Study of ! and ! Neutrino
ster il e
Oscillations with the Atmospheric Neutrino Data in
Sup er Kamiokande
Kenji Ishihara
December
Do ctor Thesis University of Tokyo
Abstract
A study of the atmospheric neutrino interactions was carried out using the data from a
kton water Cherenkov detector Sup er Kamiokande We observed fully contained
and partially contained events with an exp osure of kton year
We studied the like e like ratio of the single ring events and compared it with a
theoretcal prediction We found that the ratio was signi cantly smaller than the theo
retical prediction in b oth sub and multi GeV energy ranges In addition we studied the
zenith angle distribution of these events We found that the zenith angle distribution
of e like events were in go o d agreement with the theoretical prediction On the other
hand the zenith angle distribution of the like events showed a signi cant de cit of the
upward going events These data are explained by neutrino oscillation b etween and
or b etween and where is a new hypothetical particle which do es
ster il e ster il e
not interact with matter via charged current nor neutral current interactions From these
data we estimated the allowed region of neutrino oscillation parameters m and sin
The C L allowed region was found to b e within m eV
and sin for b oth hypothesis These observations recon rmed with a higher
statistics the atmospheric neutrino oscillation rep orted by the same exp eriment in
We have also studied partially contained events and fully contained multi ring events
These events were used to distinguish the and oscillations In
ster il e
the case of oscillation matter e ect must b e taken into account in the
ster il e
neutrino oscillation analysis Since the matter e ect suppress the oscillation for high
energy neutrinos zenith angle distribution of the partially contained events was studied to
distinguish the two neutrino oscillation mo des Fully contained multi ring events contain
a large number of neutral current events Since do es not interact with matter we
ster il e
should observe a de cit of upward going neutral current events for oscillation
ster il e
The U p D ow n ratios of these two data sets and the corresp onding predictions based
on the hypothesis agreed On the other hand the predictions based on the
hypothesis had p o orer agreements with the data By combining studies of
ster il e
partially contained events and fully contained multi ring events we concluded that the
oscillation hypothesis as the solution of the atmospheric neutrino oscillation
ster il e
was disfavored at C L for most of the region indicated by the fully contained single
ring analysis We also found that this conclusion was supp orted by the upward going
muon data
Acknowledgments
First of all I would like to express my great appreciation to my advisor Prof T Ka jita
He gave me the chance to participate in this great exp eriment from the rst stage of the
analysis on the atmospheric neutrino He introduced me to high energy physics and sup
p orted me during graduate studies His excellent guidance and continues encouragement
were very valuable to me
I would like to b e thankful to Prof Y Totsuka the sp okesman of the Sup er Kamiokande
exp eriment Prof K Nakamura Prof Y Suzuki and Prof M Nakahata They gave me
many valuable advice ab out my work on various o ccasions
I am grateful sp ecially to the members of the atmospheric neutrino and proton decay
analysis group T Hayakawa taught me the art of the physics from the basics Dr
K Okumura gave me many supp ort for my work I am indebted to Dr Y Itow Dr
M Miura M Shiozawa Dr Y Obayashi Dr S Kasuga J Kameda K Kobayashi from
ICRR Dr K Kaneyuki Dr Y Hayato Y Kanaya T Futagami from TIT K Fujita and
M Etoh from Tohoku University and the members in USA esp ecially Dr Ed Kearns
Dr C Walter Dr K Scholberg Dr M Messier M Earl Dr C McGrew C Mauger
B Viren Dr D Casp er T Barszczak Dr L Wai Dr J George and A Kibayashi
I should also thank the Upward going muon analysis group Dr M Takita K Nitta
They gave me the chance to analyze the upward going muon data
I am thankful to all the collab orators of Sup er Kamiokande for very useful suggestions
Esp ecially Dr K Inoue Dr Y Fukuda Dr Y Takeuchi Dr Y Koshio Dr H Ishino
M Oketa M Ohta N Sakurai S Nakayama S Yamada U Kobayashi and T Takeuchi who
are all members of ICRR at Kamioka and with whom I often had useful discussions ab out
the exp eriment physics and so on
Finally I gratefully acknowledge the co op eration of Kamioka Mining and Smelting
Company and nancial supp ort of the Japan So ciety of the Promotion of Science
Contents
Introduction
Atmospheric neutrino
Observation of the atmospheric neutrinos
Neutrino Oscillation
Matter e ect
Sterile neutrino
Indication of the Hot dark matter mo del
Constraints for sterile neutrino
Pseudo Dirac neutrinos mo del
Di erence b etween and in Sup er Kamiokande
s
Neutral current sample
High energy sample
Detector
Water Cherenkov detector
Water tank
Photo Multiplier Tubes
Inner PMT
Outer PMT
Water puri cation system
Water puri cation system
Radon free air system
Data acquisition system i
ii CONTENTS
Electronics for the ID
Electronics for the OD
Online and o ine systems
Calibration
Relative PMT gain calibration
Absolute PMT gain calibration
Timing calibration
Water transparency
Direct measurement with a dye laser
Cosmic ray muon metho d
Absolute energy calibration
Decay electrons
LINAC
mass
Low energy stopping cosmic ray muons
High energy stopping cosmic ray muons
Summary of the absolute energy calibration
Data reduction
Reduction outline
FC reduction
First reduction
Second reduction
Third reduction
Fourth reduction
PC reduction
First reduction
Second reduction
Third reduction
Fourth reduction
Fifth reduction
CONTENTS iii
Reduction p erformance
Scanning
Event reconstruction
Outline of reconstruction
TDC t
Point t
Cherenkov edge search
Final vertex tter
Ring counting
Search for candidate rings
Charge separation and determination of ring number
Particle identi cation
Estimate the direct photon
Estimate the scattered lights
Estimate particle type
MS t
Momentum estimation
Monte Carlo simulation
Atmospheric neutrino ux
Neutrino interaction
Quasi elastic scattering
Single pion pro duction
Coherent pion pro duction
Multi pion pro duction
Meson nuclear e ect
Detector simulation
Data summary
Data summary
Vertex p osition distribution
iv CONTENTS
Number of rings and PID distribution
Summary
Neutrino oscillation analysis using FC single ring events
e ratio
Systematic error in R
Systematic error in the atmospheric neutrino ux
Systematic error from the neutrino interaction cross sections
Systematic error related to the event reconstruction
The U p D ow n ratio
Systematic error in the U p D ow n ratio
Neutrino oscillation analysis
Summary of the single ring analysis
Tests of and oscillations
s
Partially contained events
Event selection
Summary of PC events
Systematic error in the PC U p D ow n ratio
Neutrino oscillation and the PC U p D ow n ratio
Neutral current events
Event selection
Systematic error in U p D ow n ratio for multi ring sample
Neutrino oscillation and the multi ring U p D ow n ratio
Combined analysis
Conclusion
A Upward through going muon
A Outline
A Event summary
A Vertical horizontal ratio
CONTENTS v
A analysis
A Conclusion of Upward going muon analysis
B events
B event rate
B Systematic error in the ratio
study B The future plan of the R
Chapter
Introduction
Since its rst p ostulation in by Pauli the neutrino has played a crucial role in the
understanding of particle physics The existence of the neutrino was con rmed in
by Reines and Cowan detecting anti neutrinos from a nuclear p ower reactor by the
p e n In this exp eriment anti electron neutrinos were detected Then reaction
in the muon neutrino was observed by an accelerator exp eriment via N N
where N and N are nucleons
Another imp ortant step was taken by Lee and Yang who prop osed parity violation
in b eta decay Parity violation was discovered by measurements of the angular dis
tributions of b eta decay electrons from p olarized Co atoms by Wu et al It was
recognized that parity violation in weak interactions could b e explained by a vanishing
neutrino mass
From these developments it b ecame natural to consider a theory of two comp onent
neutrino in which the neutrino was exactly massless The massless neutrino was one of
the key features of the present Standard Mo del of particle physics
However there is no fundamental reason that the neutrino must b e exactly massless
Indeed the smallness of the neutrino mass was naturally explained by the seesaw mecha
nism Exp erimentally there were lots of works to detect the small neutrino mass
Last year the evidence for neutrino mass was rep orted by the observation of atmospheric
neutrinos in a kton water Cherenkov detector Sup er Kamiokande
CHAPTER INTRODUCTION
Atmospheric neutrino
Atmospheric neutrinos are the decay pro ducts of mesons pro duced from the collisions
b etween primary cosmic rays mainly protons and particles and nuclei mainly nitrogen
and oxygen in the atmosphere
They are comp osed of and and originate principally from the following decays
e
from from
e
K e
e
L
e K
e
K
L
e
e
Figure shows a compilation of the cosmic ray sp ectra by Webber and Leziak
for hydrogen helium and CNO nuclei Based on this primary cosmic ray uxes Honda
et al calculated the atmospheric neutrino ux The sp ectrum of the atmospheric
neutrino is approximately prop ortional to E at multi GeV region is ab out and
for and resp ectively Figure shows the energy distribution of the exp ected
e
atmospheric neutrino uxes
The uncertainty in the absolute ux of the atmospheric neutrino is estimated to b e
due to the uncertainty in the absolute ux of the primary cosmic rays and the
cross sections in the collision However ratio can b e calculated with
e e
the uncertainty of less than over a broad range of energies from GeV to
GeV b ecause the pro duction of and is dominated by the pion decay chain
e
at this energy range
Figure shows the exp ected atmospheric neutrino avor ratios calculated by two
indep endent groups Figure a demonstrates the uncertainty of
e e
prediction is small at E . GeV
Moreover the zenith angle distribution of the atmospheric neutrino uxes play very
imp ortant role in this thesis Since the primary cosmic ray particles enter into the Earth
isotropically the atmospheric neutrino uxes are exp ected to b e up down symmetric
Figure shows the calculated zenith angle distributions Actually the geo magnetic
ATMOSPHERIC NEUTRINO
4 10
3 10 H 2 10 ) -1 He 1
GeV
Observed primary cosmic
10 Figure
ray uxes The solid lines show -1 -1 0 10 CNO
-2
a parameterization for solar mid the
( m sec sr -1
10
dash lines for solar min and the dotted
Flux
for solar max -2 lines 10
-3 10
-4 10 -1 0 1 2 3 10 10 10 10 10 Kinetic Energy per Nucleon (GeV) GeV) -1
sr 2 -1 10 ν e sec
-2 - ν νµ
(m e
Figure Exp ected at 2 ν E
×
neutrino uxes
- mospheric
νµ
the Kamioka site
Flux 10 at
These uxes are calculated
for the mean solar activity
1 -1 2 10 1 10 10 Eν (GeV)
CHAPTER INTRODUCTION ) -
10 ν 1.5 e / - ν (a) ν (b) + 9 e ν 8 )/(
µ 1.4 - ν
+ 7 µ
ν -
( ν ν
Exp ected atmo
6 1.3 e/ e Figure
neutrino avor ratios a 5 spheric
1.2
shows b
e e
4
shows and The solid
e
1.1 e
line shows the prediction
3 broken
Honda et al Bartol
1 by - νµ/νµ
-1 2 0.9 -1 2 10 1 10 10 10 1 10 10
Eν (GeV) Eν (GeV)
eld e ect breaks this symmetry at low E region However this asymmetry decreases
with increasing E and is negligible at E GeV
Observation of the atmospheric neutrinos
In the s massive underground exp eriments started to search for nucleon decay
These exp eriments were able to detect the atmospheric neutrinos but the study on the
atmospheric neutrino was carried out only to estimate a background to the nucleon decay
search
However the Kamiokande exp eriment which was the immediate
predecessor to the Sup er Kamiokande detector carefully studied them and consequently
discovered the existence of the so called atmospheric neutrino anomaly In the
group rep orted that the observed e ratio which is exp ected to b e at E GeV
with uncertainty was close to one This rep ort made the study of the atmospheric
neutrinos b e an imp ortant measurement on its own and motivated other underground
exp eriments to study the atmospheric neutrinos carefully
The observed e ratios were rep orted as R e e where and e are
data MC
the number of muon like like and electron like e like events observed in the detector
for b oth real data and Monte Carlo simulation If the observed value of is
e e
OBSERVATION OF THE ATMOSPHERIC NEUTRINOS
10 2 (a) 10 2 (b)
10 10 )
-1 1 1 -1 -1 GeV
-1 10 10
Θ -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 cos -1
sec 2 (c) 2 (d)
-2 10 10
10 10 Flux(m 1 1 -1 -1 10 10 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
cosΘ
Figure Exp ected zenith angle distributions of the atmospheric neutrino uxes
a for b for c for and d for The solid broken and dashed lines are
e e
for E and GeV resp ectively
CHAPTER INTRODUCTION
consistent with the Monte Carlo prediction R should b e unity Table summarizes the
atmospheric neutrino measurements The R obtained by the water Cherenkov detectors
Kamiokande and IMB Sub GeV were signi cantly smaller than unity and indicated the
existence of the atmospheric neutrino anomaly On the other hand Nusex and Frejus
which were iron calorimeter detectors rep orted that their results were in agreement with
the Monte Carlo prediction Therefore the atmospheric neutrino anomaly was sometimes
supp osed to b e a particular problem to the water Cherenkov detectors However the
other iron calorimeter Soudan I I observed small R and showed the anomaly was not
the issue due to the water Cherenkov detectors The results of these exp eriments had
large spread in the central values and relatively large uncertainties so that the more
precise exp eriments were required to con rm the existence of the atmospheric neutrino
anomaly and to nd out what is the solution of this anomaly Therefore we constructed
kton water Cherenkov detector Sup er Kamiokande which enables us to carry out a
high statistics atmospheric neutrino measurement
Exp eriment R
+ 0 07
Kamiokande sub GeV
0 06
+ 0 08
multi GeV
0 07
IMB sub GeV
+ 0 4
multi GeV
0 3
Soudan II
+ 0 35
Nusex
0 25
Frejus
Table Summary of the obtained R e e from the exp eriments
data MC
b efore Sup er Kamiokande sub GeV multi GeV indicates E GeV E
v is v is
GeV where E is the energy of an electron that would pro duce the observed amount
v is
of Cherenkov light
Recently the Sup er Kamiokande exp eriment rep orted the results based on kton
NEUTRINO OSCILLATION
year s atmospheric neutrino data
sub GeV
stat sy s
R
mul ti GeV
stat sy s
Both R were signi cantly smaller than unity by more than standard deviations These
results were consistent with that of the Kamiokande and IMB sub GeV and con rmed
the atmospheric neutrino anomaly
The other imp ortant rep ort from the Sup er Kamiokande exp eriment was on
the zenith angle distribution of the atmospheric neutrinos As mentioned the zenith angle
distributions of the atmospheric neutrino uxes should b e U p D ow n symmetric at multi
GeV region In contract to this the observed U p D ow n ratios by the Sup er Kamiokande
were
+ 0 13
e l ik e
stat sy s
0 12
U p D ow n
+ 0 06
l ik e
stat sy s
0 05
The deviation of U p D ow n for like events from unity was whereas that for e
like was consistent with the exp ected one This means that the zenith angle anomaly is
particular to like events and it is to o large to b e explained by a statistical uctuation
Neutrino Oscillation
Atmospheric neutrino data from Kamiokande and Sup er Kamiokande can b e explained
by neutrino oscillations In the standard mo del neutrinos were regarded to b e
zero mass particles However if neutrinos have nonzero mass then the eigenstates of
the mass can b e di erent from the ones of the week interactions avor eigenstate As a
result neutrinos oscillate among di erent neutrino avors This phenomenon is called as
neutrino oscillations In the case of neutrino oscillations the avor eigenstates
are expressed as combinations of mass eigenstates as follows
cos sin
A A A A
U
sin cos
CHAPTER INTRODUCTION
with b eing the mixing angle
The states and are pro duced in a weak decay pro cess However their propagation
in space time are determined by the characteristic frequencies of the mass eigenstates
iE t
1
t e
iE t
2
t e
Since momentum is conversed the states t and t must have the same momentum
p As a result if the mass m p i
i
m
i
E p
i
p
Thus the from Eq and we nd
iE t
1
t e
A A A
U U
iE t
2
t e
Supp ose we start at t with the surviving probability of at
time t t is calculated as follows
E E t
P sin sin
From this equation is rewritten as
m L
P sin sin
p
L
sin sin
l
v
where l is the oscillation length which is p m m m m and L is the
v
distance from the source
Neutrino oscillation exp eriments Neutrino oscillation is tested by using the atmo
spheric the solar the reactor and accelerator neutrinos The Sup er Kamiokande exp er
iment obtained the allowed region m v s sin for oscillation based on the
atmospheric neutrino data Figure illustrates the allowed region of sin m
MATTER EFFECT
m sin
MSW large angle solution
MSW small angle solution
MSW low m solution
vacuum oscillation
Table The allowed region from the solar neutrino observation Homestake
GALLEX SAGE and Sup er Kamiokande
obtained by the Sup er Kamiokande exp eriment This gure concluded that the atmo
spheric neutrino data were in go o d agreement with oscillation with sin
and m eV at con dence level
Also the results from the Cho oz exp eriment put stringent limits on
e
mixing in the interest region of m Therefore the hypothesis of oscillations as
e
an explanation of the atmospheric neutrino data is disfavored
Besides the atmospheric neutrino the Sup er Kamiokande exp eriment observes the
solar neutrino Additional signals of neutrino oscillations arise from solar neutrino data
This result is summarized in Table
Matter e ect
When neutrinos propagate in matter they acquire additional p otential energy from their
forward scattering amplitude This e ect was rst p ointed out by Wolfenstein see
also In the presence of matter with constant density we solve the following
equation to obtain the time evolution of neutrino
E V
d
A A A A
U U i
dt
E V
1
LSND rep orted they found the evidence of the ! oscillations Their result suggests
e
2
2 2 2
the parameter range is m eV and sin But KARMEN which is the same type
exp eriment as LSND cannot con rm it Hence I do not use the LSND result in this thesis
CHAPTER INTRODUCTION
1
νµ - ντ
-1 10 )
2 Kamiokande
-2 (eV
2 10 m ∆ Super-Kamiokande
-3 10 68% 90% 99%
-4 10 0 0.2 0.4 0.6 0.8 1
sin22θ
Figure The allowed neutrino oscillation parameter regions obtained by Kamiokande
and Sup er Kamiokande This analysis is based on the observation of the atmospheric neutrinos
MATTER EFFECT
We can solve this equation to obtain the e ective mixing angle and the oscillation
m
length l as follows
m
sin
sin
m
cos sin
l
v
p
l
m
cos sin
where
p V V
m
The p otential of V is given by
p
A T
G n L V
F
M
W
where G is the Fermi coupling constant M is the W b oson mass T is a temp erature
F W
n is a number density of photons and A is a numerical factor given by A and
e
A The quantity L is given by
L L L sin L sin L L L L
W e W p n
e
where the plus sign refers to e and the minus sign refers to Also L
n n n where n is the number densities For anti neutrinos one must replace L
by L in Eq
Matter e ect in the Earth From the ab ove discussion it is clear that the matter has
no e ect in the case of oscillation However if we assume the neutrino oscillation
b etween and a non interacting sterile neutrino the matter e ect must b e taken in
s
L b ecause the account When the oscillation o ccurs in the Earth L is
n s
density of neutrinos is negligible and the density of electrons and protons is identical
And the term related to T in Eq is negligible at the normal temp erature T K
Therefore the e ective p otential for the oscillation is given by
s
p
eV
V V V G n
s s F n
GeV
CHAPTER INTRODUCTION
where is the mass density g cm is the average mass density in the Earth Here
the neutron fraction is assumed to b e For the anti neutrino the sign of p otential
changes to plus For j j corresp onding to low neutrino energies the matter e ect
is negligible and the b ehavior of the neutrino oscillation is same as the vacuum
s
oscillation For j j high neutrino energies the e ective mixing angle and oscillation
length b ecomes
m
sin sin
m
p V
s
l k m
m
V
s
The oscillation length for the high momentum neutrino is indep endent of E or m
and closes to b e the diameter of the Earth The survival probability of at the high
energy limit is
V L m
s
sin sin P
m
p V
s
2 2 2
m L
sin In the case of short L compared to the Earth s diameter P b ecomes
4 m
p
which is the same as P in vacuum oscillation at high momentum limit For j j the
matter e ect is strongly enhanced This condition is rewritten as
m m
E GeV
msw
V m
s
atm
where m eV is the b est t value for oscillation obtained by
atm
the Sup er Kamiokande exp eriment In the case of m the oscillation
s
is enhanced around E and the oscillation is suppressed at the same energy
msw s
region For m on the contrary is enhanced suppressed This
s s
is b ecause of the di erence of sign of V Figure shows the survival probability of
s
neutrino with energy E and GeV in the case of m and sin
and Figure shows the mass density distribution of the Earth used in this
thesis
MATTER EFFECT
1.2 (a) 1.2 (b)
prob 1 prob 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 -1 -0.8 -0.6 -0.4 -0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 COSΘ COSΘ 1.2 (c) 1.2 (d)
prob 1 prob 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 -1 -0.8 -0.6 -0.4 -0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0
COSΘ COSΘ
Figure Survival probability of as a function of zenith angle cos m is set to b e
eV which is the b est t parameter obtained by Sup er Kamiokande Solid
line E GeV Broken line E GeV Dashed line E GeV a for
with sin b for with sin c for with sin
s s
d for with sin The structure of at cos is caused by
s s
the core of the Earth
CHAPTER INTRODUCTION ) 3 14
12
density (g/cm 10
Figure Mass density
8
distribution in the Earth as
6
a function of the radius of
4
the Earth
2
0 0 1000 2000 3000 4000 5000 6000 7000
radios (km)
Sterile neutrino
In this section we describ e the sterile neutrino mentioned in the previous section is
s
requested to explain the atmospheric neutrino anomaly and at the same time to interpret
neutrinos as the candidate of hot dark matter
Indication of the Hot dark matter mo del
Another interesting sub ject related to the massive neutrino physics is the hot dark matter
Neutrinos are the most natural candidates of the hot dark matter b ecause they are
solitary particles whose existence have b een con rmed In the standard big bang mo del
the contribution of the massive neutrinos to the energy density is given by
P
m
i
i
neutr ino
h eV
where h is the Hubble constant in units of k m s M pc It was rep orted
that a hot cold dark matter mixture with can explain the struc
neutr inos
. eV if has the heaviest ture formation This corresp onds to eV . m
mass among all avors of neutrino and neutrinos have the large mass di erence in the
2
Recent results from CHORUS and NOMAD excluded the ! oscillation with parameter
2
2 2 4
region m & eV and sin However if the mixing angle among and is less than
the exp erimental results are compatible with this assumption
STERILE NEUTRINO
same way as the charged leptons However this assumption is not compatible with the
eV observations of the atmospheric and solar neutrinos Figure proves M
that contradicts with Eq Accordingly another neutrino to solve this question is
introduced into the frame of neutrino oscillation The new neutrinos should not interact
with matter via weak current b ecause the number of active neutrinos with M M
z
are proved to b e by exp eriments at LEP and SLAC Therefore this new neutrino
is called sterile neutrino
Constraints for sterile neutrino
Bounds on the existence of sterile states with large mixing to the standard neutrinos have
b een obtained from cosmological considerations For large enough values of the mixing
angle and m the oscillations of standard neutrinos into sterile ones can bring the sterile
states into the thermal equilibrium with matters b efore the nucleosynthesis ep o ch The
increase in the energy density results in the overproduction of primordial helium sp oiling
the success of Big Bang Nucleosynthesis Schramm and Turner have estimated the
upp er limit C L on the number of light degrees of freedom at nucleosynthesis
as N This b ound according to the analyses in
is incompatible with the explanation of the atmospheric neutrino problem due to the
mixing b etween muon and sterile neutrinos b ecause the allowed region in the oscillation
parameter space would result in N
However a recent work has shown that this cosmological b ound can b e evaded
considering the suppression of oscillations due to the p ossible presence of a lepton asym
metry in the early universe that can b e generated by the oscillations themselves
Pseudo Dirac neutrinos mo del
Here we introduce a scenario pseudo Dirac neutrinos mo del which predicts sterile
neutrino This mo del can lead to the maximum mixing of oscillation by installing
s
the right handed neutrinos and the light Ma jonara mass The result from Sup er
Kamiokande proves neutrinos to b e massive particles It indicates the evidence of the
right handed neutrinos b ecause it is natural that the neutrino mass is derived from the
CHAPTER INTRODUCTION
coupling of the left handed and the right handed ones Moreover neutrinos can have
the Ma jonara mass term b ecause they are neutral particles Therefore a prerequisite for
the pseudo Dirac neutrinos mo del is naturally introduced from the neutrino oscillation
This mo del interprets as the right handed neutrino which dose not interact with
s
The matter via weak interaction The oscillation is thought to b e
s L
L
reason why is not but is that oscillation must conserve the angular
s R L s
momentum
Generally the neutrino mass term Dirac Ma jonara mass term can b e added to the
standard mo del Lagrangian without sp ecial mo di cations For one neutrino generation
neutrino mass eigenstates are expressed as
p
m m m m m
L R L R
D
m
where m is the Dirac mass and m m are the left and the right handed Ma jonara
D L R
masses The mixing angle b etween the two states corresp onding to the ab ove mass eigen
state is
m
D
tan
m m
R L
The pseudo Dirac neutrino mo del assumes m m m m so that Eq
R L D
can b e rewritten as
m m m
D
Therefore
m m m
D
in this scenario Also the right term in Eq go es to in nity which means sin
The maximum mixing of are conducted
s
Di erence b etween ! and ! in Sup er
s
Kamiokande
As mentioned in Sec the existence of a ects astrophysics like the big bang nucle
s
osynthesis and the hot cold dark matter scenario Thus it is interesting to distinguish
DIFFERENCE BETWEEN AND IN SUPER KAMIOKANDE
S
b etween and oscillation for the solution of the atmospheric neutrino oscil
s
lation There are two samples to distinguish from at Sup er Kamiokande
s
In this thesis the study of and in Sup er Kamiokande is presented by
s
using the following two samples
Neutral current sample
Tau neutrinos interact with a nucleon via neutral current in the same way as muon
neutrino but by de nition sterile neutrinos do not Therefore if oscillation
s
is the solution of the atmospheric neutrino oscillation we can nd a de cit of neutral
current events At present one of the promising p ossibility to identify the neutral current
e ect is to study the reaction of one neutral pion pro duction N N Another
approach to the neutral current events is the study of multi ring events b ecause the
fraction of neutral current events in the multi ring events is signi cantly higher than that
in single ring events
In this thesis we use the zenith angle distribution of multi ring event to reduce several
systematic errors
High energy sample
When neutrinos propagate in matter we must consider the matter e ect see Sec
The neutral current cross section for and are identical Accordingly the additional
p otential of is identical to the p otential of and the oscillation in matter is
the same as vacuum oscillation This e ect was rep orted in Refs As shown
in Sec however is not a ected by the matter as a result oscillation
s s
is mo di ed by matter e ect The matter e ect is signi cant at the high energy region
therefore we study the zenith angle distribution of PC events whose E GeV is
higher than that of FC single ring multi GeV events GeV
Chapter
Detector
The Sup er Kamiokande detector is a cylindrical kiloton ring imaging water Cherenkov
detector It is lo cated m underground in the Kamioka Observatory in the Kamioka
mine in Gifu Prefecture Japan The m thickness of ro ck is equivalent to m of
water At this depth the cosmic ray muon ux is reduced down to of that of the
surface The trigger rate due to cosmic ray muons is ab out Hz The principle of the
water Cherenkov detector is explained in Sec and details of the exp erimental setup
are presented in Sec
Water Cherenkov detector
In Sup er Kamiokande the Cherenkov photons are detected by Photo Multiplier Tubes
PMTs surrounding the inner water mass It can reconstruct the vertex p osition number
of Cherenkov rings direction momentum and particle type of the charged particle which
pro duced each Cherenkov ring based on the information of the photon arrival time and
pulse height from each PMT This sort of detector suppresses the cost of construction so
that we can make a large detector
Cherenkov photons are emitted from a charged particle traveling in a medium at the
velocity faster than the light velocity in the medium They are emitted on a cone with a
half op ening angle with resp ect to the particle direction The directionality of Cherenkov
light enables us to reconstruct the direction of a charged particle Let b e the velocity
CHAPTER DETECTOR
of a charged particle and n b e the index of refraction in the medium n in
water it dep ends on the wavelength of the light the relation of and n is explained
as following
cos
n
The number of Cherenkov photons emitted p er unit path length par unit frequency is
given by
d N
dxd c n
where is the ne structure constant x is the path length of the charged particle and
is the frequency of the emitted photon The number of Cherenkov photons emitted by a
charged particle with in the wavelength range of n m which is the sensitive
region of our PMT is ab out p er cm
The total number of Cherenkov photons is related to the energy of the charged particle
Esp ecially for electrons and gammas it is almost prop ortional to the energy We can
estimate the energy of the charged particle based on the ab ove relation Moreover the
number of charged particles is measured from the number of the Cherenkov rings on the
detector wall In addition it is p ossible to identify the particle type by using the photon
distribution in the Cherenkov ring
Water tank
Figure shows the view of Sup er Kamiokande The whole detector is held in a stainless
steel tank of m in diameter and m in height The detector is separated into
two parts the inner detector ID is completely surrounded by the outer detector OD
The two detectors are optically separated by a pair of opaque sheets which enclose a dead
region of cm in thickness as shown in Fig There are complicated stainless steel
frames for supp orting the PMTs in this optically insensitive region The reason for the
division is to identify entering cosmic ray muons from outside to shield gamma ray and
neutrons from the ro ck and to separate fully contained events and partially contained events
WATER TANK
LINAC room
electronics hut
control room
20" PMTs
water system
Mt. IKENOYAMA
1000m
Figure The Sup er Kamiokande detector Inset at b ottom right shows the lo cation
within the mountain
Tyvek Top 8" PMT
Black seat
Barrel
20" PMT
Bottom
Figure The schematic view of the frame which supp orts PMTs
CHAPTER DETECTOR
tank Dimensions m in diameter m in height
volume kton
ID Dimensions m in diameter m in height
volume kton
Num of PMT top and b ottom and side
OD Thickness m on top and b ottom
m on side
volume kton
Num of PMT top b ottom and side
Fiducial region Thickness m from the ID wall
volume kton
Table Several parameters of the Sup er Kamiokande detector
Magnetic eld of over mG causes the timing resolution of PMTs worse The geo
magnetic eld at the Sup er Kamiokande site is ab out mG sets of Helmholz coils
are lo cated in the tank to comp ensate for the magnetic eld The Helmholz coils reduce
the magnetic eld inside the tank to mG
The ID is m in height and m in diameter and m in volume these
dimensions are su cient to contain muons with momentum up to GeV c Water
Cherenkov detector should have a large photosensitive area to detect as many Cherenkov
photons as p ossible Therefore the ID is lined with inch PMTs uniformly The
ratio of the photosensitive area to the all surface area photo coverage is which
is twice as large as that of Kamiokande The surface of the ID is covered with black
p olyethylene terephtalate sheets called black sheet just b ehind the inner PMT s photo
catho de as shown in Fig
In the OD there are inch outward facing PMTs with wavelength shifter plates
which increase photo coverage To maximize the light detection e ciency all surfaces
of the OD are covered with white tyvek sheets with a re ectivity of ab ove The
thickness of the OD water including the dead region is m
The several parameters of Sup er Kamiokande are summarized in Table
PHOTO MULTIPLIER TUBES
cable
glass multi-seal 70000 460 ~ φ cable length φ 116 φ 82 2 < φ 520 φ 254 10
water proof structure photosensitive area >
( 610 20 )
720
~ (mm)
Figure The schematic view of the PMT used in Sup er Kamiokande
Photo Multiplier Tubes
Inner PMT
Figure shows a schematic view of the inch PMT The original inch PMT was
made by Hamamatsu Photonics Company for Kamiokande
It was improved in the dyno de shap e the bleeder chain to attain b etter timing and
energy resolutions for Sup er Kamiokande Figure shows the pulse height distribution
for single photo electron signals Figure shows the quantum e ciency of the inch
PMT Prop erties of the PMT are summarized in Table The details of the inch
PMT are presented in
Outer PMT
We use inch Hamamatsu R PMTs which were used at the IMB exp eriment
for the OD The timing resolution of the PMT is ns A cm cm cm wave
length shifter is optically coupled to each inch PMT in order to enhance light collection
The wave length shifter makes the light collection increase by whereas the timing
CHAPTER DETECTOR
Figure Single photo electron distribution of the PMT used in Sup er Kamiokande
0.2
Quantum efficiency 0.1
0 300 400 500 600 700
Wave length (nm)
Figure The quantum e ciency as a function of the wavelength of the light
WATER PURIFICATION SYSTEM
Photo catho de area cm in diameter
Shap e Hemispherical
Window material Pyrex glass mm
Photo catho de material Bialkali
Dyno des stage Venetian blind
Pressure tolerance kg cm water pro of
Quantum e ciency at nm
Gain at Volt
Dark current nA at gain
Dark pulse rate kHz at gain
Catho de non uniformity less than
Ano de non uniformity less than
Transit time spread ns
Table The prop erties of the inch PMT
resolution go es down to ns which is still enough for OD
Water puri cation system
In the Kamioka mine there is clean water owing near the detector and it can b e used
freely in large quantities In this section the water system and the radon free air system
are presented
Water puri cation system
This water is circulated through the water puri cation system The purp ose of this water
puri cation system is
To keep the water transparency as clear as p ossible Small dust metal ions like
Fe Ni Co and bacteria in the water should b e removed
To remove the radioactive material mainly Rn Ra and Th
CHAPTER DETECTOR
m
Figure A ow diagram of the water puri cation system
Fig shows the follow diagram of the water system The water puri cation system
consists of the following comp onents
m Filter
Heat exchanger To keep the water temp erature at around C to suppress bac
teria growth
Ion exchanger To remove metal ions in the water
Ultra violet sterilizer To kill bacteria According to the do cumentation the number
of bacteria can b e reduced to less than ml
Vacuum degasi er To remove gas resolved in the water It is able to remove ab out
of the oxygen gas and of the radon gas
Ultra lter UF To remove small dust even of the order of nm
Bu er tank
Reverse osmosis
DATA ACQUISITION SYSTEM
The water is taken from the top of the tank using a pump and returned to its b ottom
Its ow rate is ab out tons hour This system keeps the water transparency ab ove m
Radon free air system
There is cm space b etween the surface of the water and the top of the water tank
Radon gas contaminated in the air in the gap could dissolve in the water Radon free air
is sent to this region The concentration of radon in the mine air is of order of
Bq m It changes seasonally b ecause the ow of air in the mine changes This system
consists of the following comp onents
Compressor Air is compressed to atm
m air lter
Bu er tank
Air drier To remove moisture in the gas to improve the e ciency of removing radon
This system can remove CO in the gas to o
Carb on column To remove radon gas
m and m air lter
C cold carb on column
The concentration of radon in the air through this system is reduced to the order of a
few Bq m in all seasons
Data acquisition system
Electronics for the ID
A blo ck diagram of the electronics for the ID is shown in Fig The signals from
PMTs in ID are sent to a TKO system The TKO system consists of GONGs
1
Tristan KEK Online
2
GO and NoGo trigger distribution mo dule
CHAPTER DETECTOR
Analog Timing Mo dules ATM and SCHs
The main functions of ATM are to digitize the singles from the PMTs and to make
trigger signals ATM digitizes b oth timing and charge information of the PMT signal
ATM has the channels for each PMT to reduce the dead time If one channel is not
available the other one can b e used instead This structure enables us to detect a decay
electron signal from a which is very imp ortant for several analyses on the atmospheric
neutrino or proton decay The conversion factor is ns count and pC count for
timing and charge resp ectively The digitized data are sent to and stored in SMP every
global trigger The digital data from SMP mo dules are sent to online computers for
data acquisition
The signal exceeding the threshold value corresp onding to ab out p e generates a
rectangular pulse with the width of nanoseconds and height of mV These signals
are summed to b e used for the trigger The summing signal go es through a discriminator
that determines the trigger threshold The value of the threshold is set to mV cor
resp onding to hits or approximately MeV for electrons This means that a global
trigger is generated when PMTs are hit in any nanoseconds time window
Electronics for the OD
Signals from the OD PMT are sent to a Charge to Time Converter QTC mo dule which
generates a rectangular pulse with a width prop ortional to the input charge The pulses
which have charge and timing information are digitized in Time to Distal converters
LeCroy multi hit TDC The TDC has input channels and the minimum time unit
of the TDC is nanoseconds This TDC can record multi hits within a microsecond
window The timing of the signal windows are set to to microseconds to the global
trigger timing The TDC is a FASTBUS mo dule and its crate is controlled by a FASTBUS
Smart Carte Controller FSCC The FSCC sends the digitized PMT data from TDCs
to DPM mo dules Finally these data are read out by the OD data taking workstation
through a VME bus
3
Sup er Controller Header bus interface mo dule
4
Sup er Memory Partner
5
Dual Ported Memory
DATA ACQUISITION SYSTEM
20-inch PMT
SCH ATM
x 20 x 240 ATM GONG 20-inch PMT
SCH ATM interface SUN classic x 20 x 240 SMP ATM GONG SMP online CPU(slave) SMP SMP SMP SMP Super Memory Partner x 6
VME 20-inch PMT
SCH SUN classic ATM online CPU(slave) x 20 x 240 ATM SUN classic GONG Analog Timing Module online CPU(host) online CPU(slave) TKO SUN classic FDDI SUN sparc10 online CPU(slave)
SUN classic
online CPU(slave)
SUN classic FDDI online CPU(slave)
SUN classic
online CPU(slave)
interface online CPU SUN classic (slave) SMP SUN classic SMP online CPU(slave) SMP SMP SMP SMP Super Memory Partner interface VME VME interrupt reg. 20-inch PMT TRG
SCH ATM TRIGGER
TRIGGER x 20 PROCESSOR x 240 HIT INFORMATION ATM GONG Analog Timing Module
TKO
PMT x 11200 ATM x ~1000 SMP x 48 online CPU(slave) x 9
Figure Data accusation system for the ID
CHAPTER DETECTOR
Online and o ine systems
Each front end workstation reads out the data from electronics indep endently and trans
fers to an online host computer via FDDI They are then sent to the o ine computer
lo cated outside of the mine via an optical b er cable The data are transferred every ten
minutes and its size is ab out MByte The o ine host computer saves all the data in
a tap e library And it converts the data to o ine format ZBS ADC and TDC counts
are converted to the units of photo electrons and nanoseconds resp ectively Finally the
o ine data are distributed to analysis computers for the rst reduction
6
Zebra Bank System
Chapter
Calibration
In order to reconstruct the neutrino events precisely we calibrated the gain and timing re
sp onse of each PMT and the absolute energy and measured the water transparency This
chapter surveys the metho d of relative PMT gain calibration absolute PMT gain cali
bration timing calibration water transparency measurements and the absolute energy
calibration
Relative PMT gain calibration
A Xe lamp and scintillation ball system was used to calibrate the relative gain of PMTs
Figure illustrates the setup of the relative gain calibration system We used a Xe ash
lamp as the light source and a scintillation ball as the wavelength sifter The light was
passed through a UV lter to match the absorption wavelength of a wavelength shifter and
through ND lters to adjust the light intensity Then it is fed into the scintillation ball via
an optical b er The scintillation ball was made of acrylic resin which uniformly contains
ppm BBOT and ppm MgO p owder to emit isotopic light Where BBOT and MgO
were used to shift wavelength and di use light resp ectively The typical wavelength of
the light emitted from the scintillation ball was nm which is similar to the typical
wavelength of Cherenkov light
CHAPTER CALIBRATION
UV filter ND filter Xe Flash Lamp
Optical fiber
Figure The setup of the Xe
SK TANK
lamp and the scintillation ball
Photo Diode Photo Diode
system for the relative gain cal
Scintilator Ball ADC ibration
PMT
Scintilator Monitor 20inch Trigger
PMT
The relative gain of the i th PMT is obtained by the following equation
r Q
i I
r exp Q G
o i
i
f L
where f is a relative photosensitive area of the PMT viewed from an angle as shown
in Fig a is an angle shown in Fig b Q is a charge in units of pC detected
i
by the i th PMT L is a light attenuation length in the detector Q is a normalization
factor to adjust the average G to unity We set a high voltage HV values of each PMT
i
so that all PMTs have a common gain We to ok the data for the relative gain calibration
times by changing the p osition of the scintillation ball from to m in height from
the b ottom PMT surface in order to minimize the r and f dep endence to each PMT
i
After the relative gain correction we to ok the data with the same system again to check
the relative calibration Figure shows a gain spread of the ID PMTs According to
this gure the gain spread is reduced to b e Since the average number of hit PMTs
was ab out for atmospheric neutrino events ambiguity in the energy measurement
p
This value from the relative gain spread is estimated to b e only
is much smaller then the uncertainty in the absolute energy calibration of the
Sup er Kamiokande detector
RELATIVE PMT GAIN CALIBRATION
1 (a) (b) direction of 0.75 emitted Cerenkov photon ) θ
f( 0.5
0.25 θ i i th PMT 0 0 20 40 60 80
θ (degree)
Figure The relative photosensitive area f a shows the relative PMT photo
sensitive area as a function of b illustrates the de nition of
2000
1750 11146 PMTs σ = 7.%
1500
The gain spread
1250 Figure
the ID PMTs The
1000 of
of relative gain is re
750 spread
duced to b e 500 number of events number 250
0 0 40 80 120 160 200 3 corrected Q (p.e.) x 10
CHAPTER CALIBRATION
mean 2.055pC
3
2 Ni wire +water 200mm Cf 1
0 0 5 10 pC
190mm
Figure The single photo electron dis
Figure The view of Ni Cf source
tribution obtained by the Ni calibration
Absolute PMT gain calibration
An absolute gain of the PMT was calibrated by measuring a charge distribution of single
photo electron p e In order to take the single p e distribution we used low energy
gamma rays emitted from thermal neutron capture in nickel Ni n Ni b ecause the
number of p e in a PMT for such a low energy event is almost one Neutrons were pro
duced by sp ontaneous ssion of Cf The Ni Cf source shown in Figure was lo cated
at the center of the inner detector Figure shows the typical single p e distribution
Since a mean value of this distribution was pC the relation b etween pC and p e is
p e pC The absolute gain of the PMTs was
Timing calibration
Let us de ne T as the time when a PMT signal exceeds a threshold in the discriminator
T is di erent PMT by PMT b ecause of the di erence of transit time and the cable length
of each PMT In addition T dep ends on the pulse height b ecause of the slewing e ect
that large signals tend to exceed the threshold earlier than the small ones
In order to use the timing information in the data analyses we have to make corrections
WATER TRANSPARENCY
980
970
960
Figure TQ map of a
950
typical PMT The white cir
940
cles and the error bars show
930
p eak values and resolu 920 the
T (nsec)
at sigma level re 910 tion
900 sp ectively Linear Scale Log Scale 890
880
Q (p.e.)
to T For this purp ose we made TQ map This map is the relation table b etween the
pulse height and timing resp onse and includes the correction of transit time In order to
make this map we used a later and di using ball system b ecause the timing width of
the light source had to b e narrow compared to the width of T spread Therefore we used
the dye laser pump ed by a pulsed N laser whose pulse width is ab out nanoseconds
The laser light was passed through several optical lters to adjust light intensity and
then fed into a di using ball via an optical b er TQ map of each PMT was obtained by
the laser calibration and Fig shows a typical TQ map for a PMT In addition the
timing resolution at each pulse height was estimated from TQ map by tting the spread
of T distribution at each pulse height with Gaussian distribution as shown in Fig
This distribution is used in the detector simulation
Water transparency
The water transparency is an imp ortant information for the data analysis such as energy
reconstruction It was estimated by two indep endent metho ds one metho d was the direct
measurement by a dye laser and CCD camera the other used the cosmic ray muons
1
T timing Q charge map
CHAPTER CALIBRATION
5
4.5
4
T (nsec) 3.5 ∆
3
Figure Timing resolu
2.5
as a function of the 2 tion
1.5
pulse height 1
0.5
0 -1 2
10 1 Q(p.e.) 10 10
Direct measurement with a dye laser
Figure shows the setup of the dye laser plus CCD camera system The light emitted
from a dye laser was split into two optical b ers One was fed into a inch PMT to
monitor the intensity of the light I and the other into a di usion ball and is remitted
l aser
isotropically The relation b etween the intensity of the image of the di usion ball taken
by the CCD camera I and I is expressed as follows
CCD l aser
l I
d CCD
const exp
I L l
l aser
d
where is a wavelength L is an attenuation length l is the distance b etween the
d
L
CCD
l as a function di usion ball and the CCD Figure shows the observation of the
d
I
laser
of I for wavelength of nm By tting the data with a least square metho d the
d
attenuation length at ns was estimated to b e m Similarly the attenuation
at various wavelengths were estimated as summarized in Fig These results are used
in the detector simulation
Cosmic ray muon metho d
The attenuation length in water was also measured by the through going cosmic ray
muons The energy dep osited by the cosmic ray muon in the detector was almost inde
p endent of the muon energy M eV cm b ecause main muon interaction with water
is dominated by the ionization loss which weakly dep ends on the muon energy at high
energy region Therefore the cosmic ray muon can b e used for a calibration source Only
vertical muons are used for the calibration In contrast to the direct measurement metho d
WATER TRANSPARENCY
Figure The setup of the dye laser CCD camera system for the measurement of the
waver transparency
14-Dec-1996(420nm) ± Dec.-3,4-96 Dec.-14-96 4 L=92.2 5.2m Dec.-17-96 Dec.-27-96 10CCD/PMT Jan.-18-97 Mar.-05-97 Nov.-17-97 Apr.-18-98 -1 10
absorption attenuation coefficient(1/m)
-2 10
Rayleigh scattring Mie scattering 0 10 20 30 distance from CCD (m) -3 10 200 250 300 350 400 450 500 550 600 650 700
wavelength (nm)
Figure The observed light attenuation
Figure The L plot as a function of
length at nm
the wave length Solid lines show the attenu
ation length used in the detector simulation
CHAPTER CALIBRATION
)) 192.0 / 19 θ RUN 3106 P1 5.987 0.4609E-03
500 P2 -0.9487E-04 0.4444E-06
log(Ql/f(
Q l
The log
400 Figure
f
as a function of l The
300 plot
solid line shows the tting
200 result
0 1000 2000 3000 4000 5000
l (cm)
cosmic ray muon metho d can b e carried out during a normal data taking therefore this
metho d is useful to check a time variation of the attenuation length
Under an assumption that the light reaching PMT was only non scattered light the
observed charge Q by a PMT can b e expressed by the following equation
l f
exp Q const
l L
where l is the light path length L is the attenuation length of the Cherenkov light Figure
Q l
plot v s l in a typical run The attenuation length obtained from shows l og
f
Fig was m error of the tting Since the attenuation length in water
varied with the condition of water puri cation system it was calculated for each run to
correct for the time variation Figure shows the time variation of the attenuation
length obtained by the cosmic ray muon metho d
Absolute energy calibration
We must understand how precise the Monte Carlo simulation repro duces the absolute
energy scale b ecause the systematic uncertainty in the absolute energy scale a ects the
atmospheric neutrino ux measurements We have ve calibration sources for the absolute
energy calibration decay electrons from stopping cosmic ray muons mass LINAC low
and high energy stopping cosmic ray muons In this section we describ e these calibration metho ds
ABSOLUTE ENERGY CALIBRATION
160 140 120 100 80 60 40 20 attenuation length (m) attenuation 0 A J O J A J O J A J O J A J P U C A P U C A P U C A P U R L T N R L T N R L T N R L 9 9 9 9
6 7 8 9
Figure The time variation of light attenuation length in water measured by cosmic
ray muons Only the data after the end of May shown by an arrow are used in
this thesis
Decay electrons
We have a large number of low energy electrons by the decay of cosmic ray stopping
muons The absolute energy scale was checked by comparing the momentum of the decay
electrons from the stopping cosmic ray muons b etween the real data and the Monte Carlo
prediction Decay electrons were selected with the following criteria
electrons are detected from to micro seconds after the trigger of a parent muon
number of ID hits is less than
g oddoness is more than
l ow
the vertex p osition is reconstructed in the ducial volume
Monte Carlo events were generated uniformly in the ducial volume and randomly for
the direction Figure shows the momentum sp ectrum for electrons in the ducial
volume compared with the Monte Carlo predictions An e ect of the nucleon Column
eld caused by the atomic capture of a parent muon were considered in the sp ectrum
CHAPTER CALIBRATION
Mean DATA = 38.64 MC = 37.89
80
Figure Momentum
sp ectrum of the decay elec
60
trons from the stopping cos
mic ray muons in the du
40
cial volume The p oints
with error bars show the
and the histogram
20 data
shows Monte Carlo
0 0 20 40 60
MeV/c
of the Monte Carlo events The sp ectrum of the data agrees well with that of the Monte
Carlo The mean value of the data is higher than that of the Monte Carlo
The decay electron is also used to check the detector stability Figure shows the
time variation of the reconstructed momentum of the decay electron events This gure
illustrates that the absolute gain for relatively low energy events is stable within
LINAC
In Sup er Kamiokande an electron linear accelerator LINAC is used to understand pre
cisely the p erformance of the detector for low energy events The energy of electrons
cab b e adjusted from to MeV and energy spread at the end of the b eam pip e is less
than We used electrons with the energy of MeV The injected p osition was m
from the top PMT surface and the direction was downward LINAC electron events were
selected according to the following criteria
number of ID hits is b etween and
g oodness is more than
l ow
the distance b etween the injected p osition and the reconstructed p osition is less
than m
ABSOLUTE ENERGY CALIBRATION
45 44 43
42
Time variation
41 Figure
the reconstructed mo 40 of
± 1 %
of the decay elec 39 mentum
38 tron 37 36 Reconstructed Momentum (MeV/c) 35 0 200 400 600 800 1000 1200
elapsed days from 1/Apr/1996
Figure shows the momentum distribution for LINAC electrons compared with the
Monte Carlo events The agreement of the momentum distribution b etween the data and
Monte Carlo is satisfactory The mean value of the real data was lower than that of
the Monte Carlo
mass
Selection criteria of events are describ ed in App endix B Here we explain the result
only We estimate the uncertainty in the reconstruction e ciency to b e see
App endix B Since this uncertainty increases with increasing momentum we used
the s with momentum MeV c to reduce the uncertainty Figure shows the
distribution for the real data and the Monte Carlo The tted p eak is higher M
for the real data than for the Monte Carlo
Low energy stopping cosmic ray muons
Using the op ening angle of the Cherenkov ring for low energy muons we can estimate the
momentum indep endent of the p e information to check the systematic uncertainty of
the momentum reconstruction The relation b etween the momentum p and the op ening
CHAPTER CALIBRATION
Mean DATA = 16.97
MC = 17.38
Momentum
100 Figure
sp ectrum of LINAC elec
trons The p oints with er
ror bars shows the data and
50
the histogram shows Monte Carlo
0 0 10 20 30 MeV/c
Constant 15.24 2.526 Mean 149.9 2.265 20 (a) Sigma 16.39 1.884
10
distribu Figure M
0
tions a for data b 200
Constant 122.6 6.918
Monte Carlo prediction Mean 146.2 0.9306 for
150 (b) Sigma 19.59 0.9529
The solid line shows the re number of events number
100
sult of a Gaussian t 50
0 0 50 100 150 200 250 reconstructed M(π 0) MeV/C2
ABSOLUTE ENERGY CALIBRATION
0.4 0.4 (a) (b) 0.35 0.35 0.3 0.3 0.25 0.25 0.2 0.2
momentum (GeV/c) 30 35 40 45 30 35 40 45
opening angle (deg.)
Figure Op ening angle vs momentum plots for the stopping muon events a for the
real data b for the Monte Carlo
angle is given by
p
p m
cos
np
where n is the index of refraction of the water and m is the muon mass We used stopping
muons which enter from the top wall and have one decay electron Figure shows the
reconstructed momentum as a function of the op ening angle for the low energy stopping
muon events We calculated a momentum momentum estimated by the op ening angle
ratio R To estimated the momentum dep endence data are divided into momentum
p
bins Figure shows the R MC R data plots as a function of momentum This
p p
gure illustrates the systematic uncertainties of the momentum determination b etween
the data and the Monte Carlo The deviation from unity is less than
High energy stopping cosmic ray muons
In the high energy region the range of the stopping muon is used to check the abso
lute energy scale b ecause the range of the stopping muons is prop ortional to the muon
CHAPTER CALIBRATION
1.1
Figure R MC R data
p p (DATA)
p
as a function of momen
1 ±1.5% plots
tum Crosses show the average (MC)/R
p
of R MC R data and dot
R P
0.9 p
ted lines show 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Momentum (GeV/c)
momentum and it is easy to calculate the end p oint of the muons by nding the vertex
p osition of the muon decay electrons The range is de ned as the distance from the vertex
p osition of the stopping muon to the vertex p osition of its decay electron Figure
shows the momentum and range ratio as a function of range The energy dep osit p er
cm is ab out MeV We used the events with the range longer than m b ecause the
ambiguity of the vertex determination a ects the range determination when the range is
short Events were devised into bins by the range The average of the momentum range
ratio for the real data and the Monte Carlo were calculated and the ratio is taken Figure
shows the ratio for the real data and the Monte Carlo events The ratio for the real
data was ab out lower than that for the Monte Carlo
Moreover we checked the detector stability by using this ratio Figure shows the
time variation of the ratio and demonstrates that the absolute gain at relatively high
energy range is stable within
Summary of the absolute energy calibration
Figure summarizes the studies for the absolute energy scale Events with the mo
mentum from MeV c to ab out GeV c were examined and the energy scale for the
Monte Carlo events agreed with that for the data within and
ABSOLUTE ENERGY CALIBRATION
4
3
Figure Momentum range
ratio of the stopping muon as a
2
function of range momentum/range (MeV/c/cm) momentum/range 1 0 10 20 30 40 range(m)
4
DATA M.C.
3
Figure Momentum range
plots as a function of range momentum/range (MeV/cm) 2
1 0 1000 2000 3000 4000 range (cm)
CHAPTER CALIBRATION
2.7
2.6
2.5 ± 1 % 2.4
2.3
2.2 Momentum/Range (MeV/cm) 2.1
2 0 200 400 600 800 1000 1200
elapsed days from 1/Apr/1996
Figure Time variation of the reconstructed momentum range for the real stopping
muon events
) 5
%
Summary of 4 Figure
3
the absolute energy calibra
2
the white circle for
1 tion
LINAC the black circle for (M.C./DATA) ( 0
∆
electron the triangle -1 decay
-2
for the white squares for
-3
low energy stopping
-4 the
black squares for the -5 -2 -1 and
10 10 1 10
energy stopping Momentum(GeV/c) high
Chapter
Data reduction
Reduction outline
Atmospheric neutrino events have two basic top ologies that determine the data reduction
stream If all of the visible energy is contained within ID the event is called fully
contained event FC An event for which some pro duced particles dep osit visible energy
in the OD is called partially contained event PC Figure shows the de nitions of
the FC and PC events In this analysis we used the data set from May to April
which corresp onded to days of detector livetime and the number of recorded
events for this p erio d were ab out millions
The main backgrounds for atmospheric neutrino events are the cosmic ray muon events
and low energy radioactivity in the detector
This chapter surveys the FC and PC reductions
FC reduction
The reduction for FC sample contains four steps Figure shows the algorithm of the
FC reduction Each reduction step is describ ed b elow
CHAPTER DATA REDUCTION
FC PC µ
ν ν
Figure De nitions of the FC and PC events The FC events required that all visible
particles stop in the ID whereas the PC events have particle reaching the OD
First reduction
The rst step of FC reduction was low energy events cut and OD cut The events whose
total photo electrons within ns PE were less than p e corresp onding to
visible energy MeV were rejected These low energy events were caused by radioac
tivity such a radon in the detector or gamma ray coming from the ro ck Figure shows
the PE distributions for the data and the Monte Carlo of the atmospheric neutrino
events with visible energy greater than MeV This gure demonstrates PC cut is
safe for FC neutrino events
The cosmic ray muon events had hit OD PMTs near the entrance and exit p oints
and they were rejected by eliminating the events for which the number of the hit OD
PMT within ns NHIT was greater than After these cuts the event rate was
reduced to event day
Second reduction
In the next reduction step we required a tighter OD and a max photo electron cuts OD
cut is essentially same as the rst reduction but here the events with NHIT greater
than were removed Figure shows the NHIT distribution for the data and the
Monte Carlo prediction for FC sample This gure demonstrates NHIT cut is safe for
FC event sample
FC REDUCTION
Raw Data 6 (10 /day)
1st Reduction Cut low E(E vis <23MeV) events Cut Nhit(anti-counter)>50 (4000/day)
2nd Reduction Cut Nhit(anti-counter)>25
(500/day)
3rd Reduction Flasher cuts Remaining cosmic ray µ rejection by checking reconstructed entrance/exit v.s.anti-counter hits.
(30/day)
4th Reduction Flasher cuts
(20/day)
SCAN 1 SCAN 2
FINAL SCAN
(16/day)
Final Sample >2m from wall (22.5kton) (8.4/day)
Evis >30MeV
Figure Algorithm of the FC reduction
CHAPTER DATA REDUCTION
10 5
Figure PE distribution
for days data the white his
10 4
togram for the raw data the number of events
3
one for the Monte Carlo
10 hatched
events with visible energy
10 2
M eV These Monte Carlo
are pro duced in the du
10 events
cial volume and their rates are
by the data livetime 1 normalized 0 50 100 150 200 250 300 350 400 450 500
PE (p.e.)
line shows the PE cut
300 The
10 6
10 5
Figure NHIT distribu
4
number of events
for days data the white
10 tion
for the raw data the
10 3 histogram
hatched one for the FC Monte
10 2
Carlo sample within the ducial
The solid line shows the
10 volume
NHIT cut 1 0 10 20 30 40 50
NHIT800
FC REDUCTION
10 6
Figure PE PE distri
max
10 5
bution for days data the
4
number of events 10
white histogram for data after the
reduction and the hatched
10 3 rst
one for the atmospheric neutrino
10 2
Monte Carlo events within the
volume The Monte Carlo
10 ducial
events are normalized by the live 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
time of data
PEmax/PE300
Max photo electron cut was applied to reject the ashing PMT events If some
problems o ccur in the dyno de of a PMT this PMT can make a large charge signal To
eliminate these events we required the PE PE ratio less than where PE
max max
is a maximum number of p e in PMTs Figure shows the PE PE distribution
max
and it demonstrates that the max photo electron cut is safe for neutrino events
The number of events satis ed these criteria were ab out events day
Third reduction
The next reduction step is comp osed of more intelligent algorithms The remaining events
except for neutrino events were either through going muons stopping muons low energy
events ashing PMT events cable hole muons or an accidental events These back
grounds were rejected by the following cuts
Through going muon cut
As shown in Fig remaining through going muon events have some hits in the OD
and make many Cherenkov photons in ID Therefore the events with PE p e
max
and the number of hit PMTs were candidates of through going muons and were
applied a sp ecial tter Through going muon tter The entrance p oint was determined
by the p osition of the earliest hit ID PMT with two or more neighbor PMTs hit Many
CHAPTER DATA REDUCTION
NUM 7 RUN 4376 SUBRUN 12 EVENT 544152 DATE 97-Jul- 6 TIME 4:17:53
TOT PE: 102657.6
A typical through MAX PE: 279.7 Figure NMHIT : 9699 ANT-PE: 110.9
ANT-MX: 22.5
muon event rejected by the
NMHITA: 70 going
through going muon cut The cir
cles in the gure show the hit
PMTs and the area of the circle is
to the observed p e 90/00/00:NoYet:NoYet prop ortional 90/00/00:;R= 0:NoYet RunMODE:NORMAL R : Z : PHI : GOOD TRG ID :00001111
0.00: 0.00: 0.00:0.000 T diff.:0.140E+06us
The small gure on the CANG : RTOT : AMOM : MS : 140. ms numbers FEVSK :81002003
nOD YK/LW:20/20
left side displays OD Q thr. : 0.0 upp er BAD ch.: masked SUB EV : 0/ 1 Dec-e: 0( 0/ 0/ 0) VQ: 0 0 0 0 VT: 0 0 0 0 Comnt; VQ: 0. 0. 0. 0.
VT: 0. 0. 0. 0.
Cherenkov photons are detected around the exit p oint of a muon thus the exit p oint was
de ned as the center p osition of saturated PMTs The events satisfying the following
conditions were identi ed as the through going muons and rejected
the number of OD hit PMTs within ns timing window within a radius of m
from the entrance or exit p oint in the outer detector was greater than
Figure shows the number of OD hit PMTs distributions for the through going candi
date events and the atmospheric neutrino Monte Carlo
Stopping muon cut
Figure shows a typical stopping muon In this reduction step the Stopping muon
tter was used It searched the vertex p oint in the same way as the Through going muon
tter And the direction was estimated by maximizing of the p e within the cone with
op ening angle Selection criteria for stopping muon cut were as the following
The number of hit PMTs within ns timing window within a radius of m from
the entrance p oint OD hit was greater than
ent
OD hit was more than and the go o dness of the stopping muon t was greater
ent
than
FC REDUCTION
10 4
3
The number of OD hit PMTs 10 (a) Figure
2
a for the number of hits in the
10 distribution
near the entrance p oint of the cosmic 10 cluster
1
muon b for the exit p oint The white 0 5 10 15 20 25 30 35 40 45 50 ray
4
is for the through going muons 10 histogram
3
and the hatched one for the atmo 10 (b) event 10 2
number of events
spheric neutrino Monte Carlo events within
10
the ducial volume The exp osure of data
1
Monte Carlo is days 0 5 10 15 20 25 30 35 40 45 50 and
number of OD hits
where the de nition of go o dness is the same as TDC t see Figure shows the
OD hit distribution The event which satis ed either one of the ab ove criteria was
ent
identi ed as a stopping muon and removed
Low energy event cut
In this step low energy tter was used This tter searches for the vertex p oint with an
assumption that all photons were pro duced at a p oint See Sec for the description
of the essential idea of this tter Low energy cut excluded the event with the number of
ID hits less than and N less than Where N is the maximum number of hits
within ns window in the time residual time time of ight of Cherenkov photon This
value is almost prop ortional to the visible energy at the low energy region and N
corresp onds to visible energy M eV
Flashing PMT cut
A Flashing PMT event was de ned as the event caused by the light emitted by a PMT
with a mechanical problem in the dyno de structure internal corona discharge Most of
the events have a b oard timing distribution compared to the neutrino events therefore
ashing PMT events were selected using the width of the timing distribution We
de ne N the minimum hits within a ns sliding time window in o timing region
min
of to s after the event trigger We rejected the events satisfying either of the
CHAPTER DATA REDUCTION
NUM 4 RUN 4376 SUBRUN 11 EVENT 490179 DATE 97-Jul- 6 TIME 4: 9:33 TOT PE: 9103.2 MAX PE: 92.2 NMHIT : 2675 ANT-PE: 71.7 ANT-MX: 7.5
NMHITA: 56
Figure A typical stopping
muon event rejected by the stop
ping muon cut
90/00/00:NoYet:NoYet 90/00/00:;R= 0:NoYet RunMODE:NORMAL R : Z : PHI : GOOD TRG ID :00001111 0.00: 0.00: 0.00:0.000 T diff.:0.183E+05us CANG : RTOT : AMOM : MS : 18.3 ms FEVSK :81002003 nOD YK/LW:20/19 Q thr. : 0.0 BAD ch.: masked SUB EV : 0/ 1 Dec-e: 0( 0/ 0/ 0) VQ: 0 0 0 0 VT: 0 0 0 0 Comnt; VQ: 0. 0. 0. 0. VT: 0. 0. 0. 0.
10 4 10 3 10 2 10
number of events 1 0 5 10 15 20 25 30 35 40 45 50
number of OD hits
Figure The number of OD hit PMTs distribution for the stopping muon events The
white histogram is for the stopping muon events and the hatched one for the atmospheric
neutrino Monte Carlo events within the ducial volume The exp osure of data and Monte
Carlo is days
FC REDUCTION
following selection criteria as the ashing PMT
ID hits
N
min
otherwise
Accidental hit cut
The accidental hit cut rejected the event that had two or more indep endent particles in an
event accidentally An event was rejected as accidental if b oth of the following conditions
were satis ed
OD hits with a ns time window b etween to ns after the event trigger
was more than
The total photo electron number in ID within a ns time window b etween
to ns was more than p e
Cable hole muon cut
Cables from ID and OD PMTs were bundled in the upp er OD layer and were taken out
of the tank through the cable holes Four of the cable holes were lo cated away
from the fringe of the tank and the identi cation e ciency of the OD was low for muons
passing near these cable holes In order to comp ensate for the ine ciency of the OD
around the four cable holes we installed m m veto scintillation counters on each
of the four cable holes in April Figure shows the vertex p osition distribution of
FC sample b efore after installation of the veto scintillation counters This gure shows
that the veto counters reject the muons through the cable holes
An event satis ed b oth of the following conditions was identi ed as a cosmic ray muon
and rejected even if there were a few OD hits
One of the veto scintillation counters was hit
Vertex was reconstructed within m from the cable hole by the stopping muon tter
The number of events passing the ab ove reductions was events day
CHAPTER DATA REDUCTION
20 (a) (b) 15 10
5
0 y-axis (m) -5 -10 -15 -20 -20 -10 0 10 20 -20 -10 0 10 20
x-axis (m)
Figure The vertex p osition distribution of the FC nal sample with z m
which indicates these events are out of the ducial volume The eight circles show p ositions
of cable holes a is for the distribution b efore installation of the veto counters b is
after the installation
Fourth reduction
Next reduction was another ashing PMT cut using pattern recognition algorithm
Since some ashing PMT events had the similar timing distribution as neutrino events
they were not rejected by the third reduction The remaining ashing PMT events had
rep eated charge pattern therefore we applied a pattern recognition program to remove
them The algorithm of this program is the following
divide detector s wall into regions roughly m patches
compute the sum of charge in each patch q
i
for two indep endent events A and B compute a linear correlation
A A B B
X
q hq i q hq i
i i
r
n A B
q q
A B
A B
where hq i and is the average and the deviation of q resp ectively r
A(B )
q
i
takes the value of less than and the higher value is estimated to b e b etter matched
PC REDUCTION
≥7 ≥7
Figure match v s
(a) (b)
r planes a for
6 6 maximum
selected events by eye
5 5 the
scan b for the ashing
match 4 4
PMT events Solid lines
3 3
show the cut criterion for
2 2
the forth reduction Events
1 1
at the right of the cut
are rejected as ashing
0 0 lines
events 0.4 0.6 0.8 1 0.4 0.6 0.8 1 PMT
maximum r
de ne match which is a number of events satisfying in r r where r is the
ant ant
cut value in r
an event is eliminated by a cut in a two dimensional match maximum r plane
as shown in Fig
The events passing this reduction were reduced to events day
PC reduction
The reduction for PC contains ve steps Figure shows the algorithm of the PC
reduction Each reduction step is describ ed b elow
First reduction
In rst step of PC reduction low energy events with less than total p e were
removed corresp onding to muons electrons with momentum less than MeV c
By de nition exiting particles must have reached the OD from the inner ducial volume
CHAPTER DATA REDUCTION
Raw Data (106 /day)
1st Reduction
Reject low E(E vis <120MeV) events Reject through-going muon (1) anti-countor T distribution > 240ns (2) anti-counter cluster > 1 (2/day)
(1,4000/day) 2nd Reduction SCAN 1 SCAN 2
Reject remaining through-going muon (1) anti-counter cluster >1 (anthor method) Reject counter clippers using anti-cluster Reject stopping muon FINAL SCAN (2000/day)
3rd Reduction (0.8/day) Automatic vertex and derection fitting Require absence of OD hits in the entrance region Final Sample >2m from wall (22.5kton) (100/day) 4th Reduction (0.57/day) Reject remaining corner clipper by reconstruced vertex Reject remaining long-track muon by muon fit Require no entrance point condidate in the backward-direction fmon the particle position
5th Reduction Automatic vertex and derection fitting Require absence of OD hits in the entrance region Reject toatl p.e. < 3000 ( E < 350 MeV)
Anti-counter-cluster > 9 hits
Figure Algorithm of the PC reduction
PC REDUCTION
Figure TWID distribu out
10 6
tion for days data The
5
histogram shows the data 10 white
number of events
and the hatched one
10 4 distribution
shows the Monte Carlo predic
10 3
tion of FC PC sample which is
10 2
pro duced in the ducial volume
exp osure of Monte Carlo is
10 The
the same as that of data The 1
0 50 100 150 200 250 300 350 400 450 500
solid line shows the cut criterion
TWIDout(sec)
TWID ns
out
and therefore must have had a minimum track length of ab out m corresp onding to
muons with MeV c momentum
Most of through going muons were rejected in this reduction step using timing distri
bution of OD hits Typical through going muon events have two OD clusters and therefore
have a broad timing distribution of OD hence the events whose width of the time distri
bution of hits in the OD TWID exceeded ns were eliminated TWID is shown
out out
in Fig
Moreover we required the number of cluster in the OD should b e less than or equal
to in order to reject the through going muon events The de nition of the cluster used
in the rst reduction is that the spatial cluster of neighboring hit PMTs One cluster is
formed around PMT which has more than p e and the clusters which lie within m are
merged Figure shows the number of OD clusters N C LS T A distribution of data
and atmospheric neutrino Monte Carlo This criterion is safe for PC neutrino events
Second reduction
The second reduction is also based on a clustering of the ID and OD signals The OD
clusters are calculated by an algorithm shown in Fig Each grid is separated by
m m size in the OD The cluster is formed by lo oking at the charge gradient
CHAPTER DATA REDUCTION
10 8
10 7
Figure N C LAS T A dis
6
the white histogram 10 tribution
number of events
the data distribution and
10 5 for
the hatched one for the Monte
10 4
Carlo prediction of FC PC sam
10 3
ple which is pro duced in the du
2
volume The exp osure of data
10 cial
and Monte Carlo is days 0 1 2 3 4
NCLSTA
to the neighboring grids We required that the number of the OD cluster N C LAS T A
which have more than hit PMTs should b e less than or equal to This cut eliminates
remaining through going muons
The cosmic muons that clipp ed the edge of ID were eliminated based on the top ology
of the OD cluster Cosmic ray muons which entered and stopp ed in the ID were removed
by excluding events whose ID photo electrons within m from the OD cluster PE
were less than p e This cut was safe for PC neutrino events b ecause PC events
must have left large numbers of photo electrons near the exit p oint Figure shows
the PE distributions for the data and PC Monte Carlo events The event rate after
the PC second reduction is ab out events day
Third reduction
In the third reduction the remaining cosmic ray muon and ashing PMT events were
rejected
The ashing PMT events were rejected in the same way we did for the FC ashing
PMT events see Sec
In order to identify cosmic ray muon a simple vertex t and direction estimate Point
t see Sec were used A requirement of less than hits in OD within m
of the back extrapolated entrance p oint EHIT was imp osed to reject cosmic ray
muons Figure shows the distribution of the number of OD hits within m of the
PC REDUCTION
Figure Schematic view of
clustering algorithm in the
Clu ster 1 the
second reduction The circles in
the gure show the sum of the
charge in each cluster The ar
rows represent the vector charge
gradient Each arrow p oints the
charge neighbor for a
Clu ster 2 highest
given angular bin The angular
grid is centered up on the anti
charge distribution The
Clu ster 3 counter
angular bin sizes corresp ond to
roughly m m
10 3
Figure PE distributions
the white histogram for the
number of events
data after the rst reduc
10 2 days
tion the hatched one for the PC
Monte Carlo prediction within
ducial volume with the same
10 the
livetime as data 0 1000 2000 3000 4000 5000 6000 PE200
CHAPTER DATA REDUCTION
10 3
Figure EHIT distribu
for days data the white 2 tions
number of events 10
histogram for the data after the
second reduction the hatched one
the PC Monte Carlo predic
10 for
tion The exp osure of Monte
Carlo is also days 1 0 10 20 30 40 50 60
EHIT800
back extrapolated entrance p oint for the data and PC Monte Carlo events The event
rate after the PC third reduction was ab out day
Fourth reduction
The remaining muon events after the third reduction were muons which left few entrance
hits in OD These events were rejected by the condition that the angle subtended by the
earliest ID PMT hit the vertex and the back extrapolated entrance p oint to b e
And to reject the remaining corner clipping muons we required a tted vertex to b e
at least m away from the fringes of the ID volume
Finally Through going muon tter see Sec was also applied to reject events
with a well t muon track greater than m long The events satisfying the following
events were rejected as the through going muon
Goodness of through going muon which means this tter can get the en
trance p oint and the direction of the through going muon
The estimated muon track length by the entrance and exit p oint is grater than
m
where the de nition of g oodness will b e describ ed in Sec
The event rate after the PC rth reduction was ab out events day
REDUCTION PERFORMANCE
fraction
rst
Table The fraction of
second
Monte Carlo events for PC
third
sample within ducial vol
forth
ume at each reduction step
rth
Fifth reduction
In order to further reject cosmic ray muon entering events an optimized automatic tting
algorithm what is called TDC t see was applied Again we required less than
hits in OD within m of the more accurately back extrapolated entrance p oint
At this stage we required that the total p e numbers of the ID should b e larger
than p e This requirement corresp onded to E M eV well b elow that of any
PC events It was estimated that of the PC events in the ducial volume were
eliminated by this requirement
Finally we required the number of OD cluster hits to reject FC events
The event rate after the PC fth reduction was events day
Reduction p erformance
We applied reduction program for atmospheric neutrino MC and checked the reduction
e ciency For FC events in the ducial volume with E M eV the reduction
v is
e ciency was estimated to b e On the other hand the e ciency for PC events
in the ducial volume was estimated to b e Table shows the fraction of Monte
Carlo events for PC sample at each reduction step
Scanning
After these software reduction steps the candidate events were reduced to and
events day for FC and PC sample resp ectively All the remaining events were scanned to
CHAPTER DATA REDUCTION
category fraction
stopping
Table Fraction of each
through going
category of the events which
ashing PMT
were rejected nal scan
noise
others
b e checked data quality by two physicists indep endently When the detector p erformance
was not go o d for instance to o many ashing events or some of the PMTs were not active
these runs subruns were regarded as bad runs bad subruns and were rejected At the
same time each scanner removed the remaining background events
After the double scan the nal scan was done to check the consistency of the double
scan result and made the nal data sample Because of the double scanning the scanning
e ciency was estimated to b e b etter than Table summarizes a category of the
event rejected by the scan
Finally candidate events were selected as the FC PC data sample
Chapter
Event reconstruction
Outline of reconstruction
After the event selection pro cesses events were reconstructed by pro cedures as shown in
Fig The ow of a reconstruction pro cess was separated into two one was a pro cess for
fully contained FC events another was for partially contained PC events These
pro cedures are fully automatic Therefore there is no bias by a physicist in the event
reconstruction pro cedures
For FC events the b eginning of all pro cesses was vertex reconstruction called TDC
t Then Ring counting which estimates the number of Cherenkov rings based on
a likelihoo d metho d was applied The next step was particle identi cation which dis
tinguishes b etween showering electron e type and non showering muon type For the
events identi ed as single ring in the second step a more precise tter MS t was
applied Finally the energy of particle was estimated from the intensity of Cherenkov
light
On the other hand PC event reconstruction involved the rst vertex tter only
These pro cesses are explained in this chapter
CHAPTER EVENT RECONSTRUCTION
FC sample PC sample
TDC t TDC t
Ring counting
Particle identi cation
Ms t for single ring
Energy reconstruction
Figure The ow chart of event reconstruction
TDC t
The principle of spatial reconstruction to ol TDC t is to search for the p osition where
the timing residuals t of the entire hit PMTs are equal The timing residual t of the i th
i i
hit PMT is de ned as
t t n c jP O j hti
i i
i
is the hit time of the where n is the refractive index of water c is the light velocity t
i
i th PMT hti is the average of t P shows the p osition vector of the i th PMT and
i i
O is the p osition vector of an assumed vertex p osition of the particle TDC t considers
the track length of the charged particle by using the total charge within a Cherenkov
cone Hence this pro cess needs to know the rough vertex direction and op ening angle
of the Cherenkov cone In this pro cess for simplicity it assumes that all events consist
of single ring
TDC t estimates the vertex direction and op ening angle of Cherenkov ring in the
following steps
TDCFIT
Point t which searches for a rough vertex using only the timing information of
hit PMTs
ring edge search which searches for the direction and op ening angle of the Cherenkov
ring pro duced by the most energetic charged particle
the ne vertex tting which determines more precise vertex by taking account of
the track length of the charged particle
The steps and are iterated until the distance b etween the previous vertex and the
latest one is less than centimeters
These three steps are describ ed b elow
Point t
The principle of Point t is to search for a p osition where the timing residual t of all the
i
hit PMTs are approximately equal To search for the vertex we use go o dness G
p
X
t
i
exp G
p
N
hit
i
where N is the number of hit PMTs in ID and is the typical timing resolution We
hit
use ns Because of a technical reason this value is larger than the actual timing
resolution of PMT ns It should b e noticed that the de nition of G is the sum
p
of gaussian probabilities This way the contribution to G of scattered photons which
p
2
t
i
pro duce delayed signal and therefore exp is minimized The Point t searches
2
for the p osition where G is maximum and its vertex resolution is ab out meter
p
After determining the vertex roughly Point t estimates the direction d de ned as
p
X
P O
i
C d
i p
jP O j
i
i
where C is the charge of the i th hit PMT i
CHAPTER EVENT RECONSTRUCTION
Cherenkov edge search
This pro cess searches for the direction and op ening angle of the Cherenkov ring which
maximize Q around the estimated direction in the previous step The pro cedure involves
the following steps
Make the angular distribution of the e ective charge CH where is the op ening
angle b etween the particle direction and Cherenkov photon direction Figure a
shows CH The e ective charge means the charge corrected in acceptance and
water transparency In addition CH is smo othed by taking account of the vertex
resolution
Obtain the op ening angle of Cherenkov ring which simultaneously satis es
edg e
the following two criteria
must b e larger than the angle at p eak p osition of CH
edg e peak
2
d CH
must b e the angle nearest to among the angles which satisfy
edg e peak
2
d
see Fig b
Calculate Q de ned as follows
R
edg e
CH d
d CH
edg e C
A
Q exp
sin d
edg e
edg e
where is the Cherenkov op ening angle exp ected from the charge within the cone
C
is the op ening angle resolution
The optimization was carried out by changing the particle direction The particle
direction and which maximize Q were adopted as the nal ones
edg e
Final vertex tter
After the Cherenkov edge search we determine the vertex p osition more precisely by
considering the scattered Cherenkov light and the particle track length Two go o dnesses
TDCFIT
(a) 150
100
number of p.e.number 50
Figure The CH
a for the
0 distributions
CH distribution b the
10 (b)
second derivative of CH 0 detected edge -10 second derivative
0 10 20 30 40 50 60 70 80 90
opening angle (degree)
G and G are used G is the go o dness calculated using the PMTs which are lo cated in
I O I
the Cherenkov ring obtained in Cherenkov ring edge search The de nition of G is
I
X
t
i
G exp
I
i
i
where is the timing resolution of the i th PMT which is a function of its charge
i
G is the go o dness for the remaining hit PMTs which are considered to b e hit by
O
either direct and or scattered photons
X
t t
i
i
G max exp exp
O
T
l
i
i
where T is the typical timing delay of scattered photons It was estimated by a Monte
l
Carlo study and is set to b e ns
Finally G is de ned as
T
G G
I O
P
G
T
2
i
i
P
where is a factor to normalize G from to
T
i
i
Next the tack length of particle is considered as follows
CHAPTER EVENT RECONSTRUCTION
Estimate the total track length L from the total charge within a cone of half
t
op ening angle
Recalculate t for PMTs which are lo cated in the Cherenkov ring by taking account
i
of the particle velocity which is assumed to b e the light velocity and p osition along
the track where Cherenkov photons are emitted
Calculate G using the corrected t
I i
These pro cedures are iterated several times and nally the vertex p osition and direc
tion which maximize G are determined as b est t p oints Figure shows the pos
T
distribution for the FC PC and multi rings events where pos is the distance b e
tween the reconstructed and the real vertex p osition De ning the vertex resolution as the
distance where the of events are found within pos the resolutions are cm cm
cm and cm for FC PC and multi rings events The vertex p otion determined
by this pro cess is the nal vertex p otion for multi ring events
Ring counting
After the reconstruction of the vertex p osition direction and op ening angle of the most
energetic Cherenkov ring we tried to nd other Cherenkov rings and determine whether
the event is a singe or multi ring event The number of Cherenkov rings is a very imp ortant
information since it is used in various atmospheric neutrino analyses The Ring counting
pro cess counts the number of rings and estimates the direction and op ening angle of the
found rings The algorithm of Ring counting is
Make a sp ecial charge map
Search a candidate direction using the charge map
Determine whether the candidate is true or not by a likelihoo d metho d using charge
pattern of hit PMTs
If a new ring is found go back to the rst step to search for another ring
RING COUNTING
1800 1600 100 1400 80 1200 1000 60 800 600 40 400 20 200 0 0 0 50 100 150 200 0 50 100 150 200 cm cm ∆pos ∆pos
100 600
80 500
400 60 300 40 200 20 100
0 0 0 50 100 150 200 0 50 100 150 200 cm cm
∆pos ∆pos
Figure The pos distributions a for the FC b for the PC c for the and
d for the multi rings events The hatched area corresp onds to of the total events
CHAPTER EVENT RECONSTRUCTION
Figure Basic idea of the 42 deg. ring hit PMT
(possible center)
charge map The ring at the
center shows the Cherenkov ring
the small circles on the center ring
are hit PMTs The dashed circles
are the circles with the same ra
dius as the observed Cherenkov
ring with their centers on the each
hit PMT The crossing p oint of
center Cherenkov ring
dashed circle should b e the
(most probable) each
center of the Cherenkov ring
This pro cess searches for Cherenkov rings up to ve The detail of each part is de
scrib ed b elow
Search for candidate rings
Figure illustrates the basic concept of the search for candidate rings Assume we
observe a Cherenkov ring on a at plane If we draw circles on this plane with the center
at the p osition of the hit PMTs and with the radius same as the observed radius of the
Cherenkov ring we nd that the circles overlap at the center of the Cherenkov ring
Therefore a p oint where the maximum overlapping of the circles can give the information
of the particle direction
In the real situation rst we subtract the exp ected charge of found rings from each
hit PMTs in order to e ciently nd the rings pro duced by low energy particles Then
Ring counting pro cess makes a sp ecial charge map which is a dimensional array with
bins for azimuth angle and bins for zenith angle Each bin corresp onds to a direction
from the vertex p osition obtained by the TDC t The charge of hit PMT is distributed
to each bin with an weight of the PE This PE shows the charge distribution of an
electron event and is a function of which is the op ening angle b etween the bin direction
and the PMT direction This way of making charge map corresp onds to drawing circles
RING COUNTING
Figure The charge map
of a typical two ring event
600
This is a dimensional ar
with bins for azimuth
400 ray
angle and bins for zenith
Each bin corresp onds
200 angle
to the direction from the
Two p eaks corre
0 vertex
to the directions of 150 sp ond
θ
Cherenkov rings from (degrees)100 300 the
200
vertex p osition 50 100 φ(degrees) the
00
on the at plane describ ed ab ove Figure shows the charge map of a typical two
ring event Two p eaks on the map corresp ond to the direction of each ring
Charge separation and determination of ring number
Let n b e the number of rings already observed in an event To determine whether the
additional candidate ring is a real Cherenkov ring or not we carry out the following
pro cedures
First we de ne the exp ected charge distribution of the j th ring C j p
r ing exp
where p is the exp ected momentum of the particle corresp onding to the j th ring and
is the angle from the direction of the particle At the rst stage the exp ected charge of
the ring C j p is calculated on the assumption that all particles are electrons
r ing exp
Then the exp ected charge C i j from the j the ring at the i th PMT is calculated
exp
C i j i C j p
exp r ing exp
where is a conversion factor correcting for acceptance distance from the vertex p osition
to the PMT and the attenuation of the Cherenkov light Then the exp ected charge from
1
This map is made without subtracting the charge of the rst ring
CHAPTER EVENT RECONSTRUCTION
all rings to the i th PMT is
n
X
C i C i j
sum exp exp
j
Then we de ned a likelihoo d
q
X
C i j L j ln pr ob C i C i
exp obs sum exp
i
where C i is the observed charge for the i th PMT The function pr ob calculates the
obs
probability that the observed value is C when the exp ected one is C Its de nition
obs exp
is
Poisson distribution
corrected for single p e distribution C p e
obs
pr ob C C
exp obs
C C
exp
obs
p
exp
p
C C C p e
exp exp obs
where the factor comes from the result of a comparison b etween the real charge
resolution of PMTs and p oison statistics and the factor is derived from the uncertainty
p
C i j in Eq enhances of the relative gain calibration of the PMT The factor
exp
the contribution from PMTs around the exp ected Cherenkov ring p ositions We change
the total charge of the j th Cherenkov ring so that L j is maximized This way the b est
t total charge for each Cherenkov ring is determined
It is p ossible to estimate the contribution of the j th ring to the observed charge by
the i th PMT
C i j
exp
C i j C i
obs obs
C i
sum exp
Now by using C i j it is p ossible to re estimate C j p Then we rep eat
obs r ing exp
the same pro cedure by using new C j p This way the total charge for each
r ing exp
Cherenkov ring is determined essentially indep endent of the initial assumption of the
electron rings
Now we de ne that L n is the maximum likelihoo d of Eq for n ring as
max
sumption Then L n W n is used to determine the number of rings where W n max
PARTICLE IDENTIFICATION
is an empirical weight as a function of the op ening angle among the each ring direction
In a same way L n W n is calculate using the additional candidate ring If the
L n W n is greater than L n W n Ring counting pro cess determine the
number of ring as n otherwise the pro cess go es back to the step to search for another
ring
Finally we show a p erformance of Ring counting by using Monte Carlo events Here
we used the charged current quasi elastic CC q e interaction events and neutral current
single NC interaction events to estimate the p erformance b ecause CC q e NC
events are exp ected to b e identi ed as single ring two ring events
The fraction of CC q e events which are identi ed as single ring events is The
reasons that some CC q e events are identi ed as multi ring events are the followings
A high momentum recoil proton makes Cherenkov lights which is identi ed second
ring of CC q e events
An outgoing lepton is misidenti ed as two ring event of CC q e events
For the NN events the fraction of two ring events is This fraction
strongly dep ends on the momentum Figure B in App endix B shows the probability
of identifying two Cherenkov rings as a function of momentum The detail of
analysis will b e describ ed in App endix B
Particle identi cation
A particle identi cation PID pro cess makes use of the pattern and op ening angle of the
Cherenkov ring Figure shows typical events of e and l ik e events This gure
shows that muons pro duce shap e Cherenkov edges In contract to this electrons pro duce
electro magnetic showers and low energy electrons in particular exhibit many multiple
scattering and pro duce rather di use Cherenkov rings
For low momentum particles information of the op ening angle is imp ortant
C
b ecause cos is equal to n The PID pro cess determines a particle type in the
c
following steps
CHAPTER EVENT RECONSTRUCTION
NUM 42 NUM 34 RUN 7245 RUN 7230 SUBRUN 8 SUBRUN 4 EVENT 374118 EVENT 185450 DATE 99-Apr- 7 DATE 99-Apr- 7 TIME 23:13:12 TIME 0:53:47 TOT PE: 3788.7 TOT PE: 11505.4 MAX PE: 28.5 MAX PE: 91.4 NMHIT : 1959 NMHIT : 2185 ANT-PE: 37.5 ANT-PE: 17.9 ANT-MX: 11.8 ANT-MX: 1.9 NMHITA: 25 NMHITA: 32
99/10/08:FCNu :miuram 99/10/08:FCNu :miuram 99/10/19:FCNu :NoYet RunMODE:NORMAL 99/10/19:FCNu :NoYet RunMODE:NORMAL 99/11/02:FCNu :kanaya TRG ID :00000111 99/11/02:FCNu :kanaya TRG ID :00000111 90/00/00:NoYet:NoYet T diff.:0.713E+05us 90/00/00:NoYet:NoYet T diff.:0.555E+05us 90/00/00:;R= 0:NoYet : 71.3 ms 90/00/00:;R= 0:NoYet : 55.5 ms R : Z : PHI : GOOD FEVSK :81002803 R : Z : PHI : GOOD FEVSK :81002803 0.00: 0.00: 0.00:0.000 nOD YK/LW: 3/ 1 0.00: 0.00: 0.00:0.000 nOD YK/LW: 3/ 1 CANG : RTOT : AMOM : MS Q thr. : 0.0 CANG : RTOT : AMOM : MS Q thr. : 0.0 BAD ch.: masked BAD ch.: masked SUB EV : 0/ 1 SUB EV : 0/ 3 Dec-e: 0( 0/ 0/ 0) Dec-e: 0( 0/ 0/ 0) VQ: 0 0 0 0 VQ: 0 0 0 0 VT: 0 0 0 0 VT: 0 0 0 0 Comnt; VQ: 0. 0. 0. 0. Comnt; VQ: 0. 0. 0. 0.
VT: 0. 0. 0. 0. VT: 0. 0. 0. 0.
Figure Typical FC single ring events The left gure is for e l ik e and the right one
is for l ik e
estimate the intensity of direct light for each PMT for e like and like assumptions
estimate the scattered light
estimate the particle type
These steps are describ ed b elow
Estimate the direct photon
At rst the PID algorithm estimates the intensity of the direct photon for each PMT
under the assumption of an electron ring We made the Monte Carlo simulation for elec
tron events with momentum MeV c MeV c and MeV c with p erfect water
transparency Then we estimated the photo electron number received in a circular area of
cm diameter equal to PMT photosensitive area lo cated on a sphere of m in ra
dius Since the Cherenkov photons are emitted in a cone we averaged this photo electron
number as a function of an angle b etween the circular area and the particle direction
Let C p b e the average charge for electron events with their momentum p
MC e e
The exp ected number of photo electrons in the i th PMT pro duced by an electron is
PARTICLE IDENTIFICATION
expressed as
l m
i
f exp C dir ect i C p
i e exp e MC e
l L
i
where is the normalization factor l is a distance from the particle p osition to the i th
e i
PMT is the angle of the i th PMT from the particle direction L is the light attenuation
i
length f is the e ective photo sensitive area of the PMT see Fig The p ower
index was estimated by a Monte Carlo study
Next we explain the way of the estimation of the intensity of the direct photons for
the like assumption For like events the exp ected number of photo electrons in the
i th PMT can b e calculated numerically by the following equation
l
i
C dir ect i f sin C i exp
exp i i k nock exp
d
L
l sin l
i i i
dx
d
where is a normalization factor l comes from the ionization energy loss of the
i
dx
muon As shown in Fig sin dx l d takes into account the change in the photon
density which is caused by the change in corresp onding to the energy loss sin
i
expresses the intensity variation of the Cherenkov photons The C i shows the
k nok exp
number of the exp ected photons from the kno ck on electrons as a function of which is
i
estimated by a Monte Carlo study
Estimate the scattered lights
Scattered photon can b e separated from the direct Cherenkov photons by checking its
arrival time We rst pick up hit PMTs within a cone having an op ening angle of
C
which is the reconstructed Cherenkov op ening angle This aims to eliminate accidental
C
hits which lie mostly outside he Cherenkov cone Then a histogram of timing residuals
t is made for all the selected PMTs Scattered photons are selected with the following
i
criterion
t nsec t t nsec direct photons
peak i peak i
t nsec t scattered photons
peak i i
CHAPTER EVENT RECONSTRUCTION
dxsin θ
Θ ldθ Cherenkov l light dθ θ µ
dx
Figure Relation b etween the PMT and Cherenkov photon
where t is the p eak in the timing histogram and is the timing resolution of the i th
peak
PMT as a function of the detected number of photons
The number of photons originating from the scattered photons C scatter i is
exp
estimated from the information of the attenuation length and the distance b etween the
vertex p osition and the PMTs which detect Cherenkov photons Thus the exp ected
number of photons for the i th PMT is given by adding b oth contributions
C i C dir ect i C scatter i
e or exp e or exp exp
Estimate particle type
We now de ne a likelihoo d function for PID L as
e or
Y
P r ob i L
e or e or
i C
PARTICLE IDENTIFICATION
where P r ob i is the probability function for the i the PMT which is expressed in
e or
two di erent ways according to whether the PMT is hit by direct or scattered photons
pr ob C i C i direct photons
e or exp obs
P r ob i
e or pr ob C dir ect i
e or exp
pr ob C scatter i C i scatted photons
exp obs
where pr ob is the same function as in Eq
In order to combine the information of the Cherenkov op ening angle with the infor
mation of the ring pattern L is transformed into the distributions
x
e or ln L constant
e or
If the degree of freedom N exceeds which is normally the case the sigma of the
D
2
is approximated as distribution
p
2
N
D
In this case N is the number of PMTs within the Then the probabilities by
D C
using Cherenkov pattern can b e rewritten as
e or min e
P e or exp
patter n
2
Next the Cherenkov angle will b e considered From the reconstructed momentum
and particle type we can calculate the exp ected Cherenkov angle e or If the
exp
reconstructed Cherenkov op ening angle is given as the probability is derived as
obs
e or
exp obs
P e or exp
ang l e
Combining Eq and Eq the probability P is given by
PID
P e or P e or P e or
PID patter n ang l e
A ring with P P e is identi ed as like e like We shows the p er
PID PID
p
P formance of particle identi cation using CC p e events Figure shows a
PID
p
P e distribution of CC q e interaction events which were identi ed as single ring
PID
events This gure illustrates that our particle identi cation is very go o d for CC q e
events The misidenti cation probability of the particle identi cation is and for
CC and CC events resp ectively
e
CHAPTER EVENT RECONSTRUCTION
400 350
300
p p
number of events µ
P P e
250 e-like -like Figure
PID PID
for CC q e single ring
200 distribution
events the white histogram for CC
150
and the hatched one for CC 100 e 50 0 -10 -8 -6 -4 -2 0 2 4 6 8 10
likelihood
MS t
The vertex resolution of TDC t for single ring events is relatively p o or compared with
that of multi rings events This reason comes from the facts that a tter using timing
information is not sensitive in the longitudinal direction of a Cherenkov ring and its
vertex shift in the longitudinal direction dep ends on the particle type Therefore we use
another tter which obtains the vertex p osition using the charge pattern information for
FC single ring events to improve its vertex resolution This tter is called MS t
At this stage we already know the particle type which means that we can estimate
charge pattern distribution MS t moves the vertex p osition parallel to the particle direc
tion to search for the p osition where the observed charge distribution and the exp ected
one match the b est The comparison is carried out based on the likelihoo d de ned in
PID Then it adjusts the direction where the ab ove likelihoo d gives the maximum Next
it lo oks for the vertex p osition with the maximum go o dness used in the TDC t shifting
the vertex p erp endicular to the particle direction MS t iterates these three steps until
the change of vertex and direction relative to the previous ones is less than cm and
resp ectively
The p erformance of MS t is estimated using the Monte Carlo study and cosmic ray
muons In the Monte Carlo study we use the atmospheric neutrino events identi ed
MS FIT
(a) e-like (b) mu-like 400 800
σ = 34cm σ = 25cm
The vertex res
300 600 Figure
olution of MS t The
200 400
hatched histogram shows
events within vertex
100 200 the
p osition resolution 0 0 0 50 100 150 200 0 50 100 150 200 ∆pos(cm) ∆pos(cm)
(a) e-like (b) mu-like σ o σ o
150 = 3.2 300 = 1.9
Figure The angular
100 200
resolution of MS t The
hatched histogram shows
50 100
the events within angu
lar resolution 0 0 0 2 4 6 8 10 0 2 4 6 8 10
∆dir (degree) ∆dir (degree)
as a single ring event by Ring counting Figure represents the distribution of the
distance b etween the tted and the real vertex Let the vertex resolution b e the distance
where of events are covered Figure shows that the vertex resolution of MS t
is and centimeters for e like and like events resp ectively Figure shows the
distribution of op ening angle b etween the tted and real direction From this gure the
angular resolution is for e like events and for like events where the angular
resolution is de ned in the same way as for the vertex
CHAPTER EVENT RECONSTRUCTION
Momentum estimation
In order to estimate the momentum we use the corrected total charge R To reduce
tot
the scattered light e ect we use the PMTs satisfying the following criteria
Select the PMT whose op ening angle from the particle direction is less than
select the PMT which satisfy t ns t t ns
peak i peak
The R is corrected for the PMT acceptance and water transparency and its de nition
tot
is
X X
G cos l
MC i i
R C scatter i C i exp
tot exp R obs
G f L
i
70
i
i
50 t 250
r es
where G G is a relative PMT gain of data MC is normalization factor t
MC R r es
is a time from the p eak of time residual is an op ening angle b etween the i th PMT
i
direction from the vertex p osition and the particle one is angle of photon arriving
i
direction relative to the i th PMT facing direction and L is the attenuation length of
light in the water Figure a shows the relation b etween R and momentum which
tot
is obtained from a Monte Carlo study The momentum resolution of each particle is
p
shown in Fig b From this gure at low momentum regions P . GeV c
p
is approximately calculated as
p
for electrons
p
p
p
for muons
p
where p is the momentum of each particle in GeV c
MOMENTUM ESTIMATION
8 7 (a) 6 5
P (GeV) 4 3 2 1 0 0 5 10 15 20 25 30 3 rtot × 10 6 5 (b) 4 P (%)
σ 3 2 1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
P (GeV)
Figure The reconstructed momentum by using R a shows a reconstructed
tot
momentum p as function of R b shows a momentum resolution as function of
tot p
p Solid broken line shows e like events
Chapter
Monte Carlo simulation
In this analysis we use a Monte Carlo simulation to predict various numbers and distri
butions In addition the estimations of several criteria for reduction and reconstruction
arise from Monte Carlo studies Therefore the Monte Carlo simulation plays a vital role
Our Monte Carlo separates into the neutrino interaction and a detector simulation
Atmospheric neutrino ux
Several p ersons have calculated the atmospheric neutrino ux Here we use the Honda
et al s calculation b ecause their ux mo del considers the magnetic latitude of the
Kamioka site and covers the neutrino energy from MeV to TeV In order to estimate
the systematic errors coming from the neutrino ux we use the Bartol s ux which is
also calculated taking into account the magnetic cut o at Kamioka The discrepancy of
the calculated neutrino ux b etween these two mo dels is less than The uncertainty
of the absolute ux of the atmospheric neutrino is estimate to b e
Neutrino interaction
Our Monte Carlo considers the following neutrino interactions
Charged Current quasi elastic scattering N l N
Neutral Current elastic scattering N N
CHAPTER MONTE CARLO SIMULATION
Charged Current single pro duction N l N
Neutral Current single pro duction N N
Charged Current coherent pro duction O l O
Neutral Current coherent pro duction O O
Charged Current multi pro duction N l N n
Neutral Current multi pro duction N N n
where N and N are the nucleons l is the charged lepton n is the multiplicity of pions The
probability of the other interaction mo des is to o small compared to the ab ove interactions
therefore we neglect them in this simulation We have checked the total cross section in
each mo de with the real data The momentum distribution of outgoing lepton and
the angular distribution have b een compared with the data from the BNL fo ot bubble
chamber by Hasegawa Each interaction is presented in this chapter Then the
comparisons with the real data and the Monte Carlo prediction are presented
Quasi elastic scattering
In the calculation of the cross section for the charged current quasi elastic interaction
n l p the di erential cross section is written
d s u M G cos s u
c
A q B q C q
dq E M M
where q is a square of the momentum transfer of lepton s and u are Mandelsam vari
ables E is a neutrino energy M is a target nucleon mass is Cabibb o angle and G is
c
1
Bro okheaven National Lab oratory
NEUTRINO INTERACTION
Fermi coupling constant A q B q and C q is written as the following
m q q q
A q jF j jF j
A
V
M M M
q q F F m q
V V
j F j F F jF j
A
V V V
M M M M
q
F F F B q
A
V V
M
q
C q jF j jF j j F j
A
V V
M
where m is a lepton mass and The vector form factor F and F are explained
V V
by
q q q
F q
V
M M M
V
q q
F q
V
M M
V
In our Monte Carlo M is set to b e GeV c The axial vector form factor F is
V A
exp erimentally obtained as the follow
q
F q
A
M
A
The uncertainty of M is large and various exp eriments suggested GeV c . M .
A A
GeV c We adopt M GeV in our Monte Carlo In the case of free proton
A
target the total cross section is directly determined from Eq Figure shows the
calculated cross sections and the real data in n p and p n Figure
distribution for n p and this gure pro ofs the repro ducibility of our shows the q
Monte Carlo
On the other hand in the case that the target is a nucleon in Oxygen we take account
of nuclear e ects such as Pauli blo cking and Fermi motion of the nucleon For the Pauli
blo cking we request the momentum of the recoil nucleon should exceed the Fermi surface
momentum Fermi motion is adopted based on the Fermi gas mo del on the assumption
that nucleons are in the s states and nucleons are in p states
We also consider the neutral current elastic interaction The cross section for NC
CHAPTER MONTE CARLO SIMULATION
2 2 (a) (b) 1.5 1.5
−38 1 −38 1 (10 cm) (10 cm)
σ 0.5 σ 0.5
0 0 2 4 6 8 10 2 4 6 8 10
Energy(GeV) Energy(GeV)
Figure The calculated cross section of quasi elastic interactions compared with the
exp erimental data a for n p b for p n triangle ALN square
GGM circle Serpukhov
Figure The q distribution for n p The histogram shows the Monte Carlo
result and the p oints with error bars shows the exp erimental data from BNL
NEUTRINO INTERACTION
elastic scattering is evaluated using the relation
p p n e p
p p p e n
n n p p
n n p p
Single pion pro duction
Here single pion pro duction is de ned as the interaction which makes single pion pro
duced via the baryon resonance states as follows
N l N
N N
where N and N are the nucleon N is the baryon resonance N and In addition to
b e consistent with multi pion pro ductions see sec it is restricted to the interaction
whose hadronic invariant mass W is less than GeV
We adopt Rein Sehgal s metho d to simulate this interaction To evaluate the cross
section this mo del calculates the amplitude jT j of pro ducing resonance states shown
in Table In the next step it multiplies the resp ective amplitude by the branching
ratio that the excited baryon decays into one pion and a nucleon At this time it
E
considers interference among the resonances The di erential cross section is
X
d
jT N l N j
E
dq d M E W M
spins
Figure shows the cross section for single pion pro duction channels compared with the
exp erimental data
In the case that the target is a nucleon in Oxygen we consider that of decays
without pion
Coherent pion pro duction
The interaction of neutrinos with nuclei via charged our neutral currents can lead to the
coherent pro duction of pions which carry the same charge as the incoming current The
CHAPTER MONTE CARLO SIMULATION
) 1 ) 0.3 2 2 0.9
cm cm 0.25 0.8 (a) (b) -38 -38 0.7 0.2 0.6 0.5 0.15 0.4 0.1 0.3 0.2 0.05 cross section (x10 cross section (x10 0.1 0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Eν (GeV) Eν (GeV)
) 0.3
2
Figure The calculated cross section of
cm 0.25
single pion pro duction compared with the (c) the
-38
data In a solid broken line
0.2 exp erimental
shows P l P N l N In
0.15
b solid broken line shows N l P
N l N In c solid broken line
0.1
shows N l N P l N Trian 0.05
cross section (x10
gles squares show the data from
0
these gures we restricted that W should 0 1 2 3 4 5 6 7 8 9 10 In
E (GeV)
less than GeV c
ν b e
NEUTRINO INTERACTION
R S M M eV c M eV
E
P
P
D
S
S
S
Table Table of reso
P
nances used in this simu
D
lation R S is Resonance
D
States M is the invariant
F
Mass is the total width
P
and is the elasticity N
E
D
branching ratio
P
P
P
P
P
F
CHAPTER MONTE CARLO SIMULATION
di erential cross section of coherent pion pro duction can b e calculate based on Alder s
PCAC formula and b e expressed as follows
d Re f G M
N
N
E y f A E y
tot
dQ dy dt Im f
N
M
A
exp R jtj F
abs
M Q
A
where q is the square of the momentum transfer of lepton t is the square of the
momentum transferred to the nucleus M is the axial vector mass GeV c f
A
m f is the N scattering amplitude G is the weak coupling constant M is the
N
mass of nucleon E and E are the energy of neutrino and outgoing lepton resp ectively
l
and y E E E A is the atomic number of oxygen and R is the nuclear
l
radius is the axial vector coupling constant Because is recalling that the axial
parts of the neutral and charged currents form a triplet in isospace it takes for
N
the charged neutral current interaction is the average pion nucleon cross section
tot
which is approximately expressed as
i h
+
D D N
tot tot tot
D
where is the D total cross section F is t indep endent attenuation factor
abs
tot
representing the e ect of pion absorption in the nucleus and is expressed as
A
inel
F exp
abs
R
where R f m is the inelastic N Cross section which is taken from the data
inel
Table The cross section of coherent pion pro duction is shown in Fig
Multi pion pro duction
The total cross section of charged current multi pion pro duction is calculated by integrat
ing the following equation
y G M E y d
N
F
y C F x q y C xF x q
dxdy
M xy M M y M
N
l l l
C
M E x E E M E x
N N
M
l
C
M E x
N
NEUTRINO INTERACTION ) 2 1.4
cm
Figure The cross section -38
1.2
of the coherent pion pro duction
1
Solid broken line shows the
0.8
cross section for O l
cross section (x10
O O O
0.6
the interaction via the neu
0.4 For
current the calculated cross
0.2 tral
section is exactly half of the CC 0
0 1 2 3 4 5 6 7 8 9 10
cross section
Eν (GeV)
where M is the mass of nucleon M is the mass of lepton x q f M E E g
N l l
y E E E E and E are the energy of incoming neutrino and outgoing lepton in
l l
the lab oratory frame resp ectively In the case of takes plus otherwise it is minus
The nucleon structure function F and xF are taken from Ref
In our simulation the cross sections via neutral current are expressed by the following
relations
E GeV
N X
E
E GeV
N X
E GeV
E GeV
N X
E
E GeV
N X
E GeV
These relations are estimated from the exp erimental results
Figure shows the calculated cross section for multi pion pro duction based on Eq
The kinematics of out going mesons is calculated by two metho d At the invariant
mass range less than GeV we use our original co de From the result of Fermi lab
iis fo ot hydrogen bubble chamber exp eriment the mean multiplicity of charged pions hn
CHAPTER MONTE CARLO SIMULATION
10 9 (a) 8
7
The calculated 6 Figure 5 4
)
cross section for multi pion
2 3 2
cm 1
pro duction as a function of
-38 0
0 1 2 3 4 5 6 7 8 9 10
E a for CC b for
(10
σ 5
4.5 (b)
Solid broken lines 4 NC 3.5
3
the cross section for 2.5 show 2
1.5
n p n 1
0.5
n n 0 p 0 1 2 3 4 5 6 7 8 9 10
Eν (GeV)
estimated as
i ln W hn
+
i the mean multiplicity of pion hn i is i hn i hn Assuming hn
hn i ln W
The number of pion for each events is determined based on the KNO scaling Since the
range of W overlaps with that of the single pion pro duction we require n in this W
range of multi pion pro duction The forward backward asymmetry of pion multiplicity
F B
n n in the center of the mass system of the hadrons is obtained from the BEBC
exp eriment and included as follows
F
ln W n
B
n ln W
In the case of W GeV we use the Jetset which is frequently used for event
generation in high energy physics
Finally the total cross section is calculated by adding all the channels and is shown in
Fig
NEUTRINO INTERACTION
1.4 1.2 (a) 1 0.8 0.6 0.4 0.2
/GeV) 0 2 0 5 10 15 20 25 30 35 40 cm
-38 0.7 0.6 (b) 10
× 0.5 ( 0.4ν
/E 0.3 σ 0.2 0.1 0 0 5 10 15 20 25 30 35 40
Eν (GeV)
Figure The charged current total calculated cross section derived by E used in our
Monte Carlo simulation a for n p b for p n White circle
white square cross triangle and circle
CHAPTER MONTE CARLO SIMULATION
Meson nuclear e ect
The mesons pro duced in a O nucleus often make secondary interactions b efore leav
ing the nucleus Thus the meson interactions with nucleon have a signi cant e ect in
estimating the detection e ciency of or in the selection of single ring events
The interaction p osition r of a neutrino and the pro duction p osition of a pion in the
oxygen nucleus is set according to the Woo ds Saxon type nucleon the density distribution
r
j r j c
r exp
a
is the average density of nucleus a f m and c f m where m
are density parameters of nucleus In our Monte Carlo simulation program the pion
interaction in O includes
inelastic scattering
charge exchange
absorption
Each cross section is calculated based on the Oset mo del In selecting interaction
mo des Fermi motion of nucleus and Pauli blo cking e ect are considered If inelastic
interaction or charge exchange is selected the momentum of the recoil nucleon is requested
to exceed the Fermi surface momentum p r which is a function of the density of nucleon
F
at the interaction p osition r
r p r
F
The direction and momentum of the pion is estimated from the result of a phase shift
analysis obtained from the N scattering exp eriment
We tested this pion interaction mo del using the following three interaction data
C scattering see Fig
O scattering see Fig
DETECTOR SIMULATION
600
(mb)
Figure The calculated cross
500
sections of the pion with a C
nucleus compared with the ex 400
cross section cross
p erimental data The stars
line for the total cross
300 Solid
section the white circles broken
for the inelastic scattering
200 line
the black circles dashed line for
the crosses dashed
100 absorption
dotted line for the charge ex
0
0 100 200 300 400 500 600 change
Pπ (MeV/c)
photo pro duction of pions C X we used the cross section of
primary interaction n p from the exp erimental result see Fig
Detector simulation
The GEANT package which is used generally among high energy exp eriment is
used for detector simulation in Sup er Kamiokande For the hadronic interaction in water
we used CALOR package based on the nuclear cascade mo del b ecause this package
repro duces the pion interaction well ab ove GeV c But the repro ducibility for the low
energy pion with momentum less than GeV c is not enough for our exp eriment and
there is no package b etter than CALOR in simulating low energy pions Thus we made
our own co de based on the result of H O scattering exp eriment
Cherenkov photon radiation is also treated in the GEANT package But the tracking
part of Cherenkov photons was developed by us for this exp eriment For the short wave
length Rayleigh scattering is dominant b ecause the mean scattering length is prop ortional
to Thus we take into account this scattering For the longer wavelength measured
wavelength dep endence of the light scattering and absorption is used The attenuation
CHAPTER MONTE CARLO SIMULATION
60 60 (a) (b) 50 50 b/sr/MeV) b/sr/MeV) µ µ ( ( Ω Ω 40 40 /d /d σ σ d d 30 30
20 20
10 10
0 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Θ Θ
60
50 (c)
Figure The di erential cross b/sr/MeV) µ
(
section of O interaction a Ω 40
/d
σ
for P M eV c b for d
30
P M eV c c for P
M eV c The circles show
20
the data the histograms show the
10
Monte Carlo prediction
0 0 20 40 60 80 100 120 140 160 180 Θ
DETECTOR SIMULATION
1 1 0.8 0.8 (a) (b) 0.6 0.6 0.4 0.4 0.2 0.2 b/sr/(MeV/c) µ
p 1 1 d
Ω 0.8 0.8 (c) (d) /d σ 2 0.6 0.6 d 0.4 0.4 0.2 0.2 0 0 0 100 200 300 400 0 100 200 300 400
P (MeV/c) P (MeV/c)
Figure The di erential cross section for the pion photo pro duction a for C
X E M eV b for X E M eV c for C
X E M eV d for C X E M eV
CHAPTER MONTE CARLO SIMULATION
length shown in Fig is used in our simulation program Also shown are the results
of direct measurement of water transparency
The quantum e ciency of PMTs has b een measured as shown in Fig Also the
collection e ciency of photo electrons at the dyno de was measured to b e Based on
these results Cherenkov photon detection part of the simulation was developed
Chapter
Data summary
We observed events for the fully contained partially contained sample with
an exp osure of kton year Also we made years kton year equivalent of Monte
Carlo events and analyzed them in the same way as we did for the real data
In this chapter we summarize the nal data sample for the real data and the Monte
Carlo Then the imp ortant information in this analysis the number of ring vertex p osi
tion momentum and PID likelihoo d distribution are presented
Data summary
Final event samples were made by the following criteria
For fully contained events
E M eV
v is
D meters
w al l
Number of OD clusters hits
P M eV c for e like single ring events P M eV c for like single ring
e
events
For partially contained events
D meters
w al l
CHAPTER DATA SUMMARY
DATA MC Honda MC Bartol
sub GeV R
e like
like
R
R
multi GeV R
e like
like
R
R
PC
Table Event summary Sub GeV multi GeV indicates the event sample with E
v is
GeV
where D is the distance b etween the event vertex and the nearest inner detector wall
w al l
Table summarizes the observed events and Monte Carlo predictions based on Honda
and Bartol uxes Here we classify the events with E GeV as the
v is
sub GeV multi GeV sample E is the energy of an electron that would pro duce the
v is
observed amount of Cherenkov light E GeV for muon events corresp onds to
v is
p GeV c The numbers of the Monte Carlo events were normalized to the detector
exp osure for comparison The fraction of each interaction mo de is summarized in Table
Vertex p osition distribution
The vertex p osition distributions of neutrino events are exp ected to b e uniform in the
detector Figure and show the vertex p osition distributions pro jected to the Z and
the R X Y directions with the Monte Carlo prediction For the multi GeV like
events of b oth data and Monte Carlo the number of events with their vertex p ositions
NUMBER OF RINGS AND PID DISTRIBUTION
CC CC NC Total
e
q e non q e q e non q e
R sub GeV e like
like
multi GeV e like
like
R sub GeV
multi GeV
PC
Table The fraction of each interaction mo de for various types of events These
numbers are obtained based on Honda ux without neutrino oscillation q e indicates
quasi elastic interaction
near the wall were small compared to the ones around the center On the other hand
for the PC event sample the event rate near the wall was higher than that around the
center This is b ecause a fraction of muons near the wall can reach the anti counter and
were identi ed as PC events
We compared the shap e of the distribution of the real data with these of the Monte
Carlo prediction by using a test The results are summarized in Table This
table shows that all the distributions of the data were consistent with the corresp onding
distribution of the Monte Carlo
Number of rings and PID distribution
The number of rings and PID play imp ortant role in this analysis Therefore we need
to con rm the repro ducibility of our Monte Carlo Figure shows the number of rings
for the data and Monte Carlo without neutrino oscillations From this gure it turned
out that the Monte Carlo repro duced the shap e of the number of rings distribution of
p
P the real data well Figure shows the PID likelihoo d distribution L
PID
p
P e for single ring events where P is de ned in Eq Again our Monte
PID PID
CHAPTER DATA SUMMARY
600 400 300 400 200 200 100 0 0 -1000 0 1000 -1000 0 1000 Z(Sub-GeV e-like) Z(Sub-GeV µ-like)
100 150 100 50 50 0 0 -1000 0 1000 -1000 0 1000 Z(Multi-GeV e-like) Z(Multi-GeV µ-like) 300 400 300 200 200 100 100 0 0 -1000 0 1000 -1000 0 1000 Z(2ring) Z(more than 2) 200 150 100 50 0 -1000 0 1000
Z(PC)
Figure The vertex distribution pro jected to the Z direction Only events with R
m are plotted The arrows indicates the ducial volume
NUMBER OF RINGS AND PID DISTRIBUTION
200 300 200 100 100 0 0 0 1000 2000 0 1000 2000 3 3 x 10 x 10 Sub-GeV e-like Sub-GeV µ-like
60 60 40 40 20 20 0 0 0 1000 2000 0 1000 2000 3 3 x 10 x 10 Multi-GeV e-like Multi-GeV µ-like
200 200
100 100
0 0 0 1000 2000 0 1000 2000 3 3 x 10 x 10 2ring more than 2ring 200 150 100 50 0 0 1000 2000 3 x 10
PC
Figure The vertex distribution pro jected to the R direction Only events with
jz j m are plotted The arrows indicates the ducial volume
CHAPTER DATA SUMMARY
d o f
Z R
R sub GeV e like
like
multi GeV e like
like
R
R
PC
Table analysis of the vertex p osition distribution for events in the ducial volume
Only the shap e of the distributions is compared b etween the data and the Monte Carlo
The numbers in the parentheses shows the probability
Carlo repro duced the shap e of the distribution for e like and like events separately We
note that the relative height of the e like and like histograms is di erent b etween the
data and the Monte Carlo most probably due to neutrino oscillations
Summary
We found that the vertex p osition distributions of the events inside the ducial volume
were consistent with the exp ectation from the atmospheric neutrino interaction
We also found that various distributions such as numbers of rings are consistent with
the atmospheric neutrino Monte Carlo These distributions are almost indep endent of
neutrino oscillations and con rm the data quality and the repro ducibility of the Monte Carlo
SUMMARY Number of events 10 3
10 2
1 2 3 4 5
number of rings
Figure Number of ring distributions for FC events The black circles show the
distribution for the real data the histogram for the Monte Carlo prediction without
neutrino oscillation The prediction was calculated based on the Honda ux
400 350 300 250
200
PID likelihoo d parameter
150 Figure p
100 p
L P P e distri PID 50 PID
0
for FC single ring events In
-20 -15 -10 -5 0 5 10 15 20 butions
a the black circles show the real data
300
the histogram show the MC In b the
250
white histogram shows the L for C C
200
the hatched one for C C black one for
150 e
100
NC 50
0 -20 -15 -10 -5 0 5 10 15 20 PID likelihood 1-ring event
Chapter
Neutrino oscillation analysis using
FC single ring events
In this chapter the results of e e ratio and the zenith angle distribution
data MC
studies are presented Then a neutrino oscillation analysis using FC single ring events is
carried out Both and oscillation hypotheses are tested The allowed
s
regions of neutrino oscillation parameters from this analysis are also shown
e ratio
If neutrinos oscillate the observed atmospheric ux ratio should b e di erent from
e
that of the theoretical calculation Although the uncertainty in the absolute ux of the
atmospheric neutrino was estimated to b e as mentioned in Chapter the ratio
was calculated within uncertainty This is b ecause most neutrino
e e
is pro duced by the decay chain of e To study the
e e
ux ratio we observed the e ratio of the data and compared with the theoretical
prediction As seen from Table the e ratio approximates the ratio The
e
results were as follows We used FC single ring events with E E GeV
v is v is
CHAPTER NEUTRINO OSCILLATION ANALYSIS USING FC SINGLE RING EVENTS
for R e e in the sub GeV multi GeV region
data MC
+ 0 023
E GeV
stat sy s v is
0 022
R
+ 0 050
E GeV
stat sy s v is
0 047
In b oth cases R were signi cantly smaller than unity R should b e consistent with unity
if neutrinos do not oscillate Therefore these results con rmed the atmospheric neutrino
anomaly The systematic error in R is discussed in the next section
Systematic error in R
In this section we discuss the systematic errors in R The sources of the systematic errors
in R were separated into three parts the uncertainties in the atmospheric neutrino ux
ones in the cross section of neutrinos o nucleus ones related to reconstruction metho ds
Systematic error in the atmospheric neutrino ux
The dominant source of the systematic errors related to the atmospheric neutrino ux
is the uncertainty in the ux ratio of the atmospheric neutrino avor esp ecially the
ratio Although the uncertainty in the absolute ux of the atmospheric
e e
neutrino was estimated to b e the ratio was calculated within
e e
uncertainty This uncertainty changes R by R in the sub GeV
multi GeV energy region
In addition we need to consider the uncertainties in and ratios b ecause
e e
the cross section for N interaction is roughly a factor of larger than that of N
e e
The uncertainty of ratio with neutrino energy GeV was estimated to
e e
b e in Ref We found that sub GeV multi GeV R changes by and
and if we change the and ratios by and resp ectively
e e
Another source related to the atmospheric neutrino ux is the uncertainty of the
energy sp ectrum of the primary cosmic ray protons The energy sp ectrum of the primary
cosmic ray protons is approximately prop ortional to E where the p ower index is
in the energy range around GeV Thus the energy sp ectrum of the
SYSTEMATIC ERROR IN R
atmospheric neutrinos is prop ortional to E f E where f E is a yield function which
takes account of the energy dep endence of decay probabilities and meson pro duction cross
sections Therefore the uncertainty in the p ower index of the primary cosmic ray ux is
re ected in the neutrino energy sp ectrum In order to estimate the systematic error the
sp ectrum has b een changed by a factor of E As a result error in R R for sub GeV
multi GeV was evaluated to b e Table summarizes R as we change the
neutrino ratios and the sp ectra index within the uncertainty
uncertainty Systematic error in R
sub GeV multi GeV
e e
e e
E
total
Table The systematic error in R related to the atmospheric neutrino ux
Systematic error from the neutrino interaction cross sec
tions
First we discuss the uncertainty of the quasi elastic interaction In the case of a free
proton target the dominant uncertainty in this interaction mo de is the value of the
axial vector mass M We estimated this systematic error in R to b e in
A
the sub GeV multi GeV energy range by comparing R with M GeV to R with
A
M GeV
A
In the case of an Oxygen target in addition to the uncertainty of M we have to
A
consider some uncertainties related to the nuclear mo del Our neutrino interaction sim
ulation considers the Pauli blo cking by requiring that the momentum of a recoil nucleon
must exceed the Fermi surface momentum P which is a function of the momentum of
F
in coming neutrino We checked the parameter dep endence of R by comparing R with
CHAPTER NEUTRINO OSCILLATION ANALYSIS USING FC SINGLE RING EVENTS
the one based on a di erent nuclear mo del whose P is constant P M eV and
F F
no nuclear p otential The di erence of the two R s was small Moreover we checked the
parameter dep endence by changing P to MeV As the result R s were and
F
for sub GeV and multi GeV resp ectively Table summarizes R as we change
M and P We estimated the systematic error originating from the uncertainty of M
A F A
and nuclear e ects to b e in the sub GeV multi GeV energy region
Systematic error in R
sub GeV multi GeV
M GeV
A
nuclear p otential o P is M eV
F
P M eV
F
total
Table R as simulation parameters in quasi elastic interaction are changed P is the
F
Fermi momentum and M is the axial vector mass
A
The relative contribution of each interaction mo de in the like sample is di erent
from that of the e like one as shown in Table This di erence makes R change with
the change of the absolute value of each cross section For example we estimated the
uncertainty in the absolute cross section of the single pion pro duction was When
the absolute cross section of the single pion pro duction in b oth samples increased by
the e in the multi GeV region changed by Accordingly the systematic
MC
error coming from this uncertainty was estimated to b e We estimated the system
atic errors arising from the uncertainties of each neutrino cross section in the same way
Additionally we considered the uncertainties in the N C C C cross section ratio These
uncertainties of N C C C ratio for all the cross section channel were estimated to b e
These results are summarized in Table
Another source of the systematic error in R is the uncertainty of the simulation of the
hadron interaction in water We adapted CALOR as the hadron simulator to generate the
Monte Carlo events To estimate the uncertainty of the hadron simulation we compared
the result of another hadron simulator FLUKA with that of CALOR The di erences
SYSTEMATIC ERROR IN R
mo de uncertainty systematic error in R
sub GeV multi GeV
q e CC NC
N C C C
pi CC NC
N C C C
c pi CC NC
N C C C
m pi CC NC
N C C C
total
Table Systematic error in R coming from the cross section q e quasi elastic
interaction pi single pion interaction c pi coherent pion interaction m pi multi pion
interaction The uncertainties coming from q e are estimated in Table The
uncertainty of multi pion pro duction is conservatively taken to b e near the threshold
energy region GeV
in R b etween FLUKA and CALOR were and for sub GeV and multi GeV
resp ectively
Systematic error related to the event reconstruction
The systematic errors in R related to the event reconstruction are caused by the uncer
tainties of the several parameters used in our Monte Carlo simulation For example one
of the parameters is the timing resolution of each PMT The vertex resolution obtained
by TDC t which calculates the vertex p osition using the timing information is strongly
dep endent on the timing resolution of each PMT If our estimation of the timing resolu
tion was not very accurate then our Monte Carlo cannot repro duce the vertex resolution
of the real data To estimate these systematic errors we used several reconstruction to ols
and compared the obtained R In the case of vertex p osition resolution we used MS t
CHAPTER NEUTRINO OSCILLATION ANALYSIS USING FC SINGLE RING EVENTS
which obtains the vertex p osition using the Cherenkov charge pattern and is almost in
dep endent of the timing information Comparing the result of the TDC t and MS t we
estimated the systematic errors related to the vertex reconstruction were and
in the sub GeV and multi GeV energy region resp ectively
Next we estimated the systematic error related to the ring counting based on the
comparison to the results from two di erent versions of ring counting program and from
the manual scanning The di erences in R b etween manual scanning and our ring counting
program were estimated to b e and for sub GeV and multi GeV resp ectively The
systematic error related to the ring counting was the largest in all the errors related to
the event reconstruction
According to the Monte Carlo study the misidenti cation probability of particle iden
ti cation for single ring events was estimated to b e for sub GeV multi
GeV The systematic error in R coming from this misidenti cation was estimated to b e
for sub GeV multi GeV by simply doubling the misidenti cation probability
The uncertainty of the energy scale causes the systematic error in R of in sub
GeV region However in multi GeV region the error was estimated to b e These
numbers were obtained by changing the p e numbers by for Monte Carlo events
where is the estimated uncertainty of the absolute energy scale of the detector
The uncertainty of the reduction e ciency for FC events was negligible according to
the Monte Carlo study
The background contamination such as the ashing PMT events were considered as a
source of the systematic error The charge pattern made by the remaining ashing PMT
events is di use like single ring e like events And the cosmic induced neutrons coming
from the surrounding ro ck collide with water and sometimes make s Some of them
with relatively high momentum are identi ed as single ring e like events b ecause their
op ening angle b etween two s from decay is narrow and they tend to b e identi ed as
single ring e like events Therefore these events were thought to b e the candidate of e like
background events The cosmic s whose vertex p osition was reconstructed inside the
ducial volume by mis t were identi ed as single ring and the dominant background
of like events The e ects of these background are summarized in Table
Finally the systematic error due to the statistics of the Monte Carlo events was
SYSTEMATIC ERROR IN R
Systematic error in R
sub GeV multi GeV
ashing PMT events
cosmic ray
cosmic ray induced neutron
total
Table Systematic error in R coming from the background contamination
for sub GeV multi GeV The total systematic error in R was estimated to b e
in the sub GeV multi GeV region Table summarizes the systematic
error in R
sub GeV multi GeV
atmospheric neutrino ratio
neutrino ux E
simulation neutrino interaction
hadron simulator
reconstruction reduction
and vertex p osition
data analysis ring multi ring separation
e separation
energy calibration
background contamination
M C statistics
total systematic error
Table Summary of the systematic error in R
CHAPTER NEUTRINO OSCILLATION ANALYSIS USING FC SINGLE RING EVENTS
The U p D ow n ratio
Next we discuss the U p D ow n ratio of FC single ring sample There is a large di erence
in the path length b etween upward going km and downward going neutrinos
km If the solution of the atmospheric neutrino anomaly is the neutrino oscilla
tion the evidence can b e found in the zenith angle distribution Figure shows the
cos distributions for e like events and like events where is the zenith angle of the
particle direction and cos corresp onds to upward going downward going
The angular correlation b etween the neutrino direction and the pro duced charged lepton
direction for sub GeV multi GeV neutrinos is calculated to b e RMS
as shown in Fig Therefore the observed zenith angle distributions corresp ond to
the neutrino zenith angle distribution at high energy region Figure proves that the
observed cos distributions for e like events were in go o d agreement with the exp ected
ones For multi GeV like events the observed number of upward going events had ob
vious de cit compared with the Monte Carlo prediction although the number of observed
downward going events was consistent with the predicted one
For quantitative evaluation of a de cit of up going like events we de ned the
U p D ow n ratio where Up Down was the number of up going down going events
with cos cos Horizontal going events cos
were excluded Table summarizes the U p D ow n ratio in sub GeV and multi GeV
regions The U p D ow n ratios for like events in b oth sub GeV and multi GeV were
signi cantly smaller than unity Esp ecially the U p D ow n ratio of the multi GeV like
events deviated from unity by more than On the other hand the observed U p D ow n
ratios for e like events were consistent with the exp ected ones within uncertainties The
systematic error in the U p D ow n ratio is discussed in the next section
Systematic error in the U p D ow n ratio
Several sources of the systematic error in the U p D ow n ratio were considered First
the systematic error in the U p D ow n ratio related to the calculation of the atmospheric
neutrino ux was estimated
SYSTEMATIC ERROR IN THE U P D O W N RATIO
700 700 600 (a) 600 (b) 500 500 400 400 300 300 200 200 100 100 0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
200 200 180 180 160 (c) 160 (d)
number of events 140 140 120 120 100 100 80 80 60 60 40 40 20 20 0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
COSΘ
Figure The zenith angle distributions a for the sub GeV e like events b for the
sub GeV like events c for the multi GeV e like events and d for the multi GeV
like events cos means down going The histograms with the shaded error bars
show the Monte Carlo predictions with their statistical error
CHAPTER NEUTRINO OSCILLATION ANALYSIS USING FC SINGLE RING EVENTS
140 140 120 (a) 120 (b) 100 100 degree 80 80 60 60 40 40 20 20 0 0 0 1 2 3 0 1 2 3
Evis (GeV)
Figure Angular correlation b etween the direction of the primary neutrinos and the
reconstructed direction of the leptons as a function of the reconstructed momentum of
leptons The events are the FC single ring events The binning in this gure is the same
as the one we use for an oscillation analysis shown in this section a is for the e like
sample and b for the like sample
DATA M C
+ 0 059
sub GeV e like
stat sy s stat sy s
0 056
+ 0 041
like
stat sy s stat sy s
0 039
+ 0 116
multi GeV e like
stat sy s stat sy s
0 103
+ 0 070
like
stat sy s stat sy s
0 062
Table The U p D ow n ratio of the FC single ring sample The slop es of Monte Carlo
in sub GeV region are due to the geo magnetic eld e ects The cut o rigidity at Sup er
Kamiokande site is higher than the average The event rate of the downward gong events
in sub GeV region is therefore lower than that of upward going events at the sub GeV region
SYSTEMATIC ERROR IN THE U P D O W N RATIO
As shown in Table the exp ected U p D ow n ratios are close to unity The up
down asymmetry of these ratios are due to the geo magnetic eld e ect The cut o
rigidity at the Sup er Kamiokande site is higher than the average Therefore the low energy
downward going neutrino uxes are lower than the upward going ones We compared
two indep endent calculated uxes for e like and like events to estimate the
uncertainty from the ux calculation which dep ends on the assumption of the cut o
rigidity The di erences of the exp ected U p D ow n ratios b etween these calculations for
sub GeV e like sub GeV like multi GeV e like and multi GeV like events were
and resp ectively
The second source of the systematic error is the Mt Ikenoyama e ect Neither
calculation takes into account the existence of Mt Ikenoyama over the Sup er Kamiokande
detector This e ect is negligible at low energies At high energies however a fraction of
cosmic muons reach the ground b efore it decays therefore we must consider the height
of Mt Ikenoyama kilometer The e ect of Mt Ikenoyama on the U p D ow n ratio
was estimated to b e for e like like events in the multi GeV region Here
we note that this e ect cannot explain upward going neutrino de cit b ecause this e ect
reduces downward going events and makes the U p D ow n ratio larger
Next the systematic error related to the detector is discussed The background con
tamination can cause the up down asymmetry We must consider the p ossible contamina
tion by cosmic ray muons These events could b e background to down going like events
In addition the asher events could b e the background to e like events The systematic
error in the U p D ow n ratio from these background contamination sources were estimated
to b e and for sub GeV e like sub GeV like multi
GeV e like and multi GeV like events resp ectively These numbers were obtained by
assuming that the background contamination discussed in Sec may direct only to
the upward going or downward going direction
We estimated that the detector PMT gain could b e di erent by b etween
down going particles and up going particles by studying decay electrons from stopping
cosmic ray muons Figure shows the zenith angle distribution of the mean recon
structed energy of the decay electrons This gain di erence caused
and U p D ow n systematic error for sub GeV e like events sub GeV
CHAPTER NEUTRINO OSCILLATION ANALYSIS USING FC SINGLE RING EVENTS
like events multi GeV e like events and multi GeV like events resp ectively Table
summarizes the uncertainties in the U p D ow n ratio
Figure Mean recon
structed energy of the elec
trons from the decay of
stopping cosmic ray muons
as a function of cos where
is the zenith angle of the
decay electron The up
down di erence of the de
tector gain is estimated to
b e
COS
Neutrino oscillation analysis
We examined the hypotheses of two avor and oscillation mo des using a
s
comparison of data and Monte Carlo allowing all imp ortant Monte Carlo parameters
to vary weight by their exp ected uncertainties For this analysis we used fully contained
single ring events only The matter e ect is taken into account in
the analysis This e ect for is di erent from the one for and
s s s
the interaction cross section and kinematics are di erent b etween and Therefore
for oscillations we calculated on b oth assumptions of m and m
s
The data were binned by particle type momentum and cos A is de ned as
FC
X X
N N sin m
j data MC j
FC
j
j
cos p
where the sum is over ve bins equally spaced in cos and seven six momentum bins
for e like like events The statistical error accounts for b oth data statistics and
the Monte Carlo statistics N is the measured number of events in each bin N is
data MC
NEUTRINO OSCILLATION ANALYSIS
sub GeV multi GeV
e like like e like like
for data energy scale
background contamination
for MC ux Honda Bartol
Mt Ikenoyama e ect
Table Systematic errors in the U p D ow n ratio The systematic error from the energy
scale is due to the up down di erence of the PMT gain by The cosmic ray muon
and the asher PMTs are considered as the source of the background The systematic error
related to the exp ected neutrino ux is obtained by the comparison of the indep endent
calculations Mt Ikenoyama e ect means the de cit of the downward going neutrino
which is caused by the fact that a fraction of downward going muon reach Mt Ikenoyama
b efore it decays
the weighed sum of Monte Carlo events
X
L
data
w N
MC
L
MC
M C ev ents
L and L are the data and Monte Carlo livetimes For each Monte Carlo events the
data MC
weight w is given by
sub GeV e like
s
sub GeV like
s
i
w E E cos f sin m
s m e
mulit GeV e like
m
multi GeV like
m
i
where E is the average neutrino energy in the i th momentum bin E is an arbitrary
reference energy taken to b e GeV is the up down uncertainty of the event
s m
rate in the sub GeV multi GeV energy range The factor f weights events account
e
ing for oscillation parameters L E and the matter e ect The parameter is the
overall normalization factor is related to the systematic error in the e ratio in
s m
CHAPTER NEUTRINO OSCILLATION ANALYSIS USING FC SINGLE RING EVENTS
sub GeV multi GeV energy region is an ambiguity of the index of neutrino energy
sp ectrum The calculation of the neutrino pro duction height is taken from which
accounts for the comp eting factors of pro duction propagation and decay of muons and
mesons through the atmosphere The assigned uncertainties of these parameters and
j
tted values are summarized in Table A global scan was made on a sin log m
grid minimizing with resp ect to and at each p oint Figure
s m s m
shows the allowed parameter regions The uncertainty of L E which was estimated to
b e was taken into account by expanding the allowed region in m by
This uncertainty mainly comes from the ambiguity of the pro duction height of neutrinos
in the atmosphere The con dence levels were de ned to b e where
min
and for the C L and C L allowed regions resp ectively
The b est t neutrino oscillation parameters to the three oscillation hypotheses were
identical sin m eV The d o f at the b est t p osition of
FC
oscillation was and for oscillation was
s
FC
The b est t values of the Monte Carlo parameters were all within their exp ected errors
see Table These results mean that these hypotheses are all in go o d agreement with
our data The C L allowed parameter regions are summarized in Table for the
three oscillation assumptions
Summary of the single ring analysis
We con rmed the atmospheric neutrino oscillation by using R e e and
data MC
the U p D ow n ratio Esp ecially the U p D ow n ratio of like events cannot b e explained
by the uncertainties in the atmospheric neutrino ux and the event reconstruction
The x s neutrino oscillation hypotheses were in go o d agreements with
x
the data Finally in Fig we show the zenith angle distributions of the data tougher
1 2
For the ! oscillation analysis the b est t p ositions and the values parameters for b oth
s
2 2
m and m were identical The di erence in the oscillation b etween the two cases is due
to the di erence in the sign of the p otential of the matter e ect see Eq However this di erence
2 2
disapp ears at sin According to Eq the e ective mixing angle at sin is written as
2 2 2
2
sin sin Therefore the b ehaviors of b oth oscillations are identical at sin m
SUMMARY OF THE SINGLE RING ANALYSIS
-2 1 10
-1 10 (a)
-2 10
-3 10 -3 10 -4 10
-5 -2 10
) 10 2 -1 10 (b)
-2 | (eV 10 2
m -3 10 -3 ∆
| 10 -4 10
-5 -2 10 10
-1 10 (c)
-2 10
-3 10 -3 10 -4 10
-5 10 0 0.2 0.4 0.6 0.8 1 0.7 0.8 0.9 1
sin 2 2 Θ
Figure The allowed regions for each hypothesis from the FC single ring events a
for oscillation b for m and c for m Thick
s s
Thin line shows C L The gures on the right show the magni ed region
sin m of the gures on the left The b ehaviors of
vary according to the sign of m as we had noted However in this analysis
s
the b est t p ositions for all cases are at sin Therefore the b ehavior of the
s
oscillation with m is identical with m at sin
CHAPTER NEUTRINO OSCILLATION ANALYSIS USING FC SINGLE RING EVENTS
Monte Carlo Fit Parameters Best t uncertainty
s
overall normalization
sub GeV e ratio
s
multi GeV e ratio
m
E sp ectral index
sub GeV up down
s
multi GeV up down
m
Table Summary of Monte Carlo t parameters for and oscillations
s
We calculated the and t parameters for b oth sign of m for oscillations
s
However the b est t p ositions of oscillation were b oth at sin so that
s
and tting parameters for b oth cases were identical was estimated to have
uncertainty but was tted as a free parameter
m eV sin
m
s
m
s
Table The allowed parameter regions for three oscillation hypotheses
with the predictions of the two oscillation hypotheses for the b est t parameters As
shown in this gure b oth oscillation hypotheses were very similar and repro duced the
observed zenith angle distributions well As a result it is di cult to discriminate
and oscillation hypotheses by using the FC single ring events
s
SUMMARY OF THE SINGLE RING ANALYSIS
700 700 600 (a) 600 (b) 500 500 400 400 300 300 200 200 100 100 0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
200 200 180 180 160 (c) 160 (d)
number of events 140 140 120 120 100 100 80 80 60 60 40 40 20 20 0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
COSΘ
Figure The zenith angle distributions with the Monte Carlo prediction for the two
oscillations The circles show the observed data the solid line shows the distribution for
and the dashed line for oscillations For b oth oscillation hypotheses
s
m eV and sin are assumed The two exp ected distributions are
so similar that the two histograms are not discriminated
Chapter
Tests of ! and !
s
oscillations
The analysis of the FC single ring events demonstrates that the x s oscil
x
lations can explain the atmospheric neutrino data as describ ed in the previous chapter
It also indicates that the di erence in the exp ected signal among these hypotheses is to o
small in the FC single ring sample to discriminate them The motivation of this thesis is
to distinguish the and the solutions of the atmospheric neutrino oscilla
s
tion We checked the consistency of the and oscillation hypotheses with
s
two samples the PC events and the FC multi ring ones
Partially contained events
The and oscillation hypotheses at sin and m eV
s
are b oth in a go o d agreement with the data for FC single ring events However
s
oscillation is suppressed by the matter e ect at the high energy region as
describ ed in Chapter The mean neutrino energy of the multi GeV like sample is
GeV which is not so high that the di erence of the two oscillation hypotheses due to
the matter e ect is small at m eV On the other hand the mean energy
of the PC event sample is GeV therefore a signi cant matter e ect is exp ected in
the case of and the study of the PC events may distinguish the two solutions
s
CHAPTER TESTS OF AND OSCILLATIONS
S
Figure shows the exp ected zenith angle distribution for PC events for b oth hypotheses
with m and eV at sin The di erences in the upward
going events are due to the matter e ect In this section we try to distinguish the two
oscillation hypotheses by the U p D ow n ratio of PC sample 200 200 180 (a) 180 (b) 160 160 140 140 120 120 100 100 80 80 60 60 number of events 40 40 20 20 0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
cosΘ cosΘ
Figure Exp ected zenith angle distribution for the PC events with neutrino oscillations
at sin The event number is normalized by the livetime of the PC sample
kt yr The hatched histogram shows the exp ected distribution for oscillation
with its statistical error The solid line is for oscillation a for m
s
eV b for m eV The de cit of the upward going events
is larger for than for b ecause the matter e ect suppresses
s s
neutrino oscillation at small m region
Event selection
At rst we discuss the event selection Figure illustrates that the study of the PC
sample enables us to discriminate the two p ossibilities However at large m region
the di erence for the two oscillation hypotheses is small Thus we need to select an event
sample which shows a signi cant di erence
PARTIALLY CONTAINED EVENTS
According to Eq oscillation is suppressed at see Eq This
s
indicates that the study on the higher energy events has an analyzing p ower at larger
m region Using the value of m at the b est t p osition obtained by FC single
ring analysis the optimum neutrino energy to separate b oth oscillation hypotheses is
GeV Therefore we need to select the high energy event out of the PC sample
b ecause the typical energy of the PC sample GeV is lower than the optimum energy
Although we cannot measure the neutrino energy of PC events we can know the lower
limit of the energy by using total photo electron P etot b ecause P etot is approximately
prop ortional to the dep osit energy by secondary particles in the inner detector p e
M eV Figure shows the relation b etween the cut criterion on P etot and the
mean neutrino energy E This gure demonstrates E is almost a liner function of the
P etot cut as the following
E GeV P etot p e
From this relation E GeV corresp onds to P etot p e
40
(GeV) 35 ν
E
Figure Relation b etween E
30
the cut criterion on P etot
25 and
each circle shows the the
20 The
energy of the events with
15 mean
more than P etot and with E
10
GeV The solid line shows the
5
function Eq 0 liner 20 25 30 35 40 45 50 55 60 ×
Petot ( 1000 p.e)
At this stage we need to consider the fact that the with short path length do es not
oscillate at such high energies even if oscillation is the solution of the atmospheric
neutrino oscillation We therefore selected the events with the long path length by using
the zenith angle information In the case of upward going events the relation b etween the
CHAPTER TESTS OF AND OSCILLATIONS
S
neutrino path length L and zenith angle are expressed as L R j cos j where
e
R is the radius of the earth k m
e
Additionally we should take account of statistics of the PC event sample b ecause
tight cuts decrease the number of the PC events Therefore we decided the selection
criteria from a Monte Carlo study considering the data statistics As the result the value
of the P etot cut was adopted to b e p e which corresp onds to E GeV And
the de nition of upward downward going events was set to b e cos In
this de nition the shortest path length of the upward going event is k m which is
signi cantly longer than the typical oscillation length k m for m
Therefore the upward going can oscillate into if the oscillation o ccurs
Summary of PC events
We summarize PC events with P etot p e in this subsection Fig shows
the P etot distribution for the data and MC The MC repro duces the data distribution
reasonably well The cut is also indicated in the gure The observed number of events
with P etot p e was and the exp ected one without neutrino oscillation was
Table summarizes the fraction of each interaction mo de in this sample It is a
very pure C C sample and the contamination of NC and C C events is less than
e
140
Petot cut (45,000 p.e.)
Figure P distribution of
120 etot
the PC sample Crosses show the
number of events 100
distribution for data hatched his
80
togram for and solid
60
one for The number
s
events of Monte Carlo predic
40 of
tions are normalized by the PC
20
livetime Solid line shows P etot
0
p e 4 5 6 7 10 10 10 10
Petot (p.e.)
PARTIALLY CONTAINED EVENTS
Table The fraction of
C C q e
each interaction mo de in PC
with P etot p e
multi
This is estimated based on
others
no neutrino oscillation
Figure shows the observed zenith angle distribution of the PC events with P etot
p e and the exp ected distributions with and without neutrino oscillations The
exp ected distributions for and oscillations are for m eV and
s
sin This gure demonstrates that the oscillation hypothesis repro duces
the data well The observed number of the upward downward going events with cos
was The U p D ow n ratio was
+ 0 14
data
stat sy s
0 11
U p D ow n
MC no oscil l ation
stat sy s
The U p D ow n ratio for the real data was signi cantly di erent from the Monte Carlo
prediction and was consistent with the U p D ow n ratio for the multi GeV like events
Systematic error in the PC U p D ow n ratio
We discuss the systematic errors in the U p D ow n ratio of PC events The considered
sources of systematic error related to the data are the same as those for the FC U p D ow n
ratio background contamination and energy scale
We estimated the contamination of the cosmic ray muons as the background to the PC
sample by using a test The value was calculated by comparing the D distribution
w al l
of the data with that of the combined distribution of the Monte Carlo prediction and the
stopping muon sample Here all sample satisfy P etot cut P etot p e and zenith
angle cut j cos j The obtained contamination of the cosmic ray muon is
at the b est t p osition and at level Therefore we estimated the systematic
error due to the cosmic ray muon to b e less than b ecause most of the cosmic ray
muon is downward going Figure shows the D distributions of the PC sample the
w al l
Monte Carlo prediction and the stopping muon sample In addition the systematic error
CHAPTER TESTS OF AND OSCILLATIONS
S
40
35
30 Number of events
25
20
15
10
5
0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
cosΘ
Figure The zenith angle distributions for the PC events with P etot p e The
black circles show the distribution for the data The hatched histogram shows the Monte
Carlo prediction without oscillation with its statistical error The prediction is normalized
by the livetime of the PC data The solid broken histogram shows the distribution for
oscillation at m sin Both exp ected distriub
s
tions share the same normalization fcator which was evalurated by the test on
the assumption of oscillation cos indicates upward downward going
PARTIALLY CONTAINED EVENTS
arising from the p ossible up down gain asymmetry of the Sup er Kamiokande detector for
the PC sample is estimated to b e which was estimated in a same way as we did
for the FC single ring sample see Sec
20
Figure The D distribu
18 w al l
for the PC sample the MC
16 tion
and the stopping muon
14 prediction
sample All events were applied
number of events 12
P cut and zenith angle cut
10 etot
j cos j The black circles
8
the distribution for the ob
6 show
events The solid hatched
4 served
is for MC stop muon
2 histogram
muon sample at 0 sample stopping
0 200 400 600 800 10001200 14001600
b est t level
Dwall (cm) the
We estimated the systematic error with and without neutrino oscillation The reason
for this is that the di erence in energy distribution b etween upward going and downward
going events dep ends on neutrino oscillation Here we used the oscillation parameter
sin m eV The comparison b etween the two indep endent ux
calculations showed that the uncertainty coming from the ambiguity of the atmo
spheric neutrino ux was negligible
The Mt Ikenoyama e ect was the main systematic source related to the Monte
Carlo prediction which was estimated to b e The systematic error from energy
sp ectrum index of the atmospheric neutrinos was estimated to b e
The systematic error from neutrino interaction cross section was also considered The
neutrino oscillation dep ends on the neutrino energy and changes the ratio of q e multi pi
b etween upward going and downward going events Therefore the uncertainty in q e multi
pi ratio results in the uncertainty in U p D ow n ratio when we take account of neutrino
oscillation This error was estimated to b e the di erence in U p D ow n ratio as we change
the multi pion pro duction cross section by As the result we estimated this error to
b e less than However the relatively large uncertainty from the neutrino interaction
CHAPTER TESTS OF AND OSCILLATIONS
S
source systematic error
for data background contamination
energy scale
for MC no osc
s
ux Honda Bartol
Mt Ikenoyama e ect
E
neutrino interaction
Table Systematic errors in the U p D ow n ratio for the PC sample The systematic
error related to the Monte Carlo prediction is estimated with neutrino oscillation with
m eV and sin
cross section seems to b e due to a statistic uctuation of Monte Carlo we used to esti
mate Although we have Monte Carlo events of years equivalent the number of events
satisfying P cut and zenith angle cut is only The statistical error of the di erence
etot
in the q e multi pi b etween upward going and downward going events is It means
that the systematic error due to the neutrino cross section is consistent with the
statistical error b ecause we change the q e multi pi ratio by As the result
error is likely to b e due to the statistical error of our Monte Carlo however we adapt this
value for the systematic error coming from the uncertainty of neutrino cross section
These systematic errors are summarized in Table
Neutrino oscillation and the PC U p D ow n ratio
We estimated the exp ected U p D ow n ratio of the PC events for and
s
oscillations at a parameter region m eV and sin Figure
shows the observed U p D ow n ratio and the exp ected ones for b oth hypotheses The
observed ratio is consistent with that of oscillation at m eV within
the uncertainties In contrast to this the exp ected ratio for oscillation is larger
s
than the observed one at level at m eV
NEUTRAL CURRENT EVENTS
We tried the consistency check of the U p D ow n ratio with b oth oscillation hypotheses
by a test using the U p D ow n ratio A global scan was carried out at a parameter
region m eV and sin in which the allowed regions of
neutrino oscillation parameters by the FC single ring analysis are con ned as shown in
Fig The de nition of is as follows
PC
U p U p
data MC
pc U
D ow n D ow n
data MC
D
where is the statistical error for upward downward going events is a normal
U D
ization factor and is the systematic error in the U p D ow n ratio
Figure shows the and C L contour maps obtained by the present PC
analysis The and C L contour maps are obtained by a hypothesis test if the
value de ned in Eq is the probability that the observed large value
for d o f is due to a statistical uctuation is Figure demonstrates the
observed PC U p D ow n ratio is consistent with the exp ected one for oscillation
at m eV which includes the C L allowed region obtained by the
FC single ring analysis completely The tting parametes and at the b est t p osition
of the FC single ring analysis are and Both values are smaller
than their uncertainties However the oscillation is disfavored at C L at
s
m eV For this oscillation and at the b est t p osition are
and resp ectively
Neutral current events
As describ ed in Chapter a interacts with a nucleon via neutral current in the same
way as a dose but by de nition a dose not Therefore the di erence b etween the
s
two oscillation mo dels should b e characterized by a b ehavior of the NC events We
studied the NC events by using the zenith angle distribution of FC multi ring events
In the case of oscillation the zenith angle distribution of NC events should b e
approximately up down symmetric In the case of oscillation in contract to this
s
CHAPTER TESTS OF AND OSCILLATIONS
S
1.2
Up/Down 1
0.8
0.6
0.4
0.2
0 -3 -2 10 10
∆m2(eV2)
Figure U p D ow n for the PC sample as a function of m at sin Each thick
line shows the U p D ow n ratio and thin lines show the error Broken curves show
the exp ected values for oscillation and dotted curves for The solid
s
lines show the observed values
NEUTRAL CURRENT EVENTS
-2 10 (a)
-3 10
-2
) 10 2 (b) | (eV 2
m -3 ∆ | 10
-2 10 (c)
-3 10
0.7 0.8 0.9 1
sin22Θ
Figure Contour maps using the PC U p D ow n ratio a for oscillation
b for m and c for m Regions inside the thin
s s
solid dotted curves show the C L allowed parameter regions from the FC
single ring analysis Regions b elow the thick solid dashed curves are excluded at
C L by the PC analysis
CHAPTER TESTS OF AND OSCILLATIONS
S
the upward going events pro duced via the NC interaction should have de cit compared
to the downward going ones Thus the study of the NC U p D ow n ratio is also useful
In some cases events are used for NC study b ecause it is relatively easy to identify
using invariant mass However events are not useful to compare the rates of upward
going and downward going events As describ ed in App endix B most of the reconstructed
s are low energy Most of them are pro duced via single pro duction In this interaction
the pro duced by the neutrino interaction immediately decays into N and The
direction of emitted is almost isotropic at the center of the mass system of the
resonance Accordingly reconstructed s barely keep the directional information of
primary neutrinos Therefore we tried another approach to select NC events
In this section we discuss the U p D ow n ratio of multi ring events to discriminate
and oscillation hypotheses This study is almost indep endent of the
s
uncertainty of the atmospheric neutrino ux and NC interaction cross section The reason
why we used the multi ring sample to study NC will b e presented in the section of the
event selection
For the FC multi ring analysis we should consider C C induced events b ecause most
of induced events are classi ed as multi ring events We made the MC events and
analyzed them in the same way as we did for the real data Table summarizes the
exp ected number of events in a year with neutrino oscillation with m eV
and sin
Event selection
As describ ed in the previous section the study on the PC U p D ow n ratio was useful at
relatively small m This study disfavored oscillation at m . eV
s
at C L
For m & eV and for E . af ew GeV the matter e ect is negligibly
small In this case the neutrino oscillation probabilities are essentially the same b etween
the and oscillation hypotheses Therefore the study of the NC U p D ow n
s
ratio is exp ected to b e p owerful even for m & eV
In this study we have to enrich NC events and reject C C events which show an
NEUTRAL CURRENT EVENTS
m eV
sub GeV R
e like
like
R
R
multi GeV R
e like
like
R
R
Table The exp ected induced events in the ducial volume in one year exp osure of
the Sup er Kamiokande detector
up down asymmetry Therefore we applied two cuts N r ing cut and PID cut
max
First we introduce N r ing cut Figure a shows the number of ring distribution
for the NC and all events Figure b shows that the fraction of NC events in multi
ring events is ab out though single ring events are mostly comp osed of CC events
Therefore we used multi ring events to enrich NC events
Next PID cut is describ ed where PID is the PID result for the most energetic
max max
Cherenkov ring Figure illustrates the interaction pro ducing multi ring events for
C C and NC interactions In the case of NC interaction we detect the Cherenkov light
emitted by A pro duces more Cherenkov light than a of the same energy A
is identi ed as an e like event or a two e like ring event Hence the particle type
of the most energetic ring PID is identi ed as e like In contract to this for C C
max
events in most cases pro duces most energetic ring and PID is like Therefore
max
we require that PID is e like Figure a shows the likelihoo d function for the
max
most energetic ring in the multi ring sample If the PID likelihoo d is p ositive negative
a particle is like e like of C C events are identi ed as like as shown in Fig
CHAPTER TESTS OF AND OSCILLATIONS
S
0.5 0.45 0.4 10 4 0.35 NC/ALL 0.3 0.25 0.2 3 0.15 10 0.1 0.05 0 1 2 3 4 5 1 2 3 4 5
number of rings number of rings
Figure Number of ring distribution a shows the number of ring distribution
Hatched blank histogram shows the NC all events b shows the fraction of NC
events
b therefore PID cut is useful to reject C C events
max
Finally we apply E cut to reject the low energy events and decide the de nition of
v is
the upward downward going events Figure shows the E distribution of the events
v is
satisfy N r ing cut and PID cut This gure shows our Monte Carlo with neutrino
max
oscillation repro duces the data distribution
Here we de ne the direction of the reconstructed total momentum for the multi ring
events d
m
P
p
i
i
P
d
m
j p j
i
i
where p is the momentum of an electron that would pro duced the observed amount of
i
Cherenkov light of the i th ring Figure shows an angular correlation b etween the
d and the neutrino direction as a function of the visible energy E
m v is
The angular correlation b etween the direction of the primary neutrino and the recon
structed one gets worse with lowering the neutrino energy We however only use the
U p D ow n ratio and the angular correlation is not required to b e very go o d Of course
the requirement to the angular correlation is dep endent on the de nition of the upward
downward going events Therefore we decided the criteria of E cut and the upward
v is
downward going events from the Monte Carlo study in the similar way as we did in PC
NEUTRAL CURRENT EVENTS
CC π µ
π
Illustration of
ν Figure
multi ring events Solid
lines show the particles
which pro duce Cherenkov
Dashed lines show NC ring
π ν
and they are invisible π ν
300 (a) 140 (b) µ 250 e-like -like 120 200 100 150 80 60 100
number of events 40 50 20 0 0 -10 -5 0 5 10 -10 -5 0 5 10
likelihood likelihood
Figure The PID likelihoo d distribution for the most energetic ring PID of
max
multi ring events In a black circles are the data solid broken and dotted histogram
are the MC prediction for no oscillation m sin and
m sin resp ectively In b solid histogram shows
s
PID for C C event broken for C C dotted for NC The e like events due to C C
max e
in b are mainly multi hadron pro duction events with many Cherenkov rings overlapped
CHAPTER TESTS OF AND OSCILLATIONS
S
400
350
Figure E distribution v is
300
All samples are applied N r ing number of events
250
and PID cut Black circles
max
the data Solid broken and
200 are
histogram are the MC pre
150 dotted
diction for no oscillations
100
m sin
50
and m
s
0
sin resp ectively -2 -1 2 3 10 10 1 10 10 10
Evis (GeV)
140 120 (a) (b)
100
Figure The angular
80
b etween the re 60 correlation
40
constructed direction d m
20
the neutrino direction 1400 and
degree (c) (d)
a function of E a
120 as v is
100
shows the correlation for
80
C C induced events b
60 e
40
for C C c for NC d
20
for C C 0 0 1 2 3 0 1 2 3 E_vis (GeV)
NEUTRAL CURRENT EVENTS
mo de
s
Table Summary of multi ring
C C
events satisfying the multi ring cuts
C C
e
The fraction for each comp onent is cal
C C
culated on the assumption of m
NC
eV and sin
U p D ow n analysis We set the cut values so that a statistically maximum separation is
obtained at sin and m eV which is the upp er limit of allowed
m region from the FC single ring analysis In this analysis we considered the matter
e ect and the contribution of CC events As the result we adopted E M eV
v is
and cos for the de nition of upward downward going events
In summary we applied the following cuts to study the NC U p D ow n ratio
Nring
PID is e like
max
E M eV
v is
The number of the observed events satisfying the ab ove criteria was of which
were upward downward going events And the corresp onding number of events
in the Monte Carlo is for no neutrino oscillation Figure shows the zenith
angle distribution of the events satisfying the ab ove condition Table summarizes the
fraction of each interaction mo de satisfying the ab ove cuts Those cuts enrich NC events
and reduce CC ones
We calculated the U p D ow n ratio of the multi ring events as
+ 0 09
data
stat sy s
0 08
U p D ow n
MC no oscil l ation
stat sy s
Systematic error in U p D ow n ratio for multi ring sample
We estimated the systematic error in the U p D ow n ratio for the multi ring sample in the
same way as we did for the PC sample First we checked the systematic errors for the
CHAPTER TESTS OF AND OSCILLATIONS
S
200 180 160 140 120 100 80 60 Number of events 40 20 0 -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
cosΘ
Figure Zenith angle distributions of the multi ring events satisfying the PID
max
and the E cuts The black circles show the distribution for the data The hatched his
v is
togram shows the Monte Carlo prediction with no oscillation with its statistical error The
prediction is normalized by the livetime of the FC data The broken dotted histogram
shows the distribution for oscillation at m sin
s
Both exp ected distributions share the same normalization factor which obtained
by the test on the assumption of oscillation cos indicates
upward downward going
NEUTRAL CURRENT EVENTS
observed U p D ow n ratio The background contamination was estimated as follows As
mentioned in the FC analysis Sec the p ossible background sources were cosmic
ray stopping muons and ashing PMT s for single ring events Among them only ashing
PMT events were considered as a p ossible source of the background to the multi ring
sample b ecause cosmic ray muons are almost always single ring events Even if they are
classi ed as multi ring sample they are rejected by the PID cut We analyzed these
max
ashing PMT events in the same way we did for the data to study the b ehavior of them
These events were all typical ashing PMT event and were rejected by eye scanning We
estimated the upp er limit of the contamination of these events in multi ring sample as the
following on the assumption these events may not b e rejected by the eye scanning The
upp er limit of the contamination of these ashing PMT events in the ducial volume
were estimated to b e for single ring e like events See Sec Therefore the
number of these events in FC single ring e like sample is estimated to b e events The
ratio of multi single e of the ashing PMT events is therefore the exp ected
number of contamination of ashing PMT events in multi ring sample is events As
the result the upp er limit of the contamination of ashing PMT events in multi ring
events is estimated to b e Figure shows the D distribution of multi ring
w al l
events and it illustrates no excess due to the background contamination in the multi ring
events
The p ossible gain asymmetry of the detector for upward going was estimated to caused
uncertainty in the U p D ow n ratio
Next we considered the systematic errors related to the Monte Carlo prediction We
assumed the neutrino oscillation in the same way we did for PC events The di erence
b etween the two indep endent calculations was The Mt Ikenoyama e ect
caused uncertainty in the U p D ow n ratio Moreover we estimated the uncertainty
due to the energy index of the primary neutrino ux This value is for all cases
We considered the uncertainty related to the neutrino cross section The uncertainty
was de ned as the change of U p D ow n when we increase the NC cross section by In
the case of no oscillation the uncertainty is The main cause of this error was mainly
the statistical uctuation of our Monte Carlo though the uncertainty of the neutrino cross
section should b e canceled by taking the U p D ow n ratio for no neutrino oscillation In
CHAPTER TESTS OF AND OSCILLATIONS
S
400
Figure The D distribu
350 w al l
for the FC multi ring events
300 tion
circles for the data his 250 black
number of events
for the Monte Carlo pre
200 togram
The event number of the
150 diction
Carlo prediction is normal
100 Monte
ized by that of the PC sample
50
Solid line shows the D cut cri w al l 0 0 200 400 600 800 1000120014001600
Dwall (cm) terion
the case of oscillation m eV sin the up down symmetry is
broken by the de cit of upward going events The uncertainty is and for
and hypotheses resp ectively Although these values also contain the
s
MC statistical error dominant uncertainty is thought to b e due to the uncertainty of the
neutrino interaction cross section
As a result we con rmed that the study of up down asymmetry is almost indep en
dent of the uncertainties related to the neutrino cross section or neutrino uxes These
systematic errors are summarized in Table
Neutrino oscillation and the multi ring U p D ow n ratio
We calculated the exp ected U p D ow n ratio for b oth oscillation hypotheses Figure
shows the exp ected U p D ow n ratio as a function of m where we assume sin
The matter e ect is taken into account for
s
The data disfavored hypothesis at m eV by ab out
s
hypothesis was away from the data by However the agreement b etween
the data and hypothesis is b etter than that b etween the data and
s
hypothesis
We calculated values for b oth hypotheses The de nition of is the similar
mul ti mul ti
NEUTRAL CURRENT EVENTS
1.2
1.1 Up/Down 1
0.9 νµ → ντ 0.8 ν → ν µ s 0.7
0.6
0.5 -3 -2 10 10
∆m2(eV2)
Figure U p D ow n for the multi ring sample as a function of m at sin
Each thick line shows the U p D ow n ratio and thin lines show error Broken lines
show the exp ected values for oscillation and dashed lines for The solid
s
lines show the observed values
CHAPTER TESTS OF AND OSCILLATIONS
S
source systematic error
for data background contamination
energy scale
for MC no osc
s
ux Honda Bartol
Mt Ikenoyama e ect
E
neutrino interaction
Table Systematic errors in the U p D ow n ratio for the multi ring sample The sys
tematic error related to the Monte Carlo prediction is estimated with neutrino oscillation
with m eV and sin Assuming that these ashing PMT events
may have a strong directionality the uncertainty in the U p D w on ratio due to background
contamination should b e less than
to
PC
U p U p
data MC
U mul ti
D ow n D ow n
data MC
D
where is the statistical error for upward downward going events is a normal
U D
ization factor and is the systematic error in the U p D ow n ratio
Figure shows the and C L contour maps obtained by the multi ring
analysis The observed U p D ow n ratio do es not con ict with oscillation for
m eV The tting parameters and at the b est t p osition of the FC
single ring analysis are and resp ectively Both values are within their
uncertainties On the other hand oscillation is disfavored at C L for a
s
signi cant fraction of the allowed region obtained by the FC single ring analysis
NEUTRAL CURRENT EVENTS
-2 10 (a)
-3 10
-2
) 10 2 (b) | (eV 2
m -3 ∆ | 10
-2 10 (c)
-3 10
0.7 0.8 0.9 1
sin22Θ
Figure Contour maps using the multi ring U p D ow n ratio a for oscil
lation b for m and c for m Regions inside the
s s
thin solid dotted curves show the C L allowed parameter regions from the FC
single ring analysis For region b elow the thick solid curve is excluded at
C L by the multi ring analysis For regions ab ove the thick solid dashed curves
s
are excluded at C L by the multi ring analysis
CHAPTER TESTS OF AND OSCILLATIONS
S
Combined analysis
In this thesis we studied the distinction of from by the PC events and
s
FC multi ring events In the case of oscillations the U p D ow n ratios of the PC
and FC multi ring samples are b oth consistent with the observed ones within uncertainties
as we have shown However the multi ring U p D ow n ratio disfavors a signi cant fraction
of the parameter region allowed by the FC single ring analysis at C L And the PC
U p D ow n ratio supp orts the result of the multi ring analysis
Finally we show a result of a combined analysis of the PC and multi ring analyses
The de nition of for combined analysis is
cmb PC mul ti
Figure shows the and C L contour maps of for each oscillation
cmb
hypothesis Here and C L are de ned to b e at and since
cmb
has d o f The combined analysis demonstrates that the U p D ow n ratios of PC
cmb
and FC multi ring samples are consistent with FC single ring analysis for and
indicates that oscillation is the solution of the atmospheric neutrino oscillation
For in contract to this there is almost no allowed region at C L in the
s
C L allowed region obtained by the FC single ring analysis
COMBINED ANALYSIS
-2 10 (a)
-3 10
-2
) 10 2 (b) | (eV 2 m
∆ -3 | 10
-2 10 (c)
-3 10
0.7 0.8 0.9 1
sin22Θ
Figure Contour maps obtained by the combined analysis of PC and multi ring events
a for oscillation b for m and c for m
s s
Regions inside the thin solid dotted curves show the C L allowed parameter
regions from the FC single ring analysis For hypothesis a regions b elow the
thick solid dashed curves is excluded at C L by the combined analyses For
hypothesis a region surrounded by dashed curves are excluded at C L All
s
the regions in sin and m are excluded at C L
Chapter
Conclusion
We measured the atmospheric neutrino events in Sup er Kamiokande We observed
events for the fully contained partially contained sample with an exp osure of
kton year
We obtained the e e ratio R and the Up Down ratio from the FC
data MC
single ring events
+ 0 023
sub GeV
stat sy s
0 022
R
+ 0 050
multi GeV
stat sy s
0 047
+ 0 059
sub GeV e like
stat sy s
0 056
+ 0 041
sub GeV like
stat sy s
0 039
U p D ow n
+ 0 116
multi GeV e like
stat sy s
0 103
+ 0 070
multi GeV like
stat sy s
0 062
We found that these data can b e consistently explained by either or
s
oscillations According to the FC single ring analysis the b est t parameters to the two
oscillation hypotheses are sin m for b oth and
s
oscillations And the observed data are in go o d agreement with b oth hypotheses with
sin and m eV at C L
Then we tried to discriminate and We studied the distinction of
s
CHAPTER CONCLUSION
the two hypotheses by using the PC sample and FC multi ring sample The study of the
PC events showed that there is a signi cant di erence in the exp ected Up Down ratio
b etween the two hypotheses due to the matter e ect We obtained that the Up Down
ratio of the PC events with P otot p e was
+ 0 135
U p D ow n sy s
stat
0 109
This result disfavored the oscillation hypothesis at small m of . eV
s
at C L
For the study of FC multi ring events we also used the U p D ow n ratio in the same
way we did for PC sample to distinguish the two hypotheses The U p D ow n ratio of the
FC multi ring sample was
+ 0 09
U p D ow n
stat sy s
0 08
This result disfavored oscillation hypothesis at C L for a signi cant faction
s
of the allowed region at C L obtained by the FC single ring analysis
Finally by the combined analysis of the PC and multi ring events we conclude that
the oscillation hypothesis as the solution of the atmospheric neutrino problem is
s
disfavored at C L for most of the region indicated by the FC single ring analysis
App endix A
Upward through going muon
A Outline
As describ ed in Chapter neutrino oscillation is suppressed by the MSW e ect
s
at a high energy region We studied this e ect by using the PC sample and found that
oscillation is disfavored at C L at m eV as describ ed in Sec
s
This suppression by the matter e ect dep ends on m and the neutrino energy In
the PC up down analysis we selected the high energy PC events by applying the total
photo electron cut A still tighter cut is required to distinguish the b oth hypotheses at
larger m region However we lo ose the statistics of the PC sample rapidly with the
tighter cut Therefore we need an event sample with higher neutrino energy and higher
statistics
Sup er Kamiokande can detect the through going muon pro duced by the high energy
in the surrounding ro ck The typical neutrino energy of this sample is GeV
and the number of events of this sample is a factor more than that of upward going PC
sample Therefore this sample is useful to discriminate the two oscillation hypotheses by
using the matter e ect at m eV
In the analysis we use the upward through going muons This reason is that most of
downward through going events are the cosmic ray muons and that it is imp ossible to
select the neutrino induced events out of the downward going sample
APPENDIX A UPWARD THROUGH GOING MUON
In this thesis we don t describ e the event reconstruction pro cedure b ecause the details
of it are describ ed in
A Event summary
We observed upward through going muons during detector live days The ex
p ected background due to cosmic ray muons is events and this background is sub
tracted from the bin cos in the following analysis From this data
sample the ux of the through going muon was calculated to b e
cm s sr The exp ected ux without neutrino oscillation was
cm s sr based on Honda ux This exp ected ux was obtained by the nu
merical analysis Figure A shows the zenith angle distribution of through going muon
ux with the calculated zenith angle distribution based on the Honda ux ) -1
Sr
Figure A The zenith -1
s 3.5
-2
angle distribution of the cm
-13 3
upward through going 10
×
ux X axis shows 2.5 muon
flux (
the zenith angle
2
indicates upward going The
1.5 horizontal going
pluses show the observed
1
ux with the statistical
The histogram shows
0.5 error
calculated ux based on 0 the
-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Honda ux cosΘ the
A VERTICAL HORIZONTAL RATIO
A Vertical horizontal ratio
The calculated ux of the upward through going muons has uncertainty mostly
due to the uncertainty in the absolute cosmic ray ux In order to compare the data with
the exp ected ux for b oth oscillation hypotheses we use the vertical horizontal ratio
Taking this ratio it is p ossible to carry out the analysis without any large systematic
error Figure A a shows the exp ected ux as a function of the zenith angle for b oth
oscillation hypotheses and Fig A b shows the oscillation non oscillation ux ratio
which is the survival probability of The oscillation parameter I used for this calculation
is m eV with sin
Fig A b illustrates that the exp ected ux for is close to that of no
s
oscillation rather than that of oscillation This is due to the suppression of
oscillation by the matter e ect Let us de ne the events with cos
s
to b e V er tical going H or iz ontal going The di erence in the oscillation proba
bility b etween the two hypotheses is remarkable in the V er tical going sample while the
di erence in the H or iz ontal going sample is very small Therefore we decided to use
V er tical H or iz ontal ratio for the consistency check of the oscillation mo de determina
tion
The V er tical H or iz ontal ratio for data and the calculated ux is
data
stat sy s
V er tical H or iz ontal A
MC no oscil l ation
sy s
We estimated the systematic error as the following First we show the error related
to the observed events Here we considered the background contamination the event
reduction and the angular correlation The number of contamination by the cosmic
ray muon in this bin is estimated to b e events in the most horizontal bin
with cos Thus the uncertainty in the V er tical H or iz ontal ratio due to the
backgrounds was estimated to b e The reduction e ciency was estimated from
the Monte Carlo study We applied the reduction program which is the same as we did for
the data for the Monte Carlo events The reduction e ciency was slightly lower near the
horizontal direction This e ect caused uncertainty in the V er tical H or iz ontal
APPENDIX A UPWARD THROUGH GOING MUON
4 1.2 (a) (b) 3.5 1 3 2.5 0.8 2 0.6 1.5 0.4 1 0.5 0.2 0 0
-1 -0.8 -0.6 -0.4 -0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0
Figure A Figure a shows the exp ected zenith angle distribution of the upward
through going muon ux The solid line shows the calculated ux without neutrino
oscillation The dashed line shows the exp ected ux for oscillation with
m eV and sin The dotted line is for oscillation Both
uxes are based on the Honda ux Figure b shows the survival probability of
as a function of the zenith angle The dashed line shows the exp ected ux for
oscillation The dotted line is for oscillation The strange structure of
s
at cos is caused by the e ect that the neutrinos passing through the core of the Earth
A VERTICAL HORIZONTAL RATIO
ratio For the through going muon analysis we assume that the detected muon direction
is same as that of the primary neutrino However we need to consider the uncertainty
of the angular correlation b etween the observed muon and that of the primary neutrino
which is resulted from the multiple scattering of muon in the ro ck and from the angular
resolution of the reconstruction metho d We estimated this angular correlation to b e
The error in the ratio due to the angular correlation is estimated to b e as
we changed the angular correlation We also considered the time variations of the water
transparency and the PMT gains The errors caused by these variations are negligible
Next we discuss the error related to the calculated ux Although the uncertainty
of the absolute ux of the exp ected ux is canceled by taking the ratio the uncertainty
dep ending on the zenith angle distribution is not We considered the K ratio and
the structure of the atmosphere as the source of the uncertainty dep ending on the zenith
angle According to the private communication with Honda we estimated this error to b e
This error is very preliminary however we adopted this value Another source is
the uncertainty of the energy sp ectral index of the primary cosmic ray The higher energy
neutrino can b e pro duced in the horizontal direction than in the vertical one b ecause the
decay path length for the vertical going cosmic pion in the atmosphere b ecomes longer
than the interaction length with increasing pion energy Therefore the uncertainty of
the energy shap e is the source of the systematic error in the Vertical Horizontal ratio
This error is dep endent on the neutrino oscillation b ecause the oscillation changes with
the energy of the neutrino We estimated this error to b e and for
no oscillation and oscillation resp ectively The reason of relatively
s
small error for oscillation is that the energy shap e for the vertical going neutrino
is close to that for the horizontal going one as the low energy neutrinos disapp ear due
to the neutrino oscillation Here the oscillation parameter we used for the estimation
is m sin eV which is the b est t parameter set by the FC
single ring analysis
Table A summarizes the systematic errors related to the Vertical Horizontal ratio
The exp ected the V er tical H or iz ontal ratios for b oth hypotheses are illustrated in
Fig A
APPENDIX A UPWARD THROUGH GOING MUON
data background
detection e ciency
reduction e ciency
the gain of PMT
water transparency
calculated ux K ratio and the atmosphere mo del
ux H onda B ar tol
sp ectral index no oscil l ation
Table A Summary of the systematic error in the V er tical H or iz ontal ratio
1.2
1.1
Figure A The exp ected
ratio as 1 Vertical Horizontal
Vertical/Horizontal
function of m with
0.9 the
sin Broken dot
0.8
ted line shows the ratio for
the oscil
s
0.7
Solid line illustrates
0.6 lation
the observed ratio and thin
0.5
lines are of the data -3 -2 10 2 10 ∆m
A ANALYSIS
A analysis
We carried out the consistency check of the through going muon sample by using a
test The de nition of the is
V er tical H or iz ontal V er tical H or iz ontal
data MC
A
stat
sy s
Figure A shows the contour map of the and C L exclusions of
oscillation at the b est t p osition of FC single ring analysis is and the through
going muon data is in go o d agreement with the oscillation hypothesis On the
contrary for oscillation hypothesis is and hypothesis is again
s s
disfavored at C L there
A Conclusion of Upward going muon analysis
The through going muon data are again consistent with oscillation and disfavor
oscillation at C L at the b est t p osition obtained by the FC single ring
s analysis
APPENDIX A UPWARD THROUGH GOING MUON
-2 10 (a)
-3 10
-2
) 10 2 (b) | (eV 2
m -3 ∆ | 10
-2 10 (c)
-3 10
0.7 0.8 0.9 1
sin22Θ
Figure A Contour maps using the V er tical H or iz ontal ratio of the through going
muons a for b for m and c for m
s s
Regions inside the thin solid dotted curves show the C L allowed parameter
regions obtained by the FC single ring analysis For and m
s
regions b elow the thick solid dashed curves are excluded at C L by the upward
through going muon analysis For m all regions in this gure are
s
excluded at C L
App endix B
events
We also used events in order to study the event rate of the neutral current events
Generally is pro duced and decay as the following
N N
We can identify the events by using the invariant mass using these s At the low
. M eV c s from a are clearly detected as two e like momentum region of p
rings with a reasonable e ciency We selected by the following criteria
ring events
b oth rings are e like
no electron signal from the decay of
M M eV c M eV c
where M is an invariant mass de ned as
q
M p p cos B
where is the op ening angle b etween the directions of two rings and p is the recon
structed momentum The criterion is requested to reject the events containing a muon
APPENDIX B EVENTS
or a charged pion Figure B shows the M distribution of the events satisfying ab ove
criteria and This gure proves that the condition is reasonable
Figure B shows the relation b etween the detection e ciency and the momentum of
The decreases with increasing momentum of therefore it is di cult to identify
the high momentum as rings events This is the main reason that the detection
e ciency of the decreases with the increasing momentum
120
100
Figure B M distribution of
number of events 80
the events satisfying ring e like
and no decay e cuts The his
60
tograms with the shaded error
bars show the Monte Carlo pre
40
dictions with their statistical er
without the neutrino oscilla
20 ror tion
0 0 50 100 150 200 250 300 MeV/c2
massγγ
The events satisfying the ab ove criteria are called like events We observed
like events and the exp ected number from the Monte Carlo study was events
for the no oscillation case
like sample is summarized in Table The fraction of each interaction mo de in the
B Ab out of these like events were estimated to b e due to neutral current
events
B event rate
In order to distinguish b etween and we checked the rate of
s
like events We need to normalize like events by using something pro duced by the
B EVENT RATE
1
0.9
Figure B Detection e ciency
0.8
of as a function of its momen
0.7
tum At high momentum the
0.6
op ening angle b etween s into
detection efficency 0.5
a decays b ecomes small
0.4 which
it is di cult to iden
0.3 Therefore
a as a rings event As a
0.2 tify
the detection e ciency of
0.1 result
high momentum is lower 0 the
0 1002003004005006007008009001000
than that of low momentum
MeV/c
Table B Fraction of the
each interaction mo de in the
sample CC charged
single
current interaction NC
NC coherent
neutral current interaction
multi
Others include NC single
others
and NC q e events Most of
CC
e
NC single events identi
ed as like events are due
to charge exchange in Oxy gen
APPENDIX B EVENTS
atmospheric neutrino interaction to cancel uncertainty of the absolute ux of the
atmospheric neutrinos Here we used the FC single e like events for normalization b ecause
the number of e like events is least a ected by neutrino oscillations in the case of these
neutrino oscillations mo des We de ned a double ratio for the e ratio
e e B R
data MC
If the oscillation is the solution of the atmospheric neutrino oscillation
R for any m This is b ecause the number of the CC events and NC events
e
which are dominant comp onents of e and like samples are indep endent of oscillation
On the other hand in the case of oscillation the number of events decreases
s
was obtained as by at m eV The R
B R
stat sy s
is just unity this means the e ratio favors oscillation However the R
unfortunately data is consistent with the oscillation hypothesis to o b ecause R
s
as a function of has the large systematic uncertainty Figure B shows the exp ected R
m where we assume sin This gure shows that b oth hypotheses are consistent
in all region m which is obtained by the FC single with R
ring analysis As the result we can t discriminate b etween the two oscillation hypotheses
arises from the uncertainty of the neutrino cross The dominant systematic error in R
section as describ ed b elow
B Systematic error in the ratio
in the same way as we did for R The main We checked the systematic error in R
sources of the systematic error are describ ed b elow
First the systematic errors related to the atmospheric neutrino ux are describ ed
The cross section via the neutral current interaction is indep endent of the neutrino avors
Thus the event rates of is indep endent of the uncertainty in the ratio
e e
due However this uncertainty changes the e like event rates The systematic error in R
to the uncertainty of ratio is estimated to b e Similarly we
e e
B SYSTEMATIC ERROR IN THE RATIO
π 1.5 R 1.4
1.3
as a Figure B Exp ected R
1.2
function of m for
1.1
and oscillation Solid s
1
line shows for data solid
0.9 thick
lines are for the error of
0.8 thin
the data broken line for
0.7
and dotted line for s 0.6
0.5 -3 -2 10 10
∆ m2 (eV2)
checked the systematic error arising from uncertainties in and These errors
e e
are summarized in Table B The total systematic error related the atmospheric neutrino
ux is estimated to b e
uncertainty systematic error in R
e e
e e
related to the uncertainty of the atmospheric Table B The systematic error in R
neutrino ux
is the uncertainty in the neutrino The dominant source of the systematic errors in R
cross sections The uncertainties of the absolute cross section around GeV region were
estimated to b e and for quasi elastic single pion coherent pion and
multi pion interaction resp ectively The uncertainties of the NC CC ratio were estimated
to b e for all interaction mo des The systematic error coming from the uncertainty
in the cross section is summarized in table B The total systematic error arising from
the uncertainties of the neutrino interactions is estimated to b e
In addition we indep endently estimated the systematic error by comparing the e
APPENDIX B EVENTS
mo de uncertainty systematic error in R
q e CC NC
NC CC
pi CC NC
NC CC
c pi CC NC
NC CC
multi pi CC NC
NC CC
total systematic error
coming from the cross section q e quasi elastic Table B Systematic error in R
interaction pi single pion interaction c pi coherent pion interaction multi pi multi
pion interaction
ratios calculated by indep endent neutrino interaction simulations The maximum dif
ference among these results was Accordingly our estimation of the systematic error
is reasonable
was when Next we considered the uncertainty related to the nuclear e ect R
we changed the mean fully path of the in the oxygen nucleus by Therefore the
systematic error related to the nuclear e ect was estimated to b e
The systematic error related to the event reconstruction was estimated by comparing
the result of manual scan with the automatic event reconstruction This comparison
resulted the systematic error related to the reconstruction metho d is
Finally the statistical error of Monte Carlo was The total systematic error for
was estimated to b e Table B summarizes the systematic error for R R
study B The future plan of the R
We showed the result of the e ratio however this study do esn t enable us to discrim
inate b etween the two oscillation hypotheses due to the large systematic error We need
STUDY B THE FUTURE PLAN OF THE R
atmospheric neutrino ux
cross section neutrino interaction
nuclear interaction
event reconstruction metho d
Monte Carlo statistic
total systematic error
Table B Summary of the systematic error of R
to reduce this systematic error
From April K K KEK to Kamioka exp eriment started which is a long baseline
neutrino exp eriment In this exp eriment kton water Cherenkov tank is used as the
front detector The aim of this detector is to check the b ehavior of the water Cherenkov
detector The data analysis of this detector is carried out as the same way we do at sup er
Kamiokande Obviously it can detect events Therefore we can reduce the systematic
by comparing the rate of detected and events b etween the data and error in the R
the Monte Carlo K K exp eriment uses b eam so that e like events are not pro duced
Therefore the ratio is will b e studied
At the kton front detector s emitted for the Sup er Kamiokande do not oscillate
into or due to the short neutrino path length Therefore we can obtain ratio
s
without the e ect of neutrino oscillation We can observe so many and events at
is negligible In addition the detection kton detector that the statistical error in R
metho d at K K is the identical to that of the Sup er Kamiokande detector so that the
systematic error related to the event reconstruction is almost canceled There are several
minor di erences in the ratio b etween the front detector and the Sup er Kamiokande
detector the di erence of the neutrino avor and the energy distribution of the primary
neutrino and the detection e ciency due to the detector size and so on However we
exp ect the systematic error in e to go down to . and this study will distinguish
the two oscillation hypotheses indep endent of the metho ds describ ed in this thesis
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