generated within 1.3 µsec , the
QAC/TAC signals were digitized by an analog-to-digital converter (ADC).
Otherwise, the QAC/TAC signals were cleared.
There were two pairs of QAC/TAC channels for each PMT input signal.
It took 5.5 µsec for an ADC to process each channel. Therefore, if one pairof channels was in use during a hit, the second pair recorded the charge andtime information. This system prevented DAQ deadtime during multiple
sequential hits.
ID data was buffered so that detailed PMT hit information was recorded
for 750 ns before and after a global trigger. The ATM had a dynamic rangeof 450 pC for charge and 1300 ns for time. The corresponding resolutions
were 0.2 pC and 0.4 ns.
A basic block diagram of the input part of the ATM is depicted in Figure
4.12.
The digitized signal through the above process was read out by SCH(Super Control Head) and sent to VME memory called SMP (Super Memory
Partner). The data on SMPs were transferred to online host computers via
a high speed network.

4.3.2

OD DAQThe OD DAQ was similar to the ID in functionality. A schematic view of
OD DAQ system is shown in Figure 4.13.
Pulses from OD tubes were fed into charge-to-time converter modules(QTC), where they were split into two.
One pulse was sent to a discriminator. If the pulse was below a thresholdof -25 mV, the discriminator emitted a digital 200 ns, 20 mV hit signal. One
copy of the hit signal went to the OD HITSUM signal, which was used fortriggering.
The second copy of the PMT pulse was sent to a 50 ns delay line which
terminated at the QTC. In addition to the PMT pulse, the QTC received a80

Figure 4.12: Basic block diagram of the input part of the ATM.

81

Figure 4.13: Basic block diagram of the input part of the ATM.

82

copy of the hit signal from the discriminator. The hit signal opened a 200
ns gate during which the delayed PMT pulse was integrated. The lengthof the QTC pulse was proportional to the charge deposited in the hit OD
PMT. The QTC pulse was sent to a time-to-digital converter (TDC) which
recorded the leading edge of the pulse and also the falling edge. The QTC
had a dynamic range of 0-200 p.e. and the TDC had a resolution of 0.5 µs.
After the global trigger, the TDC channels were digitized and read out.
The duration of the digitalization process depended on the number of hit
OD PMTs, and took between 2 µs for low-energy events to > 50 µs forhigh-energy events. During this time, the information from individual PMTs
could not be recorded. This created deadtime and was subtracted from thelive time.

4.3.3

trigger system

The HITSUM, 200 nsec width and -15 mV height, signal from each PMT
was collected at the central hut through a TKO crate, from each electronics
hut. If the sum of HITSUMs exceeded the threshold, a global trigger was
generated, in other words, this global trigger was generated depending on thenumber of hit PMTs. The width of the HITSUM signal was 200 nsec because
the event duration time in Super-K was up to 200 nsec which corresponds
an event going through the tank diagonally.
There were three types of global triggers depending on energy: the highenergy trigger (HE), the low energy trigger (LE) and the super low energy
trigger (SLE). At the end of the SK-I period, the HE, LE, and SLE trigger
required 34 mV (after 1/10 attenuation), 320 mV and 186 mV, respectively.
The SLE threshold of 186 mV was equivalent to 4.6 MeV threshold in total
electron energy. Because of very low threshold, the SLE trigger rate was quite
high due to the gamma-ray background from surrounding rocks and PMTs.
Therefore, in order to reduce the huge number of SLE triggered events, asoftware trigger which removed events outside of the fiducial volume, was also
applied. The average trigger rates of each trigger during the SK-III period
were ∼ 1kHz, ∼ 35 Hz, ∼ 10 Hz for the SLE, LE, HE triggers, respectively.
The trigger conditions in each period are summarized in Table 4.4. Eventsacquired by SLE and LE triggers were used for the analysis of low energy
neutrinos such as solar neutrinos, and those of the HE trigger were used forthe analysis of high energy neutrinos such as atmospheric neutrinos. The
timing diagram of the trigger system is shown in Figure 4.14.
In addition, a periodical trigger such as the laser trigger was prepared inorder for calibration events occurring by laser. Also an anti-trigger, which
was generated when the number of hit OD PMTs exceeded the threshold,
83

SLE
LE
HE

SK-I
186 mV
320 mV
34 mV

SK-II
110 mV152 mV
18 mV

SK-III
186 mV
302 mV
32mV

Table 4.4: Trigger threshold in each data taking period. Note that the threshold voltage of HE is the values applied for the signals after 1/10 attenuation.

Figure 4.14: The timing diagram of the trigger system

84was prepared in orderto identify the events generated by particles from theoutside.
The ADC overflow effect was shown from 450 pC, and we could not
use PMT output more than 450 pC for the analysis. To solve this, FlashADCs were introduced from the SK-II period. FADC could digitize analog
signal continuously, and the deadtime was reduced. In addition, the FADC
could record the pulse shape of each event. From the rising shape and thetime width, we could estimate the charge of the pulse even if the FADC
was saturated. This FADC data was used for improving the analysis of
decaying muons which occur after high energy muon events, or high energy
fully-contained (see Chapter 6) events.

4.4

Water purification system

The 50 ktons of pure water used in Super-K is taken from undergroundwater in Kamioka mine. Small dust, ions, and bacteria are included in theunderground water. Those impurities shorten the light attenuation length,
and make worse the light collection efficiency when they adhere to the surface
of a PMT. Also, radioactive elements in the water such as 222 Rn and 238 U emit
the electrons via their beta decays, and act as serious background sources.
Therefore, a high purification system is needed to reduce the contamination of these elements as much as possible. An overview of the water
purification system is shown in Figure 4.15. The water is constantly circulated through the water purification system with a flow rate of about 30 ∼60 tons per hour.
The processes of the systems are as follows:• Water Filter:
Removes large contaminants (∼1µm) such as dust. 222 Rn attached tothe dust is also removed.
• Heat Exchanger
Keeps the temperature of the water passing through here at around14◦ C. The water heated by the pumps of the water purification systemcauses an increase of bacteria, and also increases the dark rate of the
PMTs. Also, any temperature gradient in the tank may cause strong
convection which results in poor water transparency.
• Ion Exchanger:
Removes metallic ions such as Fe2+ ,Ni2+ , etc. The resin which has an
ion-exchange group with a 3 dimensional retiform structure is installed.
85Figure 4.15: The water purification system.

86• UV sterilizer:
Kills bacteria by irradiating with ultraviolet light.
• Rn-less-air dissolving system:
Dissolves radon free air into the water to improve the radon removal
capabilities of the vacuum degasifier.
• Reverse Osmosis filter:
Filters the contaminants heavier than mass of 100 molecular weightusing a high performance membrane.
• Vacuum Degasifier system:
Removes the dissolved gases with 96% and 99% efficiency for radon andoxygen, respectively.
• Cartridge Ion Exchanger:
Further high performance ion-exchange resins selectively remove ionswith 99% elimination efficiency.
• Ultra Filter:
These filters the contamination by very tiny holes, and can remove
elements of a few nm in size.
• Membrane Degasifier:Further removes dissolved radon and oxygen gases.
By circulating the water in this purification system, contamination isremoved. After the circulation, the radon level of the injected pure water
is reduced by 10−3 Bq/m−3 level. The light attenuation length of the purewater is 80 ∼ 90 m which is enough longer than the detector size.

4.5

Air purification system and Radon hut

The radon concentration of the mine air in the access tunnel to the experimental site has a strong seasonal variation of 2000 ∼ 3000 Bq/m3 during
summer and 100 ∼ 300 Bq/m3 during winter. To keep the radon concentration lower, fresh air from outside is pumped into the Super-K dome area
at a rate of 10 m3 /min through an air duct along 1.8 km from the outside.
As a result, typical radon concentration in the Super-K dome air is 20 ∼ 30
mBq/m387

In addition, radon-free air is injected above the water surface inside theSuper-K tank to prevent the radon gas from dissolving into the pure water.
Outside the mine entrance to Super-K, there exists a prefabricated hut whichcontains the radon-free air system. Radon free air is generated by drying the
input and passing it through charcoal filters. The carbon in the charcoal
absorbs the radon gas thus preventing it from entering the detector. The airis then filtered and injected into the region above the water in the tank. The
injected air concentration is about 3 mBq/m3 . The air flow rate is about 18
m3 /hour. The schematic view of the radon-reducing air system is shown in
Figure 4.16.

Figure 4.16: The air purification system.
The processes of the air purification system are as follows:• Compressor:
Compresses air to 7 ∼ 8.5 atmospheric pressure.
• Air Filter (0.3 µm):
Removes dust in sizes of ∼ 0.3 µ m.
• Buffer Tank:
Stores the air.

88

• Air Drier:
Dries the air and removes CO2 gas to improve the radon removal capability in Carbon Columns.
• Carbon Columns:
Removes radon gas using activated charcoal.
• Air Filter (0.01 µm):
Removes smaller dust and particles of ∼ 0.01 µm.
• Cooled Charcoal Columns:
Removes the remaining radon gas further with the charcoal cooled down
to -40 ◦ C.

89

Chapter 5
Calibration
Because Super-K is essentially detecting a small number of photons travelingin the water, the precise measurement of the charge and timing for each
PMT is crucial, and the knowledge of the water quality is also important.
Those are the main subjects of all the initial detector calibration works, anddescribed in this chapter.
The initial calibrations were done at the beginning of each experimental
phase. In this thesis, we describe the calibrations based on SK-III because
the method of calibration is not so different among all the phases.

5.1

Gain calibration

5.1.1

HV determination

Before the installation of the PMTs, 420 PMTs were calibrated as “standard
PMTs” which had adjusted the applied high voltage and had gain of 6 ×
106 . A schematic view of the gain measurement for the “standard PMT”
is shown in Figure 5.1. A Xe flash lamp, placed inside a box, emitted lightthat was guided by optical fibers through a fiber bundle to two Avalanche
Photodiodes and a 20-inch PMT located in another box.
The target gain of the standard PMT was set to 6 × 106 . The relationshipbetween the gain and the applied high voltage isGain(i) = αi × HV (i)βi(5.1)

where α and β are parameters specific to each PMT. To fix the parameters, the relation of the output charge from the 20-inch PMTs and the appliedhigh voltage were measured using the setup in Figure 5.1. The light intensityof the Xe lamp was monitored and corrected by APDs. Because the output
90

Figure 5.1: Schematic view of our setup for the precise “standard PMT ” gain
measurement. A Xe flash lamp, placed inside a box, emitted light that was
guided by optical fibers through a fiber bundle to two Avalanche Photodiodes
and a 20-inch PMT located in another box.

charge was proportional to the PMT gain, we could assume the α and β in
the Eq. 5.1 for each standard PMT.
As a result, the applied high-voltages for the 420 standard PMTs were
determined. The gain dispersion among the 420 PMTs after the HV determination was 0.4% RMS.
After the PMT mounting, the standard PMTs were mounted at the positions shown in Figure 5.2
The HV determination of the “non-standard PMTs” were done after the
PMT mounting. The HV was set so that the gain for each PMT would
produce for a flash of light from the scintillator ball an observed charge thatmatched the charge observed by the standard PMTs. The schematic viewof the setup for gain calibration is shown in Figure 5.3. Light emitted fromthe Xe lamp went through the UV pass filter into the scintillator ball at theSuper-K tank center. The scintillator ball diffused input light uniformly andthe observed photoelectrons in each PMT were around 50 p.e. in this system.
Another optical fiber went to a monitor PMT and generated a calibration
trigger.
However, the received number of p.e. in each PMT was not uniform in
the method shown in Figure 5.3, since the distance of each PMT from thescintillator ball was different and also the water conditions may be different
related to the tank position. To compare the output charge of the nonstandard PMTs with near-standard PMTs, PMT grouping was done as shown
91

Figure 5.2: The location of “standard PMTs” inside the Super-K inner detector. The red points indicate the locations of standard PMTs.

in Figure 5.4. The PMTs were divided into 17 groups for barrel PMTs and 8groups for top and bottom PMTs, and each group included 9 - 12 standard
PMTs.
In addition, the fine correction of the output from each PMT was doneusing the equation
Qobs × r2
Qcorr =
(5.2)
faccept (θ)
where Qcorr is the corrected charge, Qobs is the charge observed by the PMT,
r is the distance to the scintillator ball, and θ is the acceptance angle of the
PMT to the scintillator ball. The mean of Qcorr of the standard PMTs in thesame PMT group was calculated and labeled as Qmean . The supplied HV set
for PMT i in the same group was determined from the equation
1

i
i
HVnew
= (Qicorr /Qmean ) γ × HVcurrent

(5.3)

1
is the HV applied temporarily at the calibration, and γ
where HVcurrent
is the specific value for each PMT provided from Hamamatsu.
As a result of these procedures, the relative output charge between all
the PMTs was adjusted to within 1.3%, as shown in Figure 5.5.

92

Figure 5.3: A schematic view of the setup for gain calibration using the Xe
lamp.

93

Figure 5.4: The PMT grouping method (left: for barrel PMTS, right: for
top and bottom PMTs). Each barrel PMT group had three layers; there are
17 groups. Top (bottom) PMTs were grouped by the distance from the tankcenter; there were 8 groups for both the top and bottom of the tank.

10

3

10

2

ID
Entries
Mean
RMS

10
10972
0.99980.1272E-01

10

1
0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Figure 5.5: The deviation from the target charge output after HV determination for the all PMTs. The distribution has a width of 1.3% RMS.

94

5.1.2Absolute gain calibration

The uniform PMT gain was set at the calibration as Chapter 5.1.1. To know
the initial number of photoelectrons from the obtained charge, we needed toknow the conversion factor between the charge read out by the electronics
and the inputted number of photoelectrons. This conversion factor is called“pC2p.e.” and this factor means the average absolute gain among all PMTs.
The average absolute gain can be measured by the charge distributionof the 1 photoelectron (1 p.e.) input. To input the single photons for each
PMT uniformly, we used a Ni-Cf calibration source. The schematic viewof the Ni-Cf source is shown in Figure 5.6. The 252 Cf neutron source wasput in the center of the vessel. The vessel had a cylindrical shape with 20
cm height and diameter and it was filled with Ni wire and water. 252 Cf
caused α decay or spontaneous fission with a halflife of2.645 years. When aspontaneous fission occurred, 3.8 neutrons were emitted on average. Emitted
neutrons were captured by surrounding Ni wire after it was thermalized bywater in ∼ 200 µsec and gamma-rays with 6 - 9 MeV were emitted. Those
gamma-rays had a travel length of ∼ 50 cm, and emitted gamma-rays via
Compton scattering or pair production of electrons. Those electrons could
emit the Cherenkov light if they were above the Cherenkov threshold. The
light intensity of the Cherenkov light induced from one α decay of the Cf ateach PMT was 0.004 p.e./PMT. Thus more than 99% of observed light wasdue to single p.e..
The obtained 1 p.e. distribution in SK-III is shown in Figure 5.7. The
units of the horizontal axis of Figure 5.7 are pico-Coulombs (pC), which is
the output charge from the read-out electronics. To know the conversion
factor “pC2p.e.”, we calculated the average value of the distribution shownin Figure 5.7 byP
xi yi
pC2p.e. = P(5.4)
vi
where i is the bins of the horizontal axis of Figure 5.7. From Eq. 5.4, thepC2p.e. is calculated and output charge and the input number of photoelectrons are related. This value varied due to the secular change of PMTs andthe changes of mounted PMTs in each period. The pC2p.e. values for eachSuper-K phase are shown in Table 5.1.

95


Figure 5.6: A schematic view of the Ni-Cf source.

Super-K phase
SK-I
SK-II
SK-III

pC2p.e.
2.055
2.297
2.243

Table 5.1: The pC2p.e. values for each Super-K phase.

96

eventx 10 2
9000
8000
7000
6000
5000
4000
3000
2000
1000
0

0

2

4

6

8

10

pC

Figure 5.7: The 1 p.e. distribution in SK-III. The peak around 2.2 pC is the
1 p.e. peak. The cut off around 0.5 pC come from the ATM’s threshold.

97

5.1.3

Relative gain calibration

The relationship between the output charge and number of hits seen in a
PMT is described as
Qobs (i) ∝ Nphoton (i) × QE(i) × Gain(i)Nhit (i) ∝ Nphoton (i) × QE(i)i = 1, ....,
PMT sequential number

(5.5)
(5.6)

where Nphoton is the number of photons which reached a PMT photo-cathode,QE the quantum efficiency, and “Gain(i)” the gain for each PMT. We used
Eq. 5.5 and Eq. 5.6 to remove the factor of the QE and got the gain by taking
the ratio of Qobs to Nhit as follows
Gain(i) ∝Qobs (i).
Nhit (i)(5.7)

To know the relative gain from Eq. 5.7, we made the measurement twice
using the same “diffuser ball” setup as shown in Figure 5.8. First, a N2 laser
pulse was divided in the laser module. One part of the pulse was sent toa trigger PMT, which made an external trigger for the timing calibration
event. The other part of the pulse was sent to a dye laser module, producing
a dye laser pulse. The dye laser pulse (wavelength; 398±5nm(FWHM), pulse
width 0.2nsec) was then sent through a variable filter used to adjust the laser
intensity. After traveling through a 70 m optical fiber, the dye laser pulse was
emitted in the detector from a diffuser ball. In this calibration, two different
light intensities were used. The first setup was at high light intensity; thesecond at a low intensity. The low intensity measurements were used toestablish the hit rate. The average charge seen per event in a PMT during
the high intensity setup was then divided by the hit rate of the PMT during
the low intensity runs.
The distribution of the relative gains for each PMT is shown in Figure5.9. As seen in this figure, the RMS of the relative gain was 5.9%, due to the
QE dispersion. The effect of the relative gain was corrected using this result.

5.2

Charge linearity calibration

Non-linearity effects were observed in the region less than ∼ 50 p.e. Thiseffect arose from the ATM. The charge in the QAC was affected by thecondenser discharge when the QAC was waiting to be read out by ADC.
To understand the effect of non-linearity, a calibration using a setup similar98

0.CUGTPORWNUGYKFVJPUGE&[G.CUGTPORWNUGYKFVJPUGE



5-+&



 2/6

8CTKCDNGHKNVGT 

N

Figure 5.8: Setup for the relative gain measurement.

99

Figure 5.9: Distribution of relative gains for all ID PMTs. The mean value
is normalized to be equal to 1.

to Figure 5.8 was carried out. In this calibration the diffuser ball was put
off-center and data with various laser intensities was taken. At each laser
intensity, we assigned the monitor PMTs as those which received enoughphotons in the linear p.e. region, i.e., 65 ∼ 180 p.e. Using the output fromthe monitor PMTs as a monitor of the light intensity, the linearity of the
PMTs which received photons less than 50 p.e was investigated.
The result of the linearity measurement is shown in Figure 5.10. The
horizontal axis is the expected number of p.e.s which was estimated from themonitor PMT, and the vertical axis is the deviation of the observed numberof p.e.s from the expected number of p.e.s. From this figure, about 6% nonlinearity was observed at around 1 p.e.. The non-linearity was corrected foreach ATM channel using this result.

5.3

Timing calibration

The timing of all PMTs must be calibrated so that the event vertices andtrack directions are reconstructed accurately. To obtain correct timing, thefollowing must be considered: the light intensity of each PMT, the length

100Figure 5.10: Result of the linearity measurement. The horizontal axis is
the expected number of p.e.s which is estimated from the monitor PMT,
and the vertical axis is the deviation of the observed number of p.e.s fromthe expected number of p.e.s. Red points mean the mean deviation of eachregion. The reason for the gap seen around 60 p.e. is that the normalizationof the deviation is done around here.

101T [ns]of the cable between each PMT and the electronics, and the process time ofelectronics. Different light intensities can cause different triggered timings,
the so-called “time walk”. Time walk exists because larger charge hits exceed the TDC discriminator threshold earlier than those with less charge,
even though the hit PMT gets photons with the same timing. The timing
calibration for Super-K ID PMTs was done using a correction table for time
walk and overall process time for each PMT. This calibration used the same
setup as the relative gain calibration shown in Figure 5.8.
The calibration data were taken while changing the intensity of the lightemitted from the diffuser ball. Using a variable filter, the light intensity was
adjusted from the 0 p.e. level to a level of high intensity (250p.e.), whichcaused saturation of the electronics.
The result of this calibration is shown in Figure 5.11. The horizontal axis
shows the charge of each hit and the vertical axis shows hit timing. A timing
correction based on this result is applied for the dataset.
990
980
970
960
950
940
930
920
910
900
890
















3DKP

Figure 5.11: The relationship between timing and charge. Horizontal axis
shows charge of each hit and vertical axis shows hit timing.

102

5.4

OD calibration

The OD is used primarily to identify incoming cosmic rays and neutrino
interactions with particles leaving the ID as well as to serve as a passive buffer
for low energy events. The OD has also been used for rough reconstructionof very high energy events which saturate the ID [117]. Unlike the ID, theOD is not used for precision reconstruction. Therefore, requirements for OD
calibration are not as stringent as for the ID. The OD charge reconstruction
accuracy of about 10-20% and timing to 5-10 ns are generally sufficient forSuper-K physics needs.
OD time and charge calibrations were done using cosmic ray and dark
rate data, and also using a laser the same as that used for ID calibration.
For SK-III, two methods were used to convert ADC counts to photoelectrons (p.e.). To determine charge per p.e. at low light levels, where responseof the PMT and electronics was reliably linear, the laser was flashed at very
low light levels. Occupancy was chosen such that less than 10% of hits would
correspond to multiple photoelectrons, and the mean ADC value for the hit
distribution was chosen as the single p.e. level.
A “dark rate method” for charge calibration using OD hits outside thetrigger time window was also used. Hits preceding the trigger time had a highprobability of being single photoelectrons. Single hit pedestal-subtracted
ADC distributions for each tube for times preceding normal data triggers
were accumulated, and the mean value was taken as the ADC counts per
p.e.. The results for the laser and dark rate methods were found to be inagreement within 10%, and so the dark rate method was primarily used.
The counts per p.e. for typical PMTs as a function of time, for nine example
PMTs, for a 4.5-month period during SK-III is shown in Figure 5.12.
For the timing, the timing offset between the ID and OD was calibrated
by laser and checked with cosmic ray muons. From those measurements, thetiming offset was found to be within a few ns, and the OD time resolution
within about 10 ns.

5.5

Water transparency measurement

Knowing the water condition is important for understanding the propagationof Cherenkov light and estimating the energy of primary particles. Scatteringand absorption were calibrated by laser injection. The transparency wasmeasured by cosmic ray muons.

103Counts per pe vs run, SK III
12

12

12

10

10

10

8

8

8

6

6

6

30000 31000 32000

30000 31000

32000

12

12

12

10

10

10

8

8

8

6

6

6

30000 31000 32000

30000 31000

32000

12

12

12

10

10

10

8

8

8

6

6

6

30000 31000 32000

30000 31000

32000

30000

31000 32000

30000

31000 32000

30000

31000 32000

Figure 5.12: Counts per p.e. for typical PMTs as a function of time for nine
example PMTs, for a 4.5-month period during SK-III . The horizontal axis
is the run number, which corresponds to the time, and the vertical axis is
the conversion factor from ADC counts to p.e..

104

5.5.1

Light scattering measurement using a laser

The light attenuation was determined by two scattering parameters and anabsorption parameter as
1(5.8)
αabs + αRayleigh + αM iewhere, αabs is the absorption parameter, αRayleigh is the Rayleigh scatteringparameter, and αM ie is the Mie scattering parameter.
Rayleigh scattering occurs when the light wavelength is larger than thesize of scattering particles. On the other hand, Mie scattering occurs when
the light wavelength is similar to the size of the scattering particles.
To estimate those parameters, a laser system for the water scattering
measurement was developed. The schematic view of this system is shown in
Figure 5.13. The laser flash was injected from the top hole every six seconds
during the usual data taking. Four wavelength of laser were used: 337, 371,
400, and 420 nm to measure the features of the scattering and the absorption
at the different wavelengths.
L=

LASER
Optical Fiber

Top

337nm
371nm
400nm
420nm
NUM
2
RUN
8399
EVENT
3919
DATE **-Mar- 1
TIME
5:34:38
TOT PE:
820.0
MAX PE:
19.6
NMHIT :
331
ANT-PE:
13.6
ANT-MX:
2.7
NMHITA:
17

Scattering

RunMODE:NORMALTRG ID :00010111
T diff.: 2.08
us
:0.208E-02ms
FSCC:
2FF90
TDC0: 8899.2
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 0

BottomFigure 5.13: A schematic view of the laser system for the water scattering
measurement.
The laser data and the event simulated by Monte Carlo were compared105

to tune the parameters. The parameters were tuned to make the charge andtiming distributions of the simulated events agree well with that of the laser
event. The parameters obtained by this calibration are shown in Figure 5.14.

attenuation coefficient(1/m)

Light scattering measurement

-1

10

-2

10

absorption

Rayliegh scattering-3

10
Mie scattering

300

400

500

600

700

wavelength(nm)Figure 5.14: Absorption and scattering parameters obtained by laser calibration. Stars indicate the results obtained by this measurement. Lines are
extrapolated from that result.

5.5.2

Water transparency measurement using cosmic
ray muons

Water transparency is also measured using Cherenkov light from cosmic raymuons passing through the detector. Such energetic muons are minimum
ionizing particles, and their deposited energy is around 1.5 MeV/cm.
Vertical downward muons were selected for this measurement. Under
the assumption that the light detected by each PMT is not scattered, thedetected number of photo-electron is expressed by:
µ
¶
l
f (θ)
· exp −
(5.9)
Q = Q0 ·l
Lwhere Q0 is a constant, f (θ) is the PMT acceptance, l is the photon
path length and L is the attenuation length. The muon track was recon106

structed from the position of the PMT which received the Cherenkov light.
A schematic view of this measurement is shown in Figure 5.15.

: Cherenkov
Photons

Inner Tank

20-inch
PMT

42o

li

Θi

Cosmic Muon

i’th PMT

Figure 5.15: A schematic view of the measurement for water transparency.
Arrows from the muon track show the trajectories of Cherenkov photons
and li shows the flight length of the Cherenkov photons detected by the i-th
PMT.
The value log (Q·l/f (θ)) as a function of l in a typical run is shown in
Figure 5.16. With the dataset of Figure 5.16, we can solve Eq. 5.9 and know
the attenuation length. The attenuation length was estimated to be 95 m forthis data set.
Since the cosmic ray muons are measured during the normal data taking,a continuous check of the water transparency is possible. Figure 5.17 shows
the time variation of the attenuation length of water during the entire period
from SK-I to III.

5.6

Energy scale

To know the energy of the primary particle which generated the Cherenkov
light, several sources were used for the calibration. Super-K’s physics target107

log(Ql/f( θ))500

RUN 3106

P1
P2

5.987
-0.9487E-04

1000

2000

3000

0.4609E-03
0.4444E-06

400
300
200
0

4000

5000
l (cm)

attenuation length [ m ]Figure 5.16: The value log (Q·l/f (θ)) as a function of l in a typical run

150
using bottom PMT
140
130
120
110
100
90
80
70
60
50
01/01/1996 01/01/1998 01/01/2000 01/01/2002 01/01/2004 01/01/2006 01/01/2008 01/01/2010
date

Figure 5.17: Time variation of water attenuation length from SK-I to III.

108

ranges from a few MeV to a few hundred GeV. Thus we use sources whichhave different energies for the energy scale calibration.
For energies of a few MeV to a few tens of MeV, the LINAC and DT
calibration system were used. In the former, an electron beam whose energy
is 5 - 18 MeV is injected from the electron linear accelerator (LINAC) [118].
In the latter, neutron emission from deuterium and tritium collisions is used[119]. These particles have energies from around 6 to 10 MeV depending on
the decay mode.
For energy around 50 MeV, decaying electrons from cosmic ray muons
which stopped inside the detector were used. The energy of the electron
spreads around 50 MeV.
For the energy around 130 MeV, gamma-rays from π 0 which were produced by neutrino interactions were used. The gamma-rays from the π 0
decay can be used as a calibration source since the π 0 invariant mass is fixed.
For energies of 200 ∼ 500 MeV, the Cherenkov opening angle of low
energy stopping muons can be used. Muons whose energy range is 200 ∼500 MeV are traveling with speeds that are enough smaller than the speedof light that we can see the difference of the opening angle depending on
the parent muon’s energy, as shown in Eq. 4.1. Measuring the relationshipbetween the estimated parent muon’s energy and its light emission, we cancalibrate the energy of this range.
For energies of 1 ∼ 10 GeV, the track range of high energy stopping muons
is used. In this energy range, the energy of the muon is roughly proportional
to the track length. Measuring the relationship between the estimated parent
muon’s energy from the track length and its light emission, we can calibrate
the energy of this range.
The details of each energy scale calibration are described in Reference[112].
The stability of the energy scale is shown in Figure 5.18. The meanvalue of momentum/range for the stopping muons, and the mean value of
momentum for the decay electrons are shown as a function of time. The
maximum RMS of the variation among these calibration sources is given as
0.88%, 0.55%, and 1.79% for SK-I, SK-II, and SK-III, respectively.
The summary of each absolute energy calibration is shown in Figure 5.19.
The uncertainty of the absolute energy scale was estimated to be less than
0.74%, 1.60%, and 2.08% for SK-I, SK-II, and SK-III, respectively. To consider the time variation of the energy scale, the RMS of the variation was
combined with the energy scale uncertainty. In summary, 1.1%, 1.7%, and2.7% were estimated as the energy scale uncertainties for SK-I, SK-II, and
SK-III, respectively.

109

e momentum(MeV/c)

0

43
42
41
40
39
38
37
36
2400

250

500

µ momentum/track(MeV/c/cm)±1%

750 1000 1250 1500 1750 2000
days from 1996/Apr./1

±1%

0

250

500

SK-II

2600

2800

3000
3200
3400
days from 1996/Apr./1

2.6
2.55
2.5
2.45
2.4
2.35
2.3
2.25
2.2
2400

SK-III

45
44
43
42
41
40
39
38
3800 3900 4000 4100 4200 4300 4400 4500
days from 1996/Apr./1

750 1000 1250 1500 1750 2000
days from 1996/Apr./1

SK-II

2600

2800

3000
3200
3400
days from 1996/Apr./1

SK-IIIµ momentum/track(MeV/c/cm)

e momentum(MeV/c)

SK-I

2.6
2.55
2.5
2.45
2.4
2.35
2.3
2.25
2.2

µ momentum/track(MeV/c/cm)

e momentum(MeV/c)

SK-I

45
44
43
42
41
40
39
38

2.6
2.55
2.5
2.45
2.4
2.35
2.3
2.25
2.2
3800 3900 4000 4100 4200 4300 4400 4500
days from 1996/Apr./1

Figure 5.18: The time variation of the reconstructed momentum of decay
electrons (left) and the averaged momentum/range of stopping muons (right)
as a function of elapsed days for each Super-K period. Dotted (dashed) lines
show ±1 %(±2 %) from the mean value in each Super-K period.

110(MC - DATA) / DATA (%)

SK-I
8
6
4
2
0
-2
-4
-6
-8

(MC - DATA) / DATA (%)

10

2

3

4

10
10
10
momentum range (MeV/c)

10

5

SK-II
8
6
4
2
0
-2
-4
-6
-8
10

(MC - DATA) / DATA (%)µ rangeµ angle0π massdecay eµ rangeµ angle0π massdecay e
2

3

4

10
10
10
momentum range (MeV/c)

10

5

SK-III
8
6
4
2
0
-2
-4
-6
-8
10

µ rangeµ angle0π massdecay e
2

3

4

10
10
10
momentum range (MeV/c)

105Figure 5.19: The summary of the absolute energy scale calibration for eachSuper-K period. The horizontal axis shows the momentum range and thevertical axis shows the deviation of the data from the Monte Carlo predictions.
111

Chapter 6
Analysis for the upward-going
muon events
6.1

Overview of event categories for atmospheric neutrinos

In the analysis in Super-K, the atmospheric neutrino events can be divided
into several sub categories. The neutrinos interact with the water inside thedetector or the surrounding rocks via reactions described in Chapter 6.3.2.

6.1.1

Contained eventsContained events are produced from the neutrinos which interact with thewater in the ID of Super-K. From neutrino interactions via CC and NC,
charged particles are produced as described in Chapter 6.3.2. The primary
produced charged particles, or secondary produced charged particles from thedecay of the primary particle produce Cherenkov light. The Cherenkov light
produced by such charged particles is reconstructed to obtain the position of
the neutrino interaction, energy of the particles, and so on, Contained eventsare further subdivided into two categories: fully contained (FC) and partiallycontained (PC). In the former, all of the produced secondary charged particles
stop inside the ID volume. In this category, we can reconstruct the visibleenergy. The typical energy of neutrinos which produce this category of eventsis below a few GeV. In the latter, the produced secondary charged particles gooutside the ID. The typical energy of neutrinos which produce this categoryof events is around 10 GeV.
The number of contained events due to atmospheric neutrinos as a function of the parent neutrino energy (Eν ) is shown in Figure 6.1.
112



1000




')(+*

FC ν

 

750

 



Events / 1000 days ')(+, µFC ν-.(/ * e



PC νµ

500
 

250


0 "!$# %
150

"! %


"! &


Up-Stop νµFigure 6.1: Number of contained events from atmospheric
Up-Thru νµ neutrinos as afunction of the parent neutrino energy (Eν ). Three categories of contained
event are shown: FC from νµ (dark red solid line), FC from νe (red dashedline), and PC from νµ (red line). The expected number of events in 1000days are shown.

6.1.2

100

50 going muon event
UpwardMuon neutrinos interact in the rock surrounding the detector produce muons
via charged current interactions. If the energy of the incoming neutrino ishigh enough, the muon produced by the neutrino will enter the detector
2
3 muons
4 from5 cosmic
and emit Cherenkov-2light.-1To separate neutrino-induced
ray muons, we select only upward-going muons, since the background fromdownward-going cosmic ray muons overwhelms any neutrino-induced muons
from above.
ν
Upmu events are divided into three categories: stopping, non-showering
through-going, and showering through-going. If upward-going muons stopin the detector, they are categorized as “stopping.” Stopping upmus are
the lowest energy portion of the upmu sample. Upward-going muons which
fully traverse the detector are classified as “through-going.” The category ofthrough-going is then further subdivided into “showering” (if the event has
accompanying radiation due to radiative energy loss) and “non-showering”(otherwise). Generally, neutrinos with energy range around 10 GeV produce
stopping upmus, around 100 GeV produce non-showering through-going up-

0
10

10

1

10 10 10E (GeV)

113

10

10

Events/1000 days

90
Stopping

80
Non-showering

70
Showering

60
50
40
30
20
10
0
1

10

10

2

10

3

10

4

10

5

Eν(GeV)

Figure 6.2: The number of upmu events due to atmospheric neutrinos asa function of the parent neutrino energy (Eν ). Three upmu categories areshown: stopping (black solid line), non-showering (red dashed line), andshowering (blue dotted line). The expected number of events in 1000 days
are shown.
mus, and those with more than 1 TeV produce showering upmus.
The number of upmu events due to atmospheric neutrinos as a functionof the parent neutrino energy (Eν ) is shown in Figure 6.2.
The fraction of each upmu category as a function of parent neutrinoenergy (Eν ) is shown in Figure 6.3. For typical energies, they are: A:B:C= 0.73:0.20:0.07, 0.10:0.62:0.28, 0.02:0.50:0.48 at Eν =10, 100, 1000 GeV,
respectively. These fractions were obtained from a Monte Carlo simulation.
A schematic view of the each category of events are shown in Figure 6.4.

6.2

Upmu dataset

The upmu datasets in SK-I and SK-II are summarized in Reference [81]. In
this thesis, the upmu dataset in SK-III is described. The schemes of the114fraction

1

stopping
non showering
showering

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1

10

10

2

10

3

10

4

Eν(GeV)

Figure 6.3: The fraction of each upmu category as a function of the parent
neutrino energy(Eν ). Three upmu categories: stopping (black solid), nonshowering (red dash), and showering (blue dot) are shown. The sum of thefraction for each of three categories is normalized to 1. The MC simulation
for atmospheric neutrinos is used to calculate this.
producing of the upmu datasets are basically common among those three
Super-K phases.
The rate of events which is acquired by HE trigger is around 10 Hz.
More than 80% of them are caused by background sources such as cosmic
ray muons and environmental radiation. A smart selection method is needed
to select only the upmu events from this. Especially important for the upmu
sample is to reduce the events caused by cosmic rays from the near-horizontal
direction.
A flow chart of the upmu sample’s data reduction is shown in Figure 6.5.
The detail of each step is described in the following sections.

6.2.1

Upmu fitters

To fit the PMT light pattern, several fitters were used in the 1st and 2nd
reduction stages. They can judge whether it is a stopping or through-going
muon and estimate the muon tracks. At each reduction step, the following
fitters were applied with certain criteria.

115    
0 &12     0 "#  µ$&%    %'  µ" %   &(*),+- '/.#%   -((     !

)

Figure 6.4: The categories for observed atmospheric neutrinos in Super-K.

116  ?8@ A B @ C(DEGF HICJ"J     !" #$     % '&  ()

?)KLK,A B @ C(D EGFHICJ,J*,+-/.0!
%1 /'  23.0'45   
6 782 9.:;   <, 5&,.05=>4& 
Figure 6.5: A flow chart of the upmu reduction.

117

Stopmu1st
In Super-K, pedestal data is taken every 30 minutes. In this fitter, suchpedestal events and the events which are caused when the DAQ of either the
ID or OD has a problem are removed. Also the hit pattern of light in the OD
is checked. “OD PMT clusters,” in which a couple of neighboring PMTs of
OD hits with similar timing are found, and this fitter judges particles whichpass through the OD. This information is useful to know if there are charged
particles which enter or exit from the detector.
Muboy
This fitter mainly uses the information of ID. “ID PMT clusters” in which a
couple of neighboring PMTs of ID hits with similar timing are searched for. If
this fitter find more than 2 clusters in the same event, the charge informationof the each cluster is precisely investigated. When muons penetrate the ID,
the PMTs located near the exit point of the muons receive more Cherenkov
light than PMTs located near the entrance point, due to the directivity of theCherenkov radiation. Thus, if the mean charge and maximal charge of the
PMTs forming the one of the clusters is greater than that of the other cluster,
this fitter judges the muon to enter the ID near this cluster and exits near
the other cluster. This information is useful to remove down-going muons
produced by cosmic ray muons. Also this fitter can remove “corner clippers”
which brush the corner of ID (see also Chapter 6.2.7) and “multiple-muons”
where many muons from a cosmic ray shower come into the ID with the sametiming.
Stopmu2nd
Combining the previous 2 fitters, we can choose the stopping muon events.
This fitter is applied to the events which are categorized as stopping. At
the first step, the entrance region of the muon is estimated roughly fromthe ID cluster. Next, the PMT hit pattern is simulated when the muons
travel from this entrance region to various directions, and the agreement of
the simulated pattern with real data is checked. Finally, the precise entrance
point and muon direction is estimated by this method.
Thrumu1st
This fitter is applied to the events which are categorized as through-going by
Stopmu1st and Muboy. Using the same method as Stopmu2nd, the entrance
and exit point and muon track are estimated.
118

Thrumu2nd
Sometimes Thrumu1st doesn’t work correctly. The main reason is due tomultiple muons and high energy muons with accompanying radiative energy
loss. This fitter is applied to the events which Thrumu1st failed to fit. In
this fitter, the light pattern from multiple muons and radiation from highenergy muons can be simulated, and an estimate of the entrance and exit
points and the muon track of such events is made.

6.2.2

1st reduction

The 1st reduction process is applied to all of the HE triggered events.
This reduction process is one of the contents of the realtime processes tobe applied as soon as the raw data is taken. Only Stopmu1st and Muboy
fitters are used here. In Stopmu1st, the events which occurred when either
ID or OD had problem and very low energy events in which the total numberof p.e.s in all ID PMTs is below 100 p.e. are removed. In Muboy, the events
for which the reconstructed direction by Muboy gave cosz > 0.2 for throughgoing events, and cosz > 0.3 for stopping events were removed. z means theangle between reconstructed direction of the muon and the zenith. Cosz =-1 means the upward direction and cosz = 0 means the horizontal direction.
There were 900k of HE triggered events per day. They were reduced toaround 10k events per day by this reduction.

6.2.3

2nd reduction

If both Stopmu1st and Muboy judged the event as an upward (downward)
going event with a large goodness value of the fit (> 0.35), the events was
immediately saved (removed). 90% of the events were decided as saved or
removed in this step. In Figure 6.6, an example of the Muboy goodness isshown. The judgment of the event categories in Muboy is shown in Figure
6.7. The fitted muon direction by Muboy is shown in Figure 6.8.
If Stopmu1st and Muboy judged differently, orif the goodness value of thefitting was small, Stopmu2nd, Thrumu1st and Thrumu2nd were applied. If
Stopmu2nd, Thrumu1st, or Thrumu2nd judged the event as upward (downward) going with a large goodness value of the fit, the events were saved(removed). If the muon track was almost horizontal and it was difficult tojudge, the judgments from several fitters were considered comprehensively
and the final judgment was decided as shown in Figure 6.8.
The summary of the 1st and the 2nd reduction is shown in Table 6.1.

119eventevent/10days

Good fit

goodness

Figure 6.6: Example of the goodness of the Muboy fit for the dataset of 10days in the SK-III period. We defined goodness>0.35 as a good fit. The
inconsistency seen around goodness = 0.35 is because some of the eventswith goodness>0.35 were rejected in the 1st reduction.

120

    
!" # # $ "   % '& # $(

Figure 6.7: The example of the judgment of the event categories in Muboy.
We used the same dataset as Figure 6.6.
1st reduction
fitterreject
Stopmu1st
Low E(loose cut)
ID,OD off
Muboy
Low E
(loose cut) corner clipper
multiple µsaveothersupward µ

2nd reduction
fitterreject
Stopmu1st
Low E(tight cut)pedestal
Muboy
downward µ
Stopmu2nd downward µ
Thrumu1st downward µ
Thrumu2nd downward µ

saveothersupward µ
upward µ
upward µ
upward µ

Table 6.1: The summary of the 1st and the 2nd reduction for upmu events

6.2.4

Precise fitter

To reconstruct the events more precisely, we applied the precise fitter to theupmu candidate events. For events in which the total number of p.e.s in the
ID (POTOT) was very large, the fitter didn’t work well due to the saturated
PMTs. On the other hand, for events in which POTOT was very small, thefitter didn’t work well due to the lack of light information from the PMTs.
Thus, the fitter was applied only to events with 8000 p.e. < POTOT <121

event/10days

upgoing

downward

Figure 6.8: The fitted muon direction by Muboy. We used the same dataset
as Figure 6.6 and the events which were judged as through-going events areshown. We saved the up-going muons (cosz<0) and removed down-going
muons (cosz>0.1). The events ranging 0 ≤ cosz ≤ 0.1 are judged by not
only Muboy but also used the decision from other fitters.

122

175000 p.e. The following three types of fitters were used in this step:Upmu-fit
This fitter was developed for the reconstruction of the contained events at
first. It was tuned for the event reconstruction of upmus after that. This
fitter compared the number of p.e.s observed in each PMT with the expectedvalue, given some entry points and directions. Using χ2 -statistics, the many
combinations of entry point and direction were tested to search a pair which
gives the smallest χ2 .
OD-fit
The result of the upmu fit was swayed by the edge shape of the Cherenkov
ring. If the edge of the Cherenkov ring was very clear, the Upmu-fit could
estimate the muon track with high reliability. However, if the Cherenkov
ring was produced by a muon with radiative energy loss, the edge of theCherenkov ring is not clear due to the radiation. This fitter was useful for
fitting those events. Only the OD information was used. If more than 8neighboring OD PMTs were fit in the 800 ns time window, they were defined
as an OD cluster in this fitter. If more than 2 clusters were found in the same
event, the cluster with the earliest average time of PMTs in it was chosen as
the entrance cluster and the center of the cluster was decided as the entry
point. The cluster which had the maximum number of PMTs was chosen
as the exit cluster because if a muon passes through the OD when exiting
the detector, the light emission spreads widely due to reflection effects in the
OD. Also the center of the exit cluster is decided as the exit point. This
fitter is useless for stopping events.
TDC-fitThis fit consists of roughly two steps.
First is the charge-information-based step. In this step, the muon trackis assumed to have various track lengths and directions at first. For a given
track, the shape of the Cherenkov ring is simulated, and the fit selects the
track which well-matches that of the observed event. Second is the timinginformation-based step. The vertex and direction of the track is further
refined by maximizing a goodness function which depends on the timing
residuals of the PMTs.
The first and second steps are iterated until the distance between thevertex in two iterations is less than 50 cm.

123All three of the fitters are applied to all upmu candidate events. The
result from the fitter with the most reliable condition among the three isused for the final result of the precise fitter. The details of those fitters, andcriteria for the determination of the final result of the precise fitter is written
in Appendix B of Reference [120].
The angular resolutions of the precise fitter by event type for SK-III
are 0.96◦ , 1.05◦ , and 1.40◦ for stopping, non-showering through-going, andshowering through-going, respectively.
The result of this fitter is used for the following reductions.

6.2.5

3rd reduction (selection cuts)

These cuts are applied to divide the events into stopping or through-going.
The cut criteria are defined using variables which is calculated in the precise
fitter. They are:1, Selection cuts for through-going events:
Nentod ≥ 16

(6.1)

Nexiod ≥ 16

(6.2)

L ≥ 700(6.3)

F it dir(z) ≤ 0(6.4)

2, Selection cuts for stopping events:
Nentod ≥ 16

(6.5)

Nexiod < 16

(6.6)

F it M om ≥ 1.6(6.7)

F it dir(z) ≤ 0(6.8)

where, Nentod is the number of OD hit PMTs within 8m of the muon
entry point, Nexiod is the number of OD hit PMTs within 8m of the muonexit point, L is the estimated track length, F it M om is the muon momentum(GeV/c) which is estimated from the total number of p.e.s in the Cherenkov
ring in the ID, and F it dir(z) is the estimated cosine of the vertical angle(cos z) of the muon track with the definition of cos z = -1 is upward-going,cos z = 0 is horizontal.
Eq. 6.1 and 6.2 for through-going, Eq. 6.5 and 6.6 for stopping are used
for the judgment of whether the event is through-going or stopping.
124Eq. 6.3 and 6.7 are used to ensure the accuracy of the reconstruction.
If the muon travels a very short length in the ID, the accuracy of the reconstruction becomes worse because information from the PMTs is small.
Thus, only events for which muon track length in the ID is greater than 7m
are saved. In the through-going events, the track length in the ID is easily estimated from the entrance and the exit point, and the applied cut isbased on reconstructed track length as in Eq. 6.3. However, it has larger
uncertainty to estimate the length of the muon track for the stopping event
because the precise estimation of the stopping position is difficult. Thus the
track length is estimated from the muon momentum for the stopping event.
The muon momentum can be precisely estimated from the total number of
p.e.s in the ID. As shown in Eq. 6.3, we cut events for which estimated muon
momentum is less than 1.6 GeV/c which corresponds to the muon range of
7m in the water, as shown in Figure 6.9. Eq. 6.4 and 6.8 are the cuts to save
only upward-going event. The sample of the distributions of Nentod , Nexiod ,L (for through-going muons),and F it M om (for stopping muons) which areused for the selection cuts are shown in Figures 6.10 - 6.13.

*+ )
&('
% #$
"#
!

  

    
Figure 6.9: Muon range in the water. The muon momentum of 1.6 GeV/ccorresponds to 7m of muon range.

125event/321days

save

30

25

20

15

10

5

0

10

20

30

40

50

60

70

N_entod

event/321days

Figure 6.10: The selection cut using Nentod . A 321-day SK-III dataset isshown as an example. Nentod = 16 is used for the selection criteria.

140

stopping

through going

120
100
80
60
40
20
0

0

10

20

30

40

50

60

70

N_exiod
Figure 6.11: The selection cut using Nexiod . A 321-day SK-III dataset isshown as an example. Nexiod = 16 is used for the selection criteria.
126event/321days

through going event

25

cut
20

15

10

5

0

0

1000

2000

3000

4000

5000

fitted track length(cm)Figure 6.12: The 7m muon track cut for the through-going muon events.

stopping event

event/321days

cut
20
17.5
15
12.5
10
7.5
5
2.5
0

0

5

10

15

20

25

30

fitted momentum(GeV/c)

Figure 6.13: The 1.6GeV/c muon momentum cut for stopping muon events.

1276.2.6

Showering and non-showering separation

Very high energy muons which create showering events deposit energy bycatastrophic energy loss processes such as pair production, Bremsstrahlung,and photo-nuclear interaction. The energy loss processes of muons in waterand rock are shown in Figure 6.14 [121].

Figure 6.14: Muon energy losses in pure water(left panel) and rock(rightpanel) as a function of the muon energy. In the left panel, curve “a” is loss
due to ionization, “b” is total loss due to all radiative processes, “c” is thetotal energy losses “a + b” [121].
The corrected charge, which is the estimated total charge from the Cherenkov
emission produced from a charged lepton’s track, is used in the separation algorithm. The algorithm defines a χ2 -statistic, which compares the correctedcharge deposited over consecutive 50 cm intervals of track Qicorr with thecorrected charge averaged over the track, hQcorr i. The ionization deposits
charge with near uniformity in time whereas showering is associated withsudden deposition of energy. It also compares the corrected charge averaged
over the track with the expected value for non-showering muons, Q(l), which
is a function of track length. The resulting statistic is of the following form,

χ2 =

N
−2
X
i=3

Ã

[Qicorr − hQcorr i]2 [hQcorr i − Q(l)]2
+
2
σq2i
σQ(l)

!
, Qicorr −Q(l) ≥ −2 (6.9)

2where σq2i and σQ(l)are the statistical errors in Qicorr and Q(l), respectively.
N indicates the number of 50 cm bins in which the muon track is sub-divided.

128

The bounds of the sum are chosen to be at least a meter from the walls
where it is hard to characterize the corrected charge. The sum only includes
terms where Qicorr − Q(l) ≥ −2, which correspond to fluctuations above theexpected charge deposition from non-showering muons, to avoid the case thatthe calculated Qicorr is extremely low due to misfitting .
About 0.5% of the events in the Monte Carlo consist of through-going
muons with bad fits or stopping muons which are misclassified as throughgoing muons. These events show large values of χ2 even though the total
number of p.e.s in such events is very small. To eliminate these cases, wedefine another variable to distinguish between showering and non-showering:∆ = hQcorr i − Q(l) − δQ

(6.10)

where δQ is a free tuning parameter that must be adjusted dependingon the Super-K phase. The tuning parameter δQ is set such that the Monte
Carlo distribution of ∆ is peaked at zero.
Using the variables above, the selection cuts for showering events are
tuned and defined asif χ2 > 50
if χ2 ≤ 50

∆ > 0.5∆ > 4.5 − 0.08 × χ2

(6.11)(6.12)An example of the separation between non-showering and showering using
Eq. 6.12 for 10 years of Monte Carlo events is shown in Figure 6.15. In Figure
6.15, we show them divided into two cases of event samples, true showeringand true non showering, which are defined based on the true muon energy
loss per unit track length ∆E/L, with the separation value is 2.85 MeV/cm.
From the distribution as shown in Figure 6.15, the cut selects about 70 %of true showering events correctly. Those cuts provide reasonable purity andbackground contamination in forming a sample for astrophysical studies.

6.2.7

4th reduction

By the reduction steps applied so far, almost all cosmic ray induced downwardgoing muon events are removed. However, the events in which cosmic raymuons brush the corner of the Super-K tank are difficult to fit since themuon track is short and the timing difference of each OD cluster is also
small. Those events are called corner clippers. The fitting fails for almost all
corner clipper events. An example of the event display of a corner clipper isshown in Figure 6.16.
129

Figure 6.15: Distribution of ∆ vs χ2 for events from a 10 year Monte Carlosample with true showering events which have ∆E/L > 2.85 MeV/cm (left),
and true non-showering events which have ∆E/L < 2.85 MeV/cm (right)[122]. The solid line indicates the selection cut using Eq. 6.12.

130Figure 6.16: An event display of a corner clipper. This figure is the development view of the Super-K tank. The central figure is ID, and left upper figure
is OD. The PMT hits in an event time window are shown by the points. The
PMT timing is shown in colors. The color varies green, emerald green, blue,
magenta and red in order of the earlier hit timing. The red lines are thefitting result for the Cherenkov edge from the Muboy fitter (dashed) and theprecise fitter (solid). And the fitted muon entry and exit point are shown bystars. In this event the fitting result of the precise fitter doesn’t agree wellwith the Cherenkov edge.

131

In SK-I and SK-II, to determine the number of OD clusters for the cornerclipper was difficult. From SK-III, the OD segmentation was introduced asshown in Figure 4.10, and the determination was made easier. An exampleof the effect of OD segmentation is shown in Figure 6.17.
From SK-III, the 4th reduction has been introduced to remove the cornerclippers further. A precise OD cluster-fitting algorithm based on the OD
segmentation was newly developed. When this fitter judged the number of
OD cluster to be equal to or more than two and the fitting result of the Muboyand precise fitter are so different each other, those events are removed.
The reduction steps described above are the automated reduction steps.
The efficiency of the automated reduction for the selection of the upmu eventwas ∼ 100 % at the F IT DIR(z) ∼ 1 and ∼ 98 % at the F IT DIR(z) ∼ 0.
The efficiencies were estimated from the MC events described later. Almost
all upmu event are saved after the automated reduction.

6.2.8

Eye scanning

Finally, to check the mis-fitted events and the corner clippers which still
remain, all remaining event are visually scanned by researchers. We make a
final decision of whether the events are really upmu candidates or not using
the event display. For a cross-check, all events are scanned by two or threeresearchers to reduce the arbitrary selected event.
The typical examples of event display for stopping, non-showering, andshowering event are shown in Figure 6.18, 6.19, and 6.20, respectively.
The event rate after each reduction step as a function of livetime in SK-III
is shown in Figure 6.21. Also the summary of the event rate of the whole of
the SK-III period, for which livetime was 635.6 days, is shown in Table 6.2.
Reduction Step Avg. event/day
1st reduction
9900
2nd reduction
244
Precise fitter110
3rd reduction
3.7
4th reduction
1.9
Eye scan
1.5
Table 6.2: The summary of the event rates of the whole SK-III period (livetime: 635.6 days).

132

Figure 6.17: The upper figure shows the OD segmentation, and the muontrack (Red dashed arrow) used to check the effect of the OD segmentation.
The lower figures are the simulated light pattern of OD assuming the detector
in the period of SK-I (left) and SK-III (right). In SK-I, some of the lightwent into the top region, while in SK-III the light does not pass into the top
region due to the effect of the segmentation.

133

Figure 6.18: A sample event display for a stopping upmu event. In this event,
only one cluster in the OD is found and Cherenkov light proceeds upward in
the ID.

134

Figure 6.19: A sample event display for a non-showering upmu event. In
this event, two clusters in the OD are found and Cherenkov light proceeds
upward in the ID. Also the edge of the Cherenkov ring is relatively clear.

135

Figure 6.20: A sample event display for a showering upmu event. In thisevent, two clusters in the OD are found and Cherenkov light proceeds upwardin the ID. Also the edge of the Cherenkov ring is not clear due to the radiation.

136                  !  "     #%$&'(()

Figure 6.21: The event rate after each reduction step as a function of livetime
in SK-III (livetime: 635.6 days).

6.2.9

Background subtraction

Super-K is located 1000 m underground. However there are thin region ofrock around Super-K due to the shape of the mountain. In such regions,the cosmic muon rate is increased. The zenith (cos θ) and azimuthal (φ)
scattering distribution of stopping and through-going events in the SK-III
period are shown in Figure 6.22. Note that, the events shown in Figure 6.22
are the events saved after automated reductions, but only the cuts related tothe muon direction as Eq. 6.4 for through going and Eq. 6.8 for stopping inthe 3rd reduction are not applied.
Also the azimuthal 1-dimensional event distribution of the same events as
Figure 6.22 are shown in Figure 6.23. In Figure 6.23, we plot the distributions
for the all events (cos θ < 0.1) and upward going events (cos θ < 0) separately.
From Figure 6.22, many downward events are observed the region of 100◦
< φ < 300◦ which corresponds to the thin rock region. Those events become
the contamination of the upward going events. To estimate this contamination, the range where a lot of contaminations are expected is defined fromthe distribution shown in Figure 6.23 as137

Through−going Muon Zenith Angle vs. Azimuth

cos θ

cos θ

Stopping Muon Zenith Angle vs. Azimuth

0

0

−0.2

−0.2

−0.4

−0.4

−0.6

−0.6

−0.8

−0.8

−1
0

50

100

150

200

250

−1
0

300
350
φ (degrees)

50

100

150

200

250

300
350
φ (degrees)

Figure 6.22: The zenith (cos θ) and azimuthal (φ) scattering distribution of
stopping (left) and through-going (right) events in the SK-III period.

Azimuthal Angle Distribution of Through−going Muons

Number of events

Number of events

Azimuthal Angle Distribution of Stopping Muons

10

All stopping muons (cos θ < 0.1)
Upward stopping muons (cos θ < 0)

102

(1)

(2)

(1)

3

102

10

All thru−going muons (cosθ < 0.1)
Upward thru−going muons (cosθ < 0)

(1)

(2)

(1)

1
0

50

100

150

200

250

10
0

300
350
φ (degrees)

50

100

150

200

250

300
350
φ (degrees)

Figure 6.23: The azimuthal 1-dimensional event distribution of the same
events as Figure 6.22. Those for the stopping (left) and through-going (right)
are shown. All events (cos θ < 0.1) and upward-going events (cos θ < 0) are
separately shown.

138

1, Stopping event
region1 φ < 60◦ , 310◦ < φregion2 60◦ < φ < 310◦

(6.13)(6.14)

2, Through going event
region1 φ < 60◦ , 240◦ < φregion2 60◦ < φ < 240◦
The region 2 is the region where many contaminations are expected.
The event distributions as a function of cos θ around the horizon are
shown in Figure 6.24 and 6.25 for stopping and through-going, respectively.
In those figures, the events are shown separately for region1 and region2. We
fitted to the event distribution of the region 2 for each category using the
exponential function as,
F [cosθ] = P 0 + eP 1+P 2cosθ(6.15)

We assumed the contamination is exponential form. The expected contamination within certain bin (cosθ1 - cosθ2 ) becomes,
Z cosθ2
NBG =eP 1+P 2cosθ d(cos(θ))(6.16)
cosθ1

Using Eq. 6.16, we subtracted the expected background at the nearhorizontal region as, -0.2 < cosθ < 0 for stopping, and -0.1 < cosθ < 0 for
through-going. In the case of the SK-III data set, 4 of the through-going and
17 of the stopping events in the near horizontal direction were subtracted.

6.3

Monte-Carlo simulation for upmu

In this section, the Monte-Carlo simulation of the atmospheric neutrino is
described.
In the Super-K, all categories of atmospheric neutrino event can be simulated by one package. We focus on the simulation for the upmu events inthis thesis.

6.3.1

Atmospheric neutrino flux

The flux models of atmospheric neutrinos are developed by several groups.
In our simulation for the atmospheric neutrino-induced upmu events, the139Events/day/sr

Near−Horizon Distribution, Stopping events10

χ2 / ndf
Prob
p0
p1
p2

17.48 / 15
0.29070.1184 ± 0.0000−1.331± 0.132
42.16 ± 2.08

Region (1) φ<60°, φ>310°
Region (2) 60°< φ <310°

1

10−1

−0.1 −0.08 −0.06 −0.04 −0.02

00.02 0.04 0.06 0.08
cos θ

Figure 6.24: The stopping event distribution in SK-III as a function of cos θaround the horizon. The events are shown separately for region 1 (triangles)
and region 2 (circles). The solid line is the fitting result for the events inregion 2 using Eq. 6.16.

HKKM06 model [70] and the Volkova model [123] are used. In this simulation, neutrino energy ranges from 1 GeV to 100 TeV are taken into account.
The lower bound corresponds to the cut criteria of upmu events as discussed
in Chapter 6.2. The HKKM06 model is basically used in the range νE < 10
TeV, since this model supports up to 10 TeV. For the range 10 TeV < νE <100 TeV, we use the Volkova model instead. In order to connect the expected
flux of HHKM06 and Volkova models at 10 TeV, an absolute normalization
was applied to the Volkova flux. In Figure 6.26, the atmospheric neutrino
fluxes (νµ and ν¯µ ) used for the simulation are shown. In this simulation, νµand ν¯µ are considered since upmu events are produced only from CC interactions of them. The uncertainty of the neutrino flux is ∼ ± 20 % from theabsolute amount of the flux of primary cosmic rays, and ∼ ± 10 % from thechoice of models.

6.3.2

Neutrino interactions

The upmu events in Super-K are produced via neutrino interactions in thesurrounding rock and in the water of the OD. We consider these individuallyin the simulation.
140

Events/day/sr

Near−Horizon Distribution, Thru−going non−showering events102

χ2 / ndf
Prob
p0
p1
p2

33.31 / 16
0.006727
0.2367 ± 0.0000−2.203± 0.144
75.26 ± 2.09

Region (1) φ<60°, φ>310°
Region (2) 60°< φ <310°

10

1

10−1
−0.1 −0.08 −0.06 −0.04 −0.02

00.02 0.04 0.06 0.08
cos θ

Figure 6.25: The through-going event distribution in SK-III as a functionof cos θ around the horizon. The events are shown separately for region 1(triangles) and region 2 (circles). The solid line is the fitting result for the
events in region 2 using Eq. 6.16.

The NEUT package [124] was used to simulate the neutrino interactions.
In this package we can simulate neutrino interactions assuming many types ofinteraction mode, both in the rock and the water. The following interactionsof CC and NC interactions are considered in the NEUT library:
1, CC interaction(a) quasi-elastic scatteringν + N → lepton + N 0(6.17)(b) deep inelastic scatteringν + N → lepton + N 0 + hadrons(6.18)(c) single-meson production
ν + N → lepton + N 0 + meson(6.19)(d) coherent-pion production
ν +16 O → lepton± + π ∓ +16 O
141(6.20)

Flux*E2(m-2sec-1sr-1GeV)
Flux*E2(m-2sec-1sr-1GeV)

Neutrino Flux(numu)E GeV E GeV 

Neutrino Flux(numubar)

Figure 6.26: The neutrino flux used for the simulation of atmospheric neutrino induced upmu events. The fluxes of νµ , ν¯µ are considered. Up to 10
TeV, the HKKM06 model is used. Above 10 TeV, the Volkova model is used.
The gap shown at 10 TeV is the effect of the connection between them.

142(e) single gamma production
ν + N → lepton + N 0 + γ(6.21)

2, NC interaction(a) quasi-elastic scatteringν + N → ν + N0

(6.22)(b) deep inelastic scatteringν + N → ν + N 0 + hadrons(6.23)(c) single-meson production
ν + N → ν + N 0 + meson(6.24)(d)coherent-pion production
ν +16 O → ν + π 0 +16 O(6.25)(e) single gamma production
ν + N → ν + N0 + γ(6.26)

N and N 0 in the reactions above are nucleons. The ratio of each interaction mode for νµ , ν¯µ and ν¯µ + νµ found in the simulated upmu sample
is shown in Table 6.3. From Table 6.3, we can see that more than half of
the interactions are via deep inelastic scattering. The basic calculations of
the cross section of each interaction mode which NEUT uses, are found in
Reference [125] for the quasi-elastic scattering, Reference [126] for the single
meson production, [127] for coherent pion production, and Reference [128]for the deep inelastic interaction. In addition, the GRV-98 model is assumed
for the parton distribution function which is critical to consider the deep
inelastic scattering [129]. The total cross sections of neutrino - nucleon scattering of νµ and ν¯µ as a function of neutrino energy are shown in Figure 6.27
and Figure 6.28 for interactions in the rock and the water, respectively.
From the simulated result, we can estimate that 85% of the total eventsare produced from neutrino - nucleon scattering in the rock, the remaining
15% in the OD water.
To simulate only the muons which reach the detector, the interaction
point and the muon propagation in the surrounding rock were considered asfollowing.
143

Mode
Quasi elastic
Deep inelastic
Single meson
Coherent π
Single gammaνµ (%) ν¯µ (%) Total (νµ +ν¯µ ) (%)
11.3
17.1
13.1
72.6
63.6
69.6
15.7
18.5
16.7
0.4
0.8
0.6
0.0
0.0
0.0

4

10

3

2
2

cm )/nucleon

10

10

-38

3

2

10

vµ

10

2

σ (10

4

σ (10

10

-38

cm )/nucleon

Table 6.3: The ratio of each interaction mode for νµ , ν¯µ and νµ + ν¯µ foundin the simulated upmu sample.

101vµ-bar

10

1

-1

-1

10
1

10

10

2

10

3

10

4

10

5

Ev (GeV)

10
1

10

10

2

10

3

10

4

10

5

Ev (GeV)Figure 6.27: The total cross section of neutrino - nucleon scattering in therock for νµ (left) and ν¯µ (right) as a function of neutrino energy.

144cm )/nucleon

4

10

3

2
2

10

-38

10

vµ

10

2

σ (10

3

2

10

-38

cm )/nucleon

4

σ (10

10

10

1

vµ-bar

10

1

-1

-1

10
1

10

10

2

10

3

10

4

10

5

10
1

10

10

2

Ev (GeV)

10

3

10

4

10

5

Ev (GeV)Figure 6.28: The total cross section of neutrino - nucleon scattering in thewater for νµ (left) and ν¯µ (right) as a function of neutrino energy.

The interactions are assumed to take place in “standard rock” with thefollowing properties: ρ = 2.65 g/cm3 , Z = 11, and A = 22 [130]. The propagation of daughter upmus through rock was simulated by routines developedin Reference [131]. The muon range in the rock is shown in Figure 6.29.
Each upmu has an associated volume V µ (Eµ ). through which it may
traverse, which depends on the effective muon range Ref f (Ei ,Emin ), where
Ei is the initial upmu energy and Emin = 1.6 GeV/c is the minimum upmu
momentum based on cuts described in Chapter 6.2. V µ (Eµ ) is written as
4π 3
R .,
(6.27)
3 ef f
The effective detection volume Vef f is given by the product of the effective
detector area, Aef f (θ) and the muon range Ref f (Ei ,Emin ). The effective
detector area of Super-K is shown in Figure 6.30. It is almost 1200 m2 forany choice of angle of view θ. The Vef f is written as
V µ (Eµ ) =Vef f (E0 , θ, Emin ) = Aef f (θ)Ref f (Ei , Emin ).

(6.28)

Comparing V µ (Eµ ) with Vef f , we can judge if the neutrino-induced upmu
can reach the detector. After that, we pick a random point inside V µ (Eµ )and accept it if it also lies within Vef f .
In a practical sense, the effective volume is assumed to be wider than
the real detector since a muon track may be slightly changed by multiple
145

Coulomb scattering during its propagation in the rock. Also, the neutrino
interaction point in the rock is restricted, to be within 4 km of the center ofthe detector, which is large enough when we consider the muon range of thehighest energy atmospheric neutrinos.

Figure 6.29: The range of muon when they propagate in the standard rock.

6.3.3

Detector simulation

The detector simulation has been developed based on the GEANT3 package[132]. It simulates the tracks of particles, the generation and propagation of
Cherenkov photons in water, the PMT response, and the read out electronics.
The calibration constants which were obtained by the calibration describedin Chapter 5 were used to simulate these details.

6.4

Summary of upmu dataset used for analysis

We made the data set of upmu events from SK-I to SK-III. The numbers ofevents (Nobs ), event rates (R), and livetime (Tlive ) in each upmu category aresummarized in Table 6.4.
146

1500
1400
1300
1200
1100
1000
900
800
700

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

Figure 6.30: The effective area of the Super-K detector as a function of angleof view, θ. Cos θ = 0 is the horizontal direction.

SK-I
SK-II
SK-III

Tlive
1646.0828.0
635.6

Stopping
Nobs
R
432 0.26
210 0.25
193 0.30

Non-Showering
Nobs
R
1577
0.96
725.3
0.88
612.9
0.96

Showering
Nobs
R
272
0.17
108.1 0.13
110
0.17

Table 6.4: The numbers of events (Nobs ), event rates (R), and livetime (Tlive )in each upmu category are summarized for each experimental phase.

The zenith angle distributions for each upmu category in each experimental phase are shown in Figures 6.31 - 6.33. The distributions of the real
data with applied background subtraction, as in Chapter 6.2.9 are shown by
black crosses. The distributions from Monte Carlo simulation are plotted
two ways: with and without taking into account the oscillation effect. The
Monte Carlo events without considering the oscillations are shown by blueboxes and are normalized by livetime of each experimental phase. That withthe oscillation effect are shown in red histogram and are normalized by the
number of the events of real data with oscillation parameters of sin2 2θ =1,∆m2 = 2.5 × 10 −3 eV.

147

100

Zenith angle, Stopping µ

Zenith angle, Non−showering thru−µ

EventsEvents120

300

SK−1 data (1646.0 days)
SK−1 MC, no oscillations
SK−1 MC, with oscillations

SK−1 data (1646.0 days)
SK−1 MC, no oscillations
SK−1 MC, with oscillations

250

80

200

60

150

40

100

20

50
Background subtracted

Background subtracted0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ

0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ

220
200

Zenith angle, Stopping µ60SK−1 data (1646.0 days)
SK−1 MC, no oscillations
50
SK−1 MC, with oscillations

180

SK−1 data (1646.0 days)
SK−1 MC, no oscillations
600
SK−1 MC, with oscillations

140

SK−1 data (1646.0 days)
SK−1 MC, no oscillations
SK−1 MC, with oscillations

500

40

160

Zenith angle, Non−showering thru−µ

EventsEvents240

EventsZenith angle, Showering thru−µ

400

30

120

300

100

20

80

200

10

60

Background
100 subtracted
0
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3 −0.2 −0.1 020
Background subtracted
Background subtracted
cos θ
0
0
−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ
cos θ
40

EventsFigure 6.31: The zenith angle
distributionsof upmu events in SK-I (liveZenith
angle, Showering thru−µ120time:1646.0 days) for eachupmu
category:
stopping(left upper), 2non show1 SK−1 data (1646.0 days)
SK−1 MC, no oscillations
ering (right upper), andshowering(lower).
SK−1 MC, withoscillations Black crosses indicate the real
100
data, blue boxes are MC without oscillation effect, and red histograms are80
MC with oscillation effect.
60
40
20Background subtracted0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ

148
3

40

Zenith angle, Stopping µ

Zenith angle, Non−showering thru−µ

EventsEvents50

SK−2 data (828.0 days)
SK−2 MC, no oscillations
SK−2 MC, with oscillations

SK−2 data (828.0 days)
SK−2 MC, no oscillations
SK−2 MC, with oscillations

140
120
100

30

80
20

60
40

10

20

Background subtracted

Background subtracted0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ

0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0cos θ

Events25 µZenith angle, Stopping100

SK−2 data (828.0 days)
SK−2 MC, no oscillations20
SK−2 MC, with oscillations

SK−2 data (828.0 days)
SK−2 MC, no oscillations
SK−2 MC, with oscillations
250

Zenith angle, Non−showering thru−µ

EventsEventsZenith angle, Showering thru−µ80SK−2 data (828.0 days)
SK−2 MC, no oscillations
SK−2 MC, with oscillations

200

15
60

150

10
40

100

5
20

Background50 subtracted
0
−1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3 −0.2 −0.1 0
Background subtracted
Background subtracted
cos θ
0
0
−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ
cos θ

EventsFigure 6.32: The zenith angleZenith
distributions
upmu events in SK-II (liveangle, Showering thru−ofµ
time:828.0 days) for each upmu
category:
stopping(left upper), 2non show1 SK−2 data (828.0 days)
45
SK−2 MC, no oscillations
ering (right upper), andshowering(lower).
SK−2 MC, withoscillations Black crosses indicate the real40
data, blue boxes are MC
without
oscillation
effect, and red histograms are
35
MC with oscillation effect.
30
25
20
15
10
5

Background subtracted0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ

149
3

45
40

Zenith angle, Non−showering thru−µ

EventsEventsZenith angle, Stopping µ120

SK−3 data (635.6 days)
SK−3 MC, no oscillations
SK−3 MC, with oscillations

SK−3 data (635.6 days)
SK−3 MC, no oscillations
SK−3 MC, with oscillations

100

35
80

30
25

60

20
40

15
10
5

20
Background subtracted

Background subtracted0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ

0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0cos θ

EventsZenith angle, Stopping µ

35

100

SK−3 data (635.6 days)
SK−3 MC, no oscillations30
SK−3 MC, with oscillations

80

25

SK−3 data (635.6 days)
240
SK−3 MC, no oscillations
SK−3 MC, with oscillations
220
180
160
140

15
40

120
100

10
5

20

SK−3 data (635.6 days)
SK−3 MC, no oscillations
SK−3 MC, with oscillations

200

20

60

Zenith angle, Non−showering thru−µ

EventsEventsZenith angle, Showering thru−µ8060Background40 subtracted

0−1 subtracted−0.9 −0.8 −0.7 −0.6 −0.5 −0.4
20 −0.3 −0.2 −0.1 0
Background
Background subtracted
cos θ
0
0
−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ
cos θ

EventsFigure 6.33: The zenith angleZenith
distributionsofµ upmu events in SK-III (liveangle, Showering thru−
time:635.6 days) for each upmu
category:
stopping(left upper), 2non show1 SK−3 data (635.6 days)
50
SK−3 MC, no oscillations
ering (right upper), and showering(lower).
SK−3 MC, withoscillations Black crosses indicate the realdata, blue boxes are MC
without
oscillation
effect, and red histograms are40
MC with oscillation effect.
30
20
10Background subtracted0−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0
cos θ

150
3

Chapter 7
Result of Solar WIMP analysis
7.1

Event distributions

The event distribution (SKI-III:3109.6 days) as a function of cos θsun foreach category of upmu is shown in Figure 7.2. Here, θ is the angle between
reconstructed direction of the upmu and the direction of the Sun. This θ iscalled the “cone half-angle” and a schematic view of cone half-angle is shownin Figure 7.1.
In Figure 7.2, cos θsun =1 is defined as the direction of the Sun. To
compare the data with the MC events, each MC event was assigned a timesampled from the observed upmu arrival time in order to match the livetime
distribution and the detector acceptance of the observed events. We divided
the upmu events into three categories: stopping(A), nonshowering(B), andshowering(C). We searched for an excess in each category. We took into
account the neutrino oscillation at sin2 2θ =1, ∆m2 = 2.5 × 10 −3 eV for theMC events. The number of MC events is normalized by the total number ofdata events for each category.
Since the energy spectrum of the atmospheric neutrino background isE −2.7 , while the signal spectrum from WIMPs gives a bump structure, thisenergy-dependent approach is good to reduce atmospheric neutrino background. We separately analyzed the three upmu samples then combined
the results by taking into account the neutrino spectrum from WIMP annihilations and the fraction of event category which is shown Figure 6.3.
Directional correlation between neutrinos and produced leptons depends onneutrino energies as shown in Figure 7.3. It also depends on WIMP mass
and its decay mode. Therefore we looked for possible correlation of upmu
direction to the Sun by searching for an excess of events in various cone
half-angles up to 30◦ .

151      

Figure 7.1: A schematic view of the cone half-angle using the search for solar
WIMPs.
We checked neutrino-muon angular correlation from WIMP annihilationin the Sun by DarkSUSY for various SUSY parameters and found they aresmaller than 30◦ for most of the cases. The number of events observed ineach cone half-angle toward the Sun is shown in Figure 7.4. Zero degrees
corresponds to the direction of the Sun. Crosses indicate the data from SKIIII (3109.6 days) and the histogram indicates atmospheric neutrino MC withthe same normalization as in Figure 7.2. No significant excess was observed.

7.2

Limit on upmu flux

We calculated the upper limit on upmu flux with respect to the WIMP
mass. Here we estimated the cone half-angles which contain more than 90%

152Number of events

Stopping

Non-showering

Showeringcos sunFigure 7.2: Distribution for cos θsun of upmu events relative to the Sun. Here,cos θsun =1 means the direction of the Sun. Crosses indicate the data fromSKI-III(3109.6 days) and the histogram indicates atmospheric neutrino MC,taking into account the neutrino oscillation at sin2 2θ =1, ∆m2 = 2.5 × 10
−3eV. MC events are normalized by the total number of data events in eachcategory.
of the total number of upmus expected from WIMP annihilations in theSun. We used the WIMPsim package [96] . WIMPsim simulates WIMP
annihilations, the propagation of neutrinos from the WIMP annihilations
and the propagation of muons after neutrino interactions in the rock. In
order to assume the neutrino spectrum from the WIMP annihilation, we
considered two cases: annihilation into bb̄ (soft channel), and annihilation
into W + W − (hard channel). These give the softest and the hardest neutrino
spectra, respectively. The cone half-angles obtained from these are shown in
Figure 7.5 and Figure 7.6 for the soft and the hard annihilation channels,
respectively. The cone half-angle for the soft channel is generally wider at
the same WIMP mass since many neutrinos from the annihilation via softchannel are expected to have lower energy.
The number of expected upmu events in each cone half-angle is affectedby some uncertainties such as: muon propagation in the surrounding rocks,
distribution of WIMPs in the Sun, and angular resolution of upmus. As
for muon propagation, the angular resolution of the muon direction due tomultiple Coulomb scattering is ≈ 2◦ − 3◦ for muon energy above 1 GeV. As
for the distribution of WIMP locations, since the angular size of the Sun on
153

&
'

  

 '!  #"$%Number of events

Figure 7.3: The directional correlation between neutrinos and produced leptons depends on neutrino energies. In this figure, the pictures of CC interactions of low-E and high-E muon-neutrino are shown.
Stopping

0-5

0-10

0-15

0-20

0-25

0-30

0-15

0-20

0-25

0-30

0-15

0-20

0-25

0-30

Non-showering

0-5

0-10

Showering

0-5

0-10

cone half-angle (deg.)

Figure 7.4: Number of events observed in each cone half-angle toward theSun. Here, zero degrees corresponds to the direction of the Sun. Crosses
indicate the data from SKI-III (3109.6 days) and the histogram indicatesatmospheric neutrino MC, taking into account neutrino oscillation at sin2 2θ
=1, ∆m2 = 2.5 × 10 −3 eV. MC events are normalized by the total numberof data events in each category.
Earth is 0.5◦ , it can be assumed as a point-like source [133]. These effects
are also taken into account in WIMPsim. We show the cone half-angle forsome WIMP masses in Tables 7.1 and 7.2. Table 7.2 begins from 80.3 GeV
154

cone(deg.)

30

25

20

15

10

5

0
10

2

10

3

10

4

Mass of neutralino(GeV)

cone(deg.)

Figure 7.5: Cone half-angle which contains more than 90% of the total upmus
expected from WIMP annihilations in the Sun when we assume the soft
annihilation channel. This result was obtained from WIMPsim.
30

25

20

15

10

5

0
10

2

10

3

10

4

Mass of neutralino(GeV)

Figure 7.6: Cone half-angle which contains more than 90% of the total upmus
expected from WIMP annihilations in the Sun when we assume the hardannihilation channel. This result was obtained from WIMPsim.
here, since WIMP which have mass lower than 80.3 GeV cannot annihilate
into W + W − .
For each cone half-angle which corresponds to a certain WIMP mass foreach annihilation channel, we calculated the upper Poissonian limit of the
upmu flux:
N90 (niobs , niBG , F i )
,
(7.1)
²·A·T
where A is the detector area in the direction of the expected signal averaged
over Sun directions. This area for a certain position of the Sun is calculatedwith the criterion that expected muon tracks pass through more than 7m
φ(90%C.L.) =155

in the detector. It varies from 968 m2 to 1290 m2 with the position of
the Sun as shown in Figure 6.30. ² is the detection efficiency. For upmu
samples, the inefficiency of the detection is negligible [134, 122]. T is theexperimental livetime. N90 is the upper Poissonian limit on the number of
upmu event (90% C.L) given the number of observed events (niobs ), expectedbackground (niBG ) and fraction of i-th category (F i ) of upmu. This fraction
was estimated from the neutrino spectrum of the given WIMP mass for eachannihilation channel and the fraction of the upmu categories as a function of
the parent neutrino energy as shown in Figure 6.3. These neutrino spectra
were simulated by WIMPsim as described in Chapter 3.3.1 .
This N90 was calculated combining all categories of upmu for a certain
mass based on Bayes’ theorem [20]. The likelihood function for the expectedsignal is given from the Poisson probability as
L(niobs |νs ) =i
l=3Y(νs F i + niBG )nobs −(νs F i +niBG )
e
,
i
n
!
obs
i=0

(7.2)

where νs is expected signal, l is number of categories to be combined.
Using the likelihood function in Eq. 7.2, the upper confidence level iswritten as
R Nlimit
L(niobs |νs )dνsνs =0
C.L. = R ∞.
(7.3)
L(niobs |νs )dνs
νs =0
Applying the 90% for C.L in Eq. 7.3, the upper Poissonian limit(N90 ) was
obtained.
The summaries of the numbers of upmu events and the estimated background for the cone half-angles which correspond to each WIMP mass, N90 ,andthe calculated flux limits are also shown in Tables 7.1 and Table 7.2.
The 90% confidence level flux limits as a function of WIMP mass areshown in Figure 7.7 and Figure 7.8. Results from other experiments, AMANDA [54]and IceCube [55], are also shown in these figures. The previous Super-K result [53] is also shown in Figure 7.7, but please note that it was calculated
assuming an annihilation branching ratio. That result assumed that 80%of the annihilation products were bb̄, 10% were cc̄, and 10% are τ + τ − , as a
typical branching ratio. We cannot regard this as a pure soft annihilation,
but it is shown for reference.

7.3

Limit on spin-dependent cross section

From the upmu flux limits shown in Figure 7.7 and Figure 7.8, we also
calculated the upper limit on the Spin-Dependent scattering cross section of
156

mχ
(GeV)
10
100
1000
10000

Stoppingθnobs nBG F(deg.)(%)
30
63
62.5 981010
6.7 7863
2.7 5951
1.9 28

Non-Showering
nobs nBG F(%)
184 200.3 2
1922.5 168
7.2 297
4.6 52Showeringnobs nBG F(%)
3933.7 05
3.8 6
1
1.4 12
1
0.9 20

N90
14.8
10.9
6.41
6.99

φ × 103(km−2 yr−1 )
2.8
2.1
1.2
1.3

Table 7.1: Event summary to calculate the flux limit (φ) assuming soft annihilation channel is dominant. The numbers of events (nobs ) and of theestimated background (nBG ) of each cone half-angle (θ) which corresponds
to a certain WIMP mass (mχ ) are shown for all categories of upmu. Thiscone half-angle is defined from the criterion that more than 90% of WIMPinduced upmus are contained for the assumed WIMP masses. Also we show
the estimated fraction (F ) of each upmu category for the given WIMP mass.
The calculated result of N90 and flux limit for each WIMP mass are shownin the last two columns.

mχ
(GeV)
80.3
100
1000
10000

Stoppingθnobs nBG F(deg.)(%)
84
4.2 4473
3.3 423
0
0.5 403
0
0.5 24

Non-Showering
nobs nBG F(%)
1413.4 4010
9.9 412
2.1 412
2.1 54Showeringnobs nBG F(%)
3
2.5 162
2.2 171
0.3 191
0.3 22

N90
8.4
6.9
4.2
4.5

φ × 103(km−2 yr−1 )
1.6
1.3
0.80
0.85

Table 7.2: Event summary to calculate the flux limit (φ) assuming hardannihilation channel is dominant. The meaning of each column is the sameas in Table 7.1

157

-1

Limit on WIMP-induced upmu (km y )-2

AMANDA
10

5

Soft channel

ICECUBE
SK-I
SK-I+II+III

10

4

10

3

Expected flux region(Eµ > 1 GeV )
10

2

10

3

10

4

WIMP mass(GeV/c2)

Figure 7.7: Upmu flux limit vs. WIMP mass for the soft annihilation channel.
The flux limits of AMANDA [54] (green dotted line), IceCube [55] (blue dotdash line), and this analysis (red solid line) are shown. Also shown is theprevious limit from Super-K [53] (black dashed line). Note that Super-K’s
previous limit doesn’t assume the pure soft channel, but assumes a typicalannihilation channel in which the branching ratio for the soft annihilation
channel is relatively high (80%). The shaded region is the expected WIMPinduced upmu flux from the SUSY models in which the branching ratio into
the soft channel is more than 60%. We simulated this region by DarkSUSY.
WIMPs. The conversion factors discussed in Chapter 3.3.3 were applied forthis calculation.
The calculated upper limit is shown in Figure 7.9. Also shown are results from direct detection experiments: DAMA/LIBRA allowed region [68],
KIMS [64], and PICASSO [65]; and from neutrino telescopes: AMANDA [54]and IceCube [110]. All of the limits from the neutrino telescopes (including
our limit) are calculated by the same method described in Chapter 3. The
previous limit from Super-K is also shown for reference. Note that the gaps
at WIMP masses of ∼ 80 GeV and 174 GeV in this previous result are dueto the thresholds of the W + W − and τ + τ − annihilation channels. These do
not appear in the new result because we assume only one annihilation channel. Our limit is improved at low WIMP mass (below 100 GeV), which is
158

-1

Limit on WIMP-induced upmu (km y )-2

AMANDA
10

5

Hard channel

ICECUBE
SK-I+II+III

10

4

10

3

Expected flux region(Eµ > 1 GeV )
10

2

10

3

10

4

WIMP mass(GeV/c2)

Figure 7.8: Upmu flux limit vs. WIMP mass for the hard annihilation channel. The flux limits of AMANDA [54] (green dotted line), IceCube [55] (bluedot-dash line), and this analysis (red solid line) are shown. The shaded regionis the expected WIMP-induced upmu flux from the SUSY models in which
the branching ratio into the hard channel is more than 60%. We simulated
this region by DarkSUSY.
stronger than limits from any other indirect-detection experiments. Following our method as described in Chapter 3, we achieve a stronger limit thandirect-detection experiments. We put several assumptions as Chapter 3, andthose assumptions have uncertainties as discussed in Chapter 9. Thus, notethat this comparison between the limit from indirect searches and direct
searches is not so strict.

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3

-1

-3

10-5

  "!$#&%"')(*,+.-

Figure 7.9: Limit on the WIMP-proton spin-dependent cross section as afunction of WIMP mass [57]. Limits from direct detection experiments:
DAMA/LIBRA allowed region [68] (dark red and light red filled, for withand without ion channeling, respectively), KIMS [64] (light blue crosses),and PICASSO [65] (grey dotted line) are shown. Also we show here the results of indirect detection (neutrino telescopes): AMANDA [54] (black linewith triangles), IceCube [110] (blue line with squares), and this analysis (redline with stars). Also the previous limit from Super-K (green dashed line) isshown.

160

Chapter 8
Result of Earth WIMP analysis
8.1

Event distributions

Number of events

The event distribution (SKI-III:3109.6 days) as a function of cosθ for eachcategory of upmu is shown in Figure 8.1. Here, θ is the cone half-angle (seeFigure 7.1) between the reconstructed upmu and the direction of the Earth.
Stopping

Non-showering

Showeringcos

Figure 8.1: Distribution for cos θ of upmu events relative to the Earth. Here,cos θ=-1 means the direction of the center of the Earth. Crosses indicate
the data from SKI-III(3109.6 days) and the histogram indicates atmospheric
neutrino MC (taking into account neutrino oscillation) normalized by the
total number of data events in each category.
In Figure 8.1, cos θsun =-1 is defined as the direction to the center of the161Number of events

Stopping

0-5

0-10

0-15

0-20

0-25

0-30

0-15

0-20

0-25

0-30

0-15

0-20

0-25

0-30

Non-showering

0-5

0-10

Showering

0-5

0-10

cone half-angle (deg.)

Figure 8.2: Number of events observed in each cone half-angle toward theEarth. Here, zero degrees corresponds to the direction of the center of the
Earth. Crosses indicate the data from SKI-III (3109.6 days) and the histogram indicates atmospheric neutrino MC (taking into account neutrino
oscillation) normalized by the total number of data events in each category.
Earth. The normalization and the assignment of livetime for MC events istreated the same way as the analysis for solar WIMPs (Chapter 7).
Identical to the solar WIMP case, the number of events observed in eachcone half-angle toward the center of the Earth is checked, and shown in
Figure 8.2. The neutrino-muon angular correlation from WIMP annihilationin the Earth was also checked by DarkSUSY for various SUSY parameters.
We found the angle to be smaller than 30◦ for most of the cases, as similar
to the solar case. Zero degrees corresponds to the direction of the centerof the Earth. Crosses indicate the data from SKI-III (3109.6 days) and thehistogram indicates atmospheric neutrino MC with the same normalization
as in Figure 8.1. No significant excess was observed.

8.2

Limit on upmu flux

We calculated the upper limit on upmu flux with respect to the WIMP mass.
Here we estimated the cone half-angles which contain more than 90% of thetotal number of upmus expected from WIMP annihilations in the Earth.

162

 
(


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!



45456









 

 

 
 


Figure 8.3: Cone half-angle which contains more than 90% of the total upmus
expected from WIMP annihilations in the Earth when we assume the soft
annihilation channel. This result was obtained from WIMPsim.
 
-



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.

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

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        

Figure 8.4: Cone half-angle which contains more than 90% of the total upmus
expected from WIMP annihilations in the Earth when we assume the hardannihilation channel. This result was obtained from WIMPsim.
From the WIMPsim simulation [96] and the same exercise as Chapter 7.2,
the cone half-angles were calculated, and they are shown in Figure 8.3 andFigure 8.4 for the soft and the hard annihilation channels, respectively.
The number of expected upmu events in each cone half-angle is affectedby some uncertainties such as: muon propagation in the surrounding rocks,
and angular resolution of the upmus. Those items are already discussed in
Chapter 7.2 and considered in the WIMPsim. The distribution of WIMPs
and the annihilation profile inside the Earth should be taken into account.
In Figure 8.5, the annihilation profile for WIMPs of the specified masses (mχ= 10,100,1000 GeV) as a function of x (=r/R⊗ ) is shown. Here, r is the163profile

0.14

mχ=10

0.12

mχ=1000.1mχ=1000

0.08
0.06
0.04
0.02
0

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

x=r/R⊗

Figure 8.5: The annihilation profile for WIMPs of the specified masses (mχ= 10,100,1000 GeV) . The horizontal axis is the x (=r/R⊗ ), where r is the
distance from the center of the Earth, and R⊗ is the radius of the Earth.
The scale on the vertical axis is arbitrary.
distance from the center of the Earth, and R⊗ is the radius of the Earth. In
the WIMPsim simulation, these profiles are also considered.
To obtain the flux limit, the same calculation as was done for solar WIMPs
was done, as described in Chapter 7.2 using Eq. 7.1 - 7.3. Note that, in Eq.
7.1, we consider the effective area for each mass of WIMP, taking into accountthe annihilation profile as in Figure 8.5. The averaged effective area is 1022.56
cm2 (mχ =10 GeV) and 897.35 cm2 (mχ =10000 GeV), for example. The
summaries of the numbers of upmu events and the estimated backgroundfor the cone half-angles which correspond to each WIMP mass, N90 , and thecalculated flux limits are also shown in Table 8.1 and Table 8.2.
The 90% confidence level flux limits as a function of WIMP mass areshown in Figure 8.6 and Figure 8.7. Results from other experiments, AMANDA [135]and BAIKAL [56] (only in Figure 8.7), are also shown in these figures.

8.3

Limit on spin-independent cross section

From the upmu flux limits shown in Figure 8.6 and Figure 8.7, we also
calculated the upper limit on the Spin-Independent scattering cross sectionof WIMPs. The conversion factors discussed in Chapter 3.3.3 were applied
164

mχ
(GeV)
10
100
1000
10000

Stoppingθnobs nBG F(deg.)(%)
30
85
72.1 98109
7.8 725
0
0.3 352
0
0.3 14

Non-Showering
nobs nBG F(%)
190 184.1 2
13
15.8 206
3.8 4500.6 56

Showeringnobs nBG F(%)
2433.5 04
4.0 8
0
1.3 200
0.3 30φ × 102(km−2 y −1 )
26.8
31
8.6
11
4.5
5.9
2.3
3.0

N90

Table 8.1: Event summary to calculate the flux limit (φ) assuming the soft
annihilation channel is dominant for the Earth WIMPs. The numbers ofevents (nobs ) and of the estimated background (nBG ) of each cone half-angle(θ) which corresponds to a certain WIMP mass (mχ ) are shown for all categories of upmu. This cone half-angle is defined from the criterion that morethan 90% of WIMP-induced upmus are contained for the assumed WIMP
masses. Also we show the estimated fraction (F ) of each upmu category forthe given WIMP mass. The calculated result of N90 and flux limit for each
WIMP mass are shown in the last two columns

mχ
(GeV)
80.3
100
1000
10000

Stoppingθnobs nBG F(deg.)(%)
98
6.5 408
6
5.3 373
0
0.7 15
2
0
0.3 4

Non-Showering
nobs nBG F(%)
1012.5 4299.6 452
1.3 520
0.6 44Showeringnobs nBG F(%)
2
3.6 181
2.8 1800.5 3300.3 52

N90
7.8
7.1
3.7
2.3

φ × 102(km−2 y −1 )
9.7
9.0
4.8
3.0

Table 8.2: Event summary to calculate the flux limit (φ) assuming the hardannihilation channel is dominant for the Earth WIMPs. The meaning of eachcolumn is the same as for Table 8.1

165

TU Q

R QSF
OP A
N G @M
HNCN AA   
M

>L
JK

HGI
F

B E@
BC ?DA "!#$ %&# ')(+* ,(+-/.10.23-4'#* 
5 687:9;)#+<=

> ?@VXW ZY-4[ \]5;^#\<_ $&`a
Figure 8.6: Upmu flux limit vs. WIMP mass for Earth WIMPs. We assumed the soft annihilation channel here. The flux limits of AMANDA [135](Blue),and this analysis (Red) are shown. The shaded region is the expected
flux region from DarkSUSY.
for this calculation. We set the limit for three cases of degree of equilibrium(1, 0.1, 0.01).
Putting the three values (1, 0.1, 0.01) for degree of equilibrium t¯ /τ in
Eq. 3.5, we consider the conversion factor from upmu flux into SI crosssection. Since the predicted degree of equilibrium is less than 1, as shown in
Figure 3.6, Eq. 3.17 can be approximated as1Φfµ ∼ Cc η f (mχ )(t/τ )2 .
(8.1)
2Thus, the upmu flux is just scaled as the square of degree of equilibrium.
Taking into account this scaling, we can obtain the conversion factor for eachvalue of degree of equilibrium from Figure 3.15. The results are shown in
Figure 8.8 assuming the soft and the hard annihilation channels.
For the most optimistic case, the degree of equilibrium is 1, we compared
our limit with other direct detection experiments. The result is shown in
Figure 8.9. Limits from direct detection experiments: XENON10 [62] andCDMS [61] are also shown. Also the previous limit from Super-K [53] isshown. The bumps shown in the previous limit from Super-K are the same
source as described in Chapter 7.3.
166

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

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




 



]^G P`_Q.6a%8b8 9 ?cbA7d%#efBFigure 8.7: Upmu flux limit vs. WIMP mass for Earth WIMPs. We assumed
the hard annihilation channel here. The flux limits of BAIKAL [56] (Black),
AMANDA [135] (Blue), and this analysis (Red) are shown. The shaded
region is the expected flux region from DarkSUSY.
Our limit is not stronger than direct-detection experiments, though we
could set a limit on the SI cross section from the Earth WIMP indirect search.

167

EF

CD

@ AB

   
! !"#%$ #&

EF

CD

@ AB

   
! !"#%$ #&

#%$ &

#%$ &

&

&

')( *,+.-0/1213547628:9;=<?>')( *,+.-0/1213547628:9;=<?>

Figure 8.8: Limit on the WIMP-nucleon spin-independent cross section as afunction of WIMP mass. The soft annihilation channel (left panel) and hardannihilation channel (right panel) are assumed. The three values of degreeof equilibrium are considered.

168

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576

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34
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  
     ! "# $%  & '#(!)
# $% *+-, .

>@? ACBEDGFHIHKJ%LMKNO
Figure 8.9: Limit on the WIMP-nucleon spin-independent cross section as
a function of WIMP mass. Our limits when setting the degree of equilibrium equal to 1 are shown assuming the soft (blue solid line) and hard (redsolid line) annihilation channels. Limits from direct detection experiments:
XENON10 [62] (black dashed line), and CDMS [61] (green dashed line) arealso shown. Also the previous limit from Super-K [53] (brown dotted line) isshown. This plot was made from [57].

169

Chapter 9
Discussions of uncertainties
In this section we discuss the uncertainties on the conversion of the neutrino
flux to a WIMP nucleon scattering cross section and provide a description for
the treatment of uncertainties. Systematic uncertainties can be grouped into
three independent categories: uncertainty on the annihilation rate ΓequiatA
equilibrium, uncertainty on the neutrino flux related to the neutrino propagation from creation to Earth, and uncertainty related to the flux measurement
at the detector and propagation through Earth.
The first two categories are common to all neutrino telescopes, while thethird category is experiment-dependent. As the experimental uncertainties
are highly detector-dependent, we leave a detailed treatment to them andmerely provide a summary of the relevant effects. We also consider propagation through the Earth as part of the last category as its effect depends onthe detector location.

9.1

Uncertainties from astrophysical models

The annihilation rate ΓA is solely determined by the capture rate, CC , atequilibrium. We neglected evaporation effects because the impact of thiseffect is only relevant for light WIMPs (∼ 4 GeV) [106]. A variety of uncertainties need to be considered in capturing process, which are related to thedark matter halo density and velocity distribution at the solar galactic orbit,
capture mechanism, and composition of the Sun or the Earth.
The average dark matter halo density at 8.5 kpc from the Galactic centeris estimated to be about ρ8.5kpc = 0.3 GeV/cm3 . The capture rate in the
Sun or the Earth depends linearly on the dark matter density as ∆ΓA /Γa =∆ρDM /ρDM .
The capture rate depends in a complex manner on the circular velocity of170

the solar system vSun (relative to the halo) and the WIMP velocity dispersion
vd . We assume a Maxwellian velocity distribution with vd = 270 km/s anddispersion of vSun = 220 km/s. The change in capture rate for different haloparameters is shown in Figure 9.1.

Figure 9.1: Change in capture rate as function of WIMP mass and haloparameters compared to the nominal model assuming a circular velocity of
220 km/s and a velocity dispersion of 270 km/s.
Recently, not only the Maxwellian distribution but also the various typesof velocity distributions are discussed. We have not included those effects,
but it may affect the result. The actual choice of halo profile [97, 136, 137],
does not introduce an uncertainty.
Substructure which would naturally lead to varying dark matter densityand velocity distributions can be addressed with the same error treatment described above, assuming extremes between dense and depleted regions. Contributions from additional dark matter populations such as dark disk [138]as the Milky Way may have acquired during its complex merger history falls
in the same category and is not discussed in further detail. However recent
N-body simulations disfavor any significant substructure at around the circulation radius of the solar system in the galaxy [139]. Small variationsin the local dark matter density and velocity distribution can generally becovered by the overall uncertainty on the average dark matter density andvelocity distribution. We do not consider extreme scenario with significant
substructure, as for such cases it would be impossible to derive a conversion
factor without detailed knowledge of the solar substructure history.
171

Due to the poor knowledge of the actual distribution of the matter in
the Sun or the Earth, we used only the standard material distribution in
DarkSUSY. However, the composition of the Sun or the Earth will also alter
the capture rate. For example, if the Sun contains much more metal than
expected, the SD scattering probability will be decreased.
We assume the equilibrium time scale is much smaller than the solar age
when analyzing the solar WIMPs. Though, we should consider how thisassumption is guaranteed over the scanned SUSY parameter space. The
detail of this effect has already described in Chapter 3. In the analysis for
the Earth WIMPs, we treated the equilibrium time scale in special way, andthis is already described in Chapter 3.

9.2

Uncertainties in neutrino propagation

The second class of uncertainties, which can be treated independently fromthe uncertainty on the annihilation rate ΓA , is related to the neutrino fluxφν and flavor ratio. The uncertainties on the neutrino flux are given by neutrino oscillation effects in the Sun, while propagating and at Earth, neutrino
absorption and regeneration of (tau) neutrinos in the Sun. The details of
this have already been discussed in Chapter 3.
These are fully treated in DarkSUSY and their associated uncertainties
are generally small compared to the uncertainty associated with the annihilation rate.

9.3

Detector uncertainties

The impact of detector related uncertainties is highly dependent on the experiment and we just provide an overview of the relevant uncertainties. Underlying to all detectors is the uncertainty on the neutrino interaction crosssection, which is only known to from a few to a few tens of percent for eachinteraction mode, which are listed in Chapter 2.1.
Detector specific systematic effects are around several percent, dominatedby photon propagation in the detector medium, absolute PMT efficiency, as
well as reconstruction related uncertainties [53].

172Chapter 10
Conclusion
We have performed an updated indirect search for WIMPs using the SuperKamiokande data of SKI-III (3109.6 days). A WIMP-induced neutrino signal
was searched for in the direction of the Sun and the Earth.
We compared upward-going muon events with the estimated backgroundof atmospheric neutrinos. No significant excess was observed.
To calculate the upmu flux limit, we used a new method with the DarkSUSY simulator. Cone half-angles which contained more than 90% upmu
signal for each WIMP mass were extracted from the simulation. The 90%
C.L. upper limits of upward-going muon flux induced by WIMPs of 100
GeV/c2 which annihilate in the Sun were 2.1 ×103 km−2 y−1 and 1.3 ×103
km−2 y−1 for the soft and hard annihilation channels, respectively. Those of
the Earth were 1.1 ×103 km−2 y−1 and 9.0 ×102 km−2 y−1 for the soft andhard annihilation channels, respectively. Our limit extends into the region of
expected upmu flux estimated by some SUSY models.
Also the conversion factors between upmu flux and the WIMP-nucleon
scattering cross section were also obtained from the DarkSUSY. The flux
limits from the Sun correspond to upper limits of 4.5 ×10−3 pb and 2.7 ×10−4
pb for spin-dependent WIMP-nucleon scattering cross sections in the soft andhard annihilation channels, respectively. Those from the Earth correspond to
upper limits of 8.1×10−6 pb and 7.0 ×10−7 pb for spin-independent WIMPnucleon scattering cross sections in the soft and hard annihilation channels,
respectively. In the low mass region (below 100 GeV), our limit on the
WIMP-proton spin-dependent cross section is better than other experiments
for both direct-detection and indirect-detection experiments. For the limiton the WIMP-nucleon spin-independent cross section, our most optimistic
limits are at a similar level to those from direct detection.

173

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