PHYSICAL REVIEW D 85, 112001 (2012)

Search for nucleon decay into charged antilepton plus meson inSuper-Kamiokande I and II
H. Nishino,2,† K. Abe,1 Y. Hayato,1,27 T. Iida,1 M. Ikeda,1 J. Kameda,1 Y. Koshio,1 M. Miura,1 S. Moriyama,1,27
M. Nakahata,1,27 S. Nakayama,1 Y. Obayashi,1 H. Sekiya,1 M. Shiozawa,1,27 Y. Suzuki,1,27 A. Takeda,1 Y. Takenaga,1
Y. Takeuchi,1,27 K. Ueno,1 K. Ueshima,1 H. Watanabe,1 S. Yamada,1 S. Hazama,2 I. Higuchi,2 C. Ishihara,2 H. Kaji,2
T. Kajita,2,27 K. Kaneyuki,2,27,* G. Mitsuka,2 K. Okumura,2 N. Tanimoto,2 F. Dufour,3 E. Kearns,3,27 M. Litos,3 J. L. Raaf,3
J. L. Stone,3,27 L. R. Sulak,3 M. Goldhaber,4,* K. Bays,5 J. P. Cravens,5 W. R. Kropp,5 S. Mine,5 C. Regis,5 M. B. Smy,5,27
H. W. Sobel,5,27 K. S. Ganezer,6 J. Hill,6 W. E. Keig,6 J. S. Jang,7 J. Y. Kim,7 I. T. Lim,7 J. B. Albert,8 K. Scholberg,8,27
C. W. Walter,8,27 R. Wendell,8 T. Ishizuka,9 S. Tasaka,10 J. G. Learned,11 S. Matsuno,11 Y. Watanabe,12 T. Hasegawa,13
T. Ishida,13 T. Ishii,13 T. Kobayashi,13 T. Nakadaira,13 K. Nakamura,13,27 K. Nishikawa,13 Y. Oyama,13 K. Sakashita,13
T. Sekiguchi,13 T. Tsukamoto,13 A. T. Suzuki,14 A. Minamino,15 T. Nakaya,15,27 M. Yokoyama,15 Y. Fukuda,16 Y. Itow,17
T. Tanaka,17 C. K. Jung,18 G. Lopez,18 C. McGrew,18 C. Yanagisawa,18 N. Tamura,19 Y. Idehara,20 M. Sakuda,20 Y. Kuno,21
M. Yoshida,21 S. B. Kim,22 B. S. Yang,22 H. Okazawa,23 Y. Choi,24 H. K. Seo,24 Y. Furuse,25 K. Nishijima,25
Y. Yokosawa,25 M. Koshiba,26 Y. Totsuka,26,* M. R. Vagins,27,5 S. Chen,28 Y. Heng,28 J. Liu,28 Z. Yang,28 H. Zhang,28
D. Kielczewska,29 K. Connolly,30 E. Thrane,30 and R. J. Wilkes30(The Super-Kamiokande Collaboration)
1

2

Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan3
Department of Physics, Boston University, Boston, Massachusetts 02215, USA
4
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
5
Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697-4575, USA
6
Department of Physics, California State University Dominguez Hills, Carson, California 90747, USA
7
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
8
Department of Physics, Duke University, Durham, North Carolina 27708, USA
9
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan10
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
11
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
12
Physics Division, Department of Engineering, Kanagawa University, Kanagawa, Yokohama 221-8686, Japan
13
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
14
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
15
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
16
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
17
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan18
Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794-3800, USA
19
Department of Physics, Niigata University, Niigata, Niigata 950-2181, Japan20
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
21
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
22
Department of Physics, Seoul National University, Seoul 151-742, Korea
23
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan
24
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
25
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
26
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
27
Institute for the Physics and Mathematics of the Universe, Todai Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba 277-8582, Japan
28
Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
29
Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland
30
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 18 March 2012; published 5 June 2012)
Searches for a nucleon decay into a charged antilepton (eþ or þ ) plus a light meson (0 ,  , , 0 , , !) were performed using the Super-Kamiokande I and II data. Twelve nucleon decay modes were
*Deceased.
†
Present address: University of California, Berkeley, CA 94720, USA.

1550-7998= 2012=85(11)=112001(24)112001-1

Ó 2012 American Physical Society

H. NISHINO et al.

PHYSICAL REVIEW D 85, 112001 (2012)searched for. The total exposure is 140:9 kiloton  years, which includes a 91:7 kiloton  year exposure(1489.2 live days) of Super-Kamiokande-I and a 49:2 kiloton  year exposure (798.6 live days) of SuperKamiokande II. The number of candidate events in the data was consistent with the atmospheric neutrino
background expectation. No significant evidence for a nucleon decay was observed in the data. Thus,
lower limits on the nucleon partial lifetime at 90% confidence level were obtained. The limits range from
3:6  1031 to 8:2  1033 years, depending on the decay modes.
DOI: 10.1103/PhysRevD.85.112001

PACS numbers: 13.30.Ce, 11.30.Fs, 14.20.Dh, 29.40.Ka

I. INTRODUCTION
The standard model of particle physics has been successful in explaining most experimental results. However,it contains many empirical parameters, such as masses andgenerations of fermions, coupling constants, mixing angles, and so on. Grand unified theories (GUTs) have been
proposed to account for these parameters. The basic idea of
GUTs is that the SUð2Þ  Uð1Þ symmetry of electroweak
interactions and the SU(3) color symmetry of strong interactions are incorporated into a larger symmetry groupbroken at an ultrahigh energy scale. GUTs predict newinteractions in which leptons and quarks can transform one
into the other by exchanging a superheavy gauge boson.
This type of interaction can lead to baryon number violating nucleon decays. The simplest GUT, minimal SU(5) [1],predicts the partial lifetime of a proton via the mode p !
eþ 0 to be 10311 years [2,3], which was excluded by
the IMB and KAMIOKANDE experiments [4,5].
There are various viable GUTs (see, e.g., [6–12]), suchas models incorporating SUSY, models with a symmetrygroup like SO(10), flipped SU(5) models, and models
in extra dimensions. Predictions for the lifetime of thenucleon strongly depend on the models and also have large
uncertainties. Some models predict the partial lifetimeof the proton to be in the accessible range of the SuperKamiokande experiment.
The Super-Kamiokande Collaboration previously published the results of p ! eþ 0 and p ! þ 0 searches[13]. Updated results have also been presented since thattime [14]. No candidate events for proton decay were
found. Although the p ! eþ 0 mode is considered to be
the dominant decay mode in many GUT models, branchingratios for the other modes are not necessarily negligible.
Many possibilities for nucleon decays are theoretically
proposed. In some SU(5) and SO(10) GUT models([15–18]), branching ratios for p ! eþ , p ! eþ 0 or
p ! eþ ! can be as high as 10–20% and the proton andbound neutron lifetimes are expected to be comparable toeach other. Also, N ! þ þ meson modes can be inducedby mixing effects between lepton families. Though typicalSU(5) GUT models predict very small branching ratios forthe muon modes (see, e.g., [15,19]), the flipped SU(5) GUT[12] shows that the p ! þ 0 mode can have a comparable branching ratio with the p ! eþ 0 mode. Therefore,
nucleon decay modes mediated by the exchange of super-heavy gauge bosons are important for most of the GUT
models. In spite of the importance of investigating all
possible decay modes, so far only the p ! eþ 0 and p !
þ 0 searches, and the searches for several modes favoredby supersymmetry (SUSY) GUTs [20] have been published by the Super-Kamiokande experiment. In this paper,
we search for nucleon decays into a charged antilepton (eþand þ ) plus an unflavored light meson (, ,  and !)using the Super-Kamiokande I and II data. Eight modes
were studied for proton decay, and four for neutron decay.
The results of the p ! eþ 0 and p ! þ 0 mode are
identical to those reported in an earlier article [13], however more details of the analysis are described in this paper.
In addition, we briefly report the results of the search inthese two channels based on a longer exposure, includingSuper-Kamiokande III and IV data.
II. SUPER-KAMIOKANDE DETECTOR
Super-Kamiokande is a 50-kiloton water Cherenkov detector located in the Kamioka Observatory in Japan, under1000 m of rock overburden. The Super-Kamiokande detector is made of a cylindrical stainless steel tank, 39.3 m indiameter and 41.4 m in height. The detector is opticallyseparated into two regions: an inner detector (ID), and anouter detector (OD). On the surface of the ID, 20-inch
photomultiplier tubes (PMTs) are uniformly attached todetect Cherenkov light radiated by relativistic charged
particles. The OD, which surrounds the ID with a 2 m
thickness of water, is used to reject cosmic ray muon eventsand to tag exiting charged particles with 1885 outwardfacing 8-inch PMTs. The OD region also serves as a shieldfrom radioactivity from materials outside the detector wall.
The Super-Kamiokande experiment started data taking
in April, 1996, and had continued observation for five years
until the detector maintenance in July 2001 (SK-I). On
November 2001, while filling the tank with water after the
maintenance, an accident occurred which destroyed morethan half of the PMTs. The detector was partially rebuiltwith half the density of photosensor coverage in the ID.
Observation began again in October 2002 and stopped in
October 2005 (SK-II) for a full detector reconstruction.
The next phase, SK-III, started October 2006 and wasswitched to SK-IV with newly developed electronics andonline systems in September 2008. This paper reports
nucleon decay search results from the first two periods:

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SEARCH FOR NUCLEON DECAY INTO . . . . I AND IIPHYSICAL REVIEW D 85, 112001 (2012)

SK-I and SK-II. The ID photosensor coverage in the SK-I
period was 40% with 11 146 20-inch PMTs. In the SK-II
period, the coverage reduced to 19% with 5182 20-inch
PMTs. All of the ID PMTs have been equipped with acrylic
covers and fiber-reinforced plastic cases since the start of
SK-II to avoid a cascade of implosions of PMTs. Details of
the detector configuration and performance for SK-I havebeen published [21].
III. SIMULATION
A. Nucleon decay simulation
In order to estimate the detection efficiencies of nucleon
decays, a nucleon decay Monte Carlo (MC) simulation wasdeveloped. The number of background events was estimated by simulations of the atmospheric neutrino fluxand neutrino interactions.
In an H2 O molecule, there are two free protons in thehydrogen nuclei, and eight bound protons and eight boundneutrons in the oxygen nucleus. The decay probabilities offree protons and bound protons were assumed to be equalin the simulation. All of the decay modes studied in thisanalysis are two-body decays, meaning that the charged
lepton and meson are back-to-back with a monochromatic
momentum in the nucleon rest frame.
For the decay of bound nucleons in oxygen, the simulation takes into account the effect of Fermi motion of thenucleons, correlation with another nucleon, and mesonnucleon interactions in the nucleus (nuclear effects).
Nucleon momentum and nuclear binding energy in the
nucleus were calculated as described in [22]. Goodagreement of the calculations with an electron scatteringexperiment on 12 C is also shown in [22].
Mesons generated in an oxygen nucleus interact with
nucleons until they escape from the nucleus. The positionof the nucleon decay in a nucleus was determined by the
Woods-Saxon nuclear density distribution in the simulation. From this position, ,  and ! mesons were tracked
in an oxygen nucleus. The lifetime of the  meson is so
short ( ’ 0:3 fm) that it decays immediately inside thenucleus into 2 mesons; therefore, the nuclear effects ofthe  meson itself were not considered in the simulation.
The mass of the  meson was assumed to have a BreitWigner type distribution with a width of  ¼ 149 MeV.
For these reasons, particles generated via the modes including a  meson do not have monochromatic momentum, even in the case of free proton decay.
Ten percent of nucleons in oxygen were assumed todecay correlating with another nucleon [23]. In such correlated decay events, the invariant mass of eþ and 0 issmaller than the mass of the nucleon because of the invisible momentum of another correlated nucleon.
Simulated particles of nucleon decays and atmospheric
neutrino interactions were passed through a GEANT-3 [24]custom detector simulation. Hadronic interactions weretreated by CALOR [25] for nucleons and charged pionsof p > 500 MeV=c, and by a custom simulation program[26] for charged pions of p  500 MeV=c.
1.  meson nuclear effects
In considering pion nuclear effects, inelastic scattering,absorption, charge exchange and pion production weretaken into account in the simulation. Pion production
hardly occurs in nucleon decay events since the crosssection for low momentum pions (p < 500 MeV=c) is
negligibly small. Cross sections for these processes were
calculated based on the model of Oset et al. [27]. The
angular and momentum distributions of pions were determined from the results of -N scattering experiments [28].
Because of the Pauli exclusion principle, the momentumof the scattered nucleon is required to be greater than the
Fermi surface momentum, given by pF ðrÞ ¼ ð32 2 ðrÞÞ1=3 ,where ðrÞ is the nuclear density distribution and r is the
distance from the center of the nucleus.
The 0 momentum from the decay mode of p ! eþ 0
is 459 MeV=c in the rest frame of the nucleon. At thismomentum, 37% of 0 s were simulated to be absorbed or
charged-exchanged in the nucleus. This is a major reason
for the inefficiency of the p ! eþ 0 and p ! þ 0modes. The probability for a 0 to escape from a nucleus
without any scattering was estimated to be 44%.
2.  meson nuclear effect
The interactions of s and nucleons in the nucleus wereconsidered through a baryon resonance of S11 ð1535Þ.
 þ N ! S11 ð1535Þ
S11 ð1535Þ ! N 0 þ mesonð; ; Þ:(1)

The cross section for -nucleon interactions shown in
Fig. 1 was calculated by the Breit-Wigner formula asfollows:
¼

N ðtotal  N Þ;2k ðECMS  Mres Þ2 þ 2total =4(2)where ECMS is the center-of-mass energy of -N, Mres is
the mass of the resonance, total is the total width of
Sð1535Þ resonance, N is the partial width of Sð1535Þ !
N, and k is the wave number (p=ℏ). The net nuclear effectof the  meson in an oxygen nucleus is estimated by using
this cross section as well as considering the nuclear density
distribution, nucleon momentum distribution and the Pauli
exclusion principle effect in an nucleus. Since pions can begenerated by the decay of the resonance, nuclear effects for mesons were also considered according to Sec. III A 1.
Approximately 56% of  mesons generated by p ! eþ 
escaped from the nucleus without any scattering, while

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PHYSICAL REVIEW D 85, 112001 (2012)50

MAINZ (1996)

0.25

dσphoto/dp [ µb/MeV]

w/o nuc. effectCross section (mb)

40

30

0.2
w/ nuc. effect

0.15

0.1

0.05

20

0
0

10

10
100

20
200

30
300

40
400

50
500

600

η Momentum (MeV/c)
0

0

200

400

600

800

1000

η Momentum in CMS (MeV/c)

FIG. 1. Calculated cross section of -nucleon interaction considering S11 ð1535Þ resonance in the custom simulation code.

38% of  mesons were absorbed or decayed into otherparticles from the resonance.
The  meson nuclear effects simulation were checked
by a comparison with the experimental cross section of 
photoproduction on a 12 C target measured at MAINZ [29].
Since photons are insensitive to strong interactions andable to probe the inside of nuclei, meson photoproduction
data were used for the study of the nuclear effects. The
peak momentum of the  meson in the photoproduction
experiment is approximately 300 MeV=c, which is equivalent to the  momentum generated by p ! eþ ðor þ Þ .
In order to simulate the  photoproduction on a 12 C target, mesons were generated following the cross section dataof a proton target from the SAID calculation [30], andtracked in nuclei while suffering the -N interaction described above. The cross section on a neutron was assumed
to be 2=3 of that of a proton target, since this assumption
reproduces the experimental cross sections of a deuterontarget [31].
Figure 2 shows a comparison of the experimental 
photoproduction cross section for a 12 C target and the crosssection simulated by our nuclear effects simulation. The
simulation predicted well the reduction of the photoproduction cross section by the nuclear effects. The difference
between the experiment and the simulation was taken as
the uncertainty of the  nuclear effects. The uncertainty of
the cross section of the  nuclear effects was estimated to
be a factor of 2.
3. ! meson nuclear effect
The width of the ! meson resonance is  ¼ 8:49 MeV
and its lifetime is  ¼ ℏ= ¼ 0:77  1022 sec . In the
proton decay of p ! eþ !, the ! meson momentum is140 MeV=c so that the mean free path () of the !

FIG. 2. The differential cross sections of photoproduction ofan  meson on a 12 C target with  energy of 735–765 MeV. The
experimental data at MAINZ [29] are shown as circles. The solidline shows the simulated production cross section, and its shaded
region corresponds to a factor 2 difference in the cross section of nuclear effects. The dashed line shows the production crosssection without nuclear effects.

meson is 4 fm. The decay of !’s was taken into accountin the ! meson tracking in the nucleus because the mean
free path is comparable to the size of the radius of a
nucleus.
The ! meson interactions with a nucleon in an oxygen
nucleus were calculated with a boson exchange model by
Lykasov et al. [32]. The coupling constants and the form
factor of this model were fixed by the experimental data.
The simulation takes into account reactions such as !N !
!N, !N ! N 0 , !N ! N 0 , !N ! N 0 , !N !
N 0 and !N ! N. Approximately 53% of ! mesons
generated in p ! eþ ! decayed in the nucleus. Therefore,
the nuclear effects of secondary pions was also considered.
The CBELSA/TAPS Collaboration measured the ! photoproduction cross section on the various nucleus targets of
C, Ca, Nb, and Pb [33]. They extracted the !N crosssection from the photoproduction cross sections and compared it with the calculated cross section by Lykasov et al.
The cross section obtained by the experiment is approximately 3 times larger at most than the calculated crosssection. We took this difference as an uncertainty in the
cross section of ! meson nuclear effects.
B. Atmospheric neutrino simulation
Atmospheric neutrino interactions are backgrounds fornucleon decay searches in Super-Kamiokande. Charged
current single (multi) pion production can be the dominantbackground source for the search modes. A charged current quasielastic scattering can also contribute the background because a nucleon produced by the neutrino
interaction can produce pions by hadronic interactions inwater. Atmospheric neutrino events were simulated using
the NEUT [34] neutrino interaction MC with an atmospheric
neutrino flux calculated by Honda et al. [35]. Complete

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SEARCH FOR NUCLEON DECAY INTO . . . . I AND IIPHYSICAL REVIEW D 85, 112001 (2012)details of the simulation are described in [36]. Atmospheric
neutrino simulation MC equivalent to a 500-year observation (11:25 megaton  year exposure) were generated toestimate the nucleon decay search background for each
SK-I and SK-II. Pure  to  oscillation with m2 ¼
2:5  103 eV2 and sin2 2 ¼ 1:0 was assumed for theestimation.
IV. DATA SET AND DATA REDUCTION
We used data from a 91:7 kiloton  year exposure of1489.2 live days during SK-I and a 49:2 kiloton  year
exposure of 798.6 live days of during SK-II. The dataacquisition trigger threshold for this analysis corresponds
to a 5.7 MeV electron in SK-I and 8 MeV in SK-II. The
trigger rate was about 11 Hz, resulting in approximately
106 events every day. Most of those are events caused by acosmic ray muon, or a low energy background from theradioactivity of materials around the detector wall, or flashing PMTs. Several stages of data reduction were applied tothese events before proceeding to further detailed event
reconstruction processes that are described in Sec. V. The
details of the data reduction can be found in [36].
For nucleon decay searches, fully contained (FC) events,
which have an activity only in the inner detector, wereselected by requiring a vertex to be inside the 22.5 kiloton
fiducial volume (2 m away from the ID detector wall),visible energy to be greater than 30 MeV and no hit-PMT
clusters in the outer detector. The rate of FC events was
8:18  0:07 (stat.) events per day for SK-I and 8:26  0:10
(stat.) events per day for SK-II. In total, we obtained 12 232
and 6584 FC events in the SK-I and SK-II data, respectively. The background contamination other than atmospheric neutrinos was estimated to be less than 1%.
The same reduction criteria were also applied to the
nucleon decay MC. For nucleon decays via the N ! eþmeson modes, the reduction survival efficiencies were
estimated to be greater than 97%. On the other hand, for
the N ! þ ð or !Þ modes, the survival efficiencies are
relatively lower because the muon can be invisible due tothe large meson mass, and because the meson sometimes
cannot escape from the nucleus or it can be immediately
absorbed by nucleons in water. That results in no detectable event signal in a water Cherenkov detector. The
reduction survival efficiencies for all of the search modes
are shown in Table I.
V. EVENT RECONSTRUCTION
A. Event reconstruction for nucleon decay search
Event reconstruction processes were applied to the fully
contained events which passed the data reduction. The
same reconstruction algorithms were applied both for theobserved data and the MC simulation. Most of the processes are common with atmospheric neutrino analyses in

TABLE I. The survival efficiency by the data reduction criteria
for the nucleon decay MC events in the fiducial volume for SK-I
and SK-II. The fiducial volume cut is not included.
Mode
p ! e þ 0

p ! þ 0
p ! eþ 
p ! þ 
p ! eþ 0
p ! þ 0

SK-I
>99%
>99%
>99%
>99%
98%
81%

SK-II

Mode

SK-I

SK-II

>99%
>99%
>99%
>99%
98%
82%

p ! eþ !

>99%
93%
>99%
>99%
97%
83%

>99%
94%
>99%
>99%
97%
84%

p ! þ !
n ! e þ 
n ! þ 
n ! eþ 
n ! þ Super-Kamiokande. The details of their algorithms aredescribed in [36].
A vertex position was determined by the time-of-flight
subtracted timing distribution. Vertex resolutions for thefree proton decay events of p ! eþ 0 are 18.1 (20.1) cm
in SK-I (SK-II). A particle identification (PID) algorithm
classified found Cherenkov rings into shower-type (e-like)or non shower-type (-like). This classification basically
exploits the ring pattern difference between a fuzzy ringpattern of electromagnetic showers by an electron or a
-ray and a sharper Cherenkov ring edge produced by amuon or a charged pion. The misidentification probabilities for the free proton decay MC samples were estimatedto be 3.3% (3.4%) and 4.8% (5.4%) for p ! eþ 0 and p !
þ 0 respectively, in SK-I (SK-II). Additionally, for nucleon decay searches expecting a low momentum muon
and/or a charged pion, a reconstructed Cherenkov opening
angle was also used to improve the PID efficiency.
The momentum of each ring was estimated by the
charge detected inside each Cherenkov ring cone. In multiring events such as nucleon decay events, Cherenkov
photons radiated from different particles pile up in each
PMT. The detected charge at each PMT was separated into
the contribution from each particle using an expectedcharge distribution which takes into account light scattering in water, reflection on PMT surfaces and the vertex
shift due to the ’s conversion length. The momentum
resolutions for the proton decay MC were estimated by
the monochromatic momentum positron of p ! eþ 0 to
be 4.9% in SK-I and 6.0% in SK-II, as shown in Fig. 3.
Likewise, the muon momentum resolution was found from(p ! þ 0 ) to be 2.8% in SK-I and 4.1% in SK-II. The
momentum of charged pions is more difficult to reconstructusing only the total detected charge because charged pions
suffer from interactions with nucleons in the water. The
momentum resolution for charged pions was improved byusing the Cherenkov opening angle as well as the total
charge. The momentum resolution for charged pions in the
n ! eþ  MC was estimated to be 9.2% (9.7%) in SK-I
(SK-II). Figure 4 shows the charged pion momentum distribution in n ! eþ  , including the smearing of the true
pion momentum due to the Fermi motion of a decaying
nucleon.

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PHYSICAL REVIEW D 85, 112001 (2012)

140

Number of Events

120

100

80

60

40

20

0
300

350

400

450

500

550

600

Positron Momentum (MeV/c)

FIG. 3 (color online). The reconstructed momentum distributions for positrons in the free proton decay of p ! eþ 0 in SK-I
(solid) and SK-II (dashed). The momentum resolution for the
positron, as shown by the width of the distribution, is 4.9% in
SK-I and 6.0% in SK-II.

decay events from atmospheric neutrino events using their
total invariant mass and momentum.
The absolute momentum scale was checked by theMichel electron momentum spectrum from stoppingmuons, the invariant mass of 0 s, and the Cherenkov
opening angles and track lengths of stopping muons. The
calibrated momentum ranges from a few tens of MeV=c toabout 10 GeV=c. The uncertainty of the absolute momentum scale was estimated to be less than 0.74% (1.60%) for
SK-I (SK-II). The time variation of the momentum scale
was monitored by stopping muon and Michel electron
events and estimated to be 0.83% (0.53%) in RMS for
SK-I (SK-II).
The detector nonuniformity of the energy scale is also
important for the systematic error of the total momentum
reconstruction. It was checked by the Michel electron
momentum to be uniform within 0:6% for both SK-I
and SK-II.
VI. NUCLEON DECAY ANALYSIS
A. Event selection
1. Summary of selection criteria

B. Calibration
The characterization of the Super-Kamiokande detector
has been performed in a variety of calibrations, which aredescribed in detail in [21,36]. One of the most importantcalibrations for nucleon decay searches is the determination of the energy scale because we distinguish nucleon

220
200

Number of Events

180
160
140
120
100
80
60
40

The data used in this nucleon decay search are the FCdata from the SK-I and SK-II periods. We have to extract
only nucleon decay signals from the FC data which are
dominated by atmospheric neutrino events. Using the nucleon decay simulation and the atmospheric neutrino simulation, optimal criteria were determined. The atmospheric
neutrino MC was normalized with the observed data using
the number of single-ring e-like events, which are assumed
to have a negligible neutrino oscillation effect. In order tostudy many nucleon decay modes systematically, event
selection criteria were chosen to be as simple and common
as possible. The primary for determining the criteria was toobtain a low enough background level.
The following reconstructed information was used in theevent selection criteria:(1) the number of Cherenkov rings,(2) the particle type of each ring,(3) the meson invariant mass (if it is possible to bereconstructed),(4) the number of Michel electrons,(5) the total invariant mass and the total momentum (ifit is possible to be reconstructed).

20
0

0

100 200

300

400

500 600

700

800 900 1000

charged pion momentum (MeV/c)

FIG. 4 (color online). The charged pion momentum distribution for the n ! eþ  MC in SK-I. The solid line and thedashed line show the reconstructed and true pion momentum
distributions, respectively. The charged pion momentum canbe well reconstructed with a resolution of 9.2% (9.7%) in SK-I
(SK-II).

The detailed numbers of event selection criteria for all thesearches are summarized in Table II.
All of the nucleon decay modes in this study are
expected to have multiple Cherenkov rings. The criterion
and efficiency of the number of rings cut for each modeare shown in Table III. More than half of the atmospheric
neutrino MC events are single-ring events, as shown in
Fig. 5, and they were rejected by the cut on number ofrings.

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TABLE II. Summary of the selection criteria. The numbers in parentheses correspond to the numbers of selection criteria describedin Sec. VI A 1. For example, for the p ! þ  (30 ) mode, this table means that the selection criteria requires that (1) the number of
Cherenkov rings is 4 or 5, (2) one ring is non shower-type and all other rings are shower-type, (3) reconstructed  meson invariant
mass is in between 400 and 700 MeV=c2 , (4) the number of Michel electron is 1, and (5) reconstructed total invariant mass is in
between 800 and 1050 MeV=c2 and reconstructed total momentum is less than 250 MeV=c. S and N in the PID column stand forshower-type rings and non shower-type rings, respectively. Asterisks in PID indicate that a PID using both Cherenkov ring pattern andopening angle was used for identifying low momentum muons (p < 300 MeV=c) or charged pions. All the invariant mass andmomenta are written in units of MeV=c2 and MeV=c, respectively. For the p ! eþ ! (3) mode, a positron momentum cut is applied(100 < Peþ < 200). For the n ! lþ  mode, a 0 invariant mass cut is also applied.
Modes

(1)
Ring

(2)
PID

(3)
Mmeson(4)
decay-e

Mtot

Ptot

p ! eþ 0
p ! þ 0
p ! eþ  (2)
p ! þ  (2)
p ! eþ  (30 )p ! þ  (30 )p ! eþ 0
p ! þ 0
p ! eþ ! (0 )
p ! þ ! (0 )
p ! eþ ! (þ  0 )p ! þ ! (þ  0 )n ! e þ 
n !  þ 
n ! eþ  
n ! þ 

2, 3
2, 3
3
3
4, 5
4, 5
3
3
3, 4
2, 3
4
3
2
2
4
3

SS(S)
NS(S)
SSS
NSS*
SSSS(S)
NSSS(S)*
SNN*NNN*
SSS(S)
SS(S)
SSSN*
SSN*
SN
NN
SSSN*
SSN*

85–185 (0 )85–185 (0 )480–620 ()480–620 ()
400–700 ()
400–700 ()600–900 (0 )
600–900 (0 )650–900 (!)
650–900 (!)
85–185 (0 )85–185 (0 )
600–900 ( )600–900 ( )

0
1
0
1
0
1
0, 1
1, 2
0
1
0, 1
2
0
1
0
1

800–1050
800–1050
800–1050
800–1050
800–1050
800–1050
800–1050
800–1050
800–1050
600–800
450–700
800–1050
800–1050
800–1050
-

<250
<250
<250
<250
<150
<250
<150
<250
<150
<200
<200
<200
<250
<250
<250
<150

For the particle identification, two types of algorithm
were used in this analysis, as described in Sec. VA. The
PID using both a Cherenkov ring pattern and an opening
angle was used for the modes in which we search for
low momentum muons (p < 300 MeV=c) or charged
pions.
The number of Michel electrons was required to beconsistent with a nucleon decay signal. With this requirement, the background events can be effectively reduced,
while the loss of the signal detection efficiency is negligible for the modes in which no Michel electrons are
expected.
The total momentum Ptot , the total energy Etot , and thetotal invariant mass Mtot are defined as


all


X






~
Ptot ¼ 
p
(3)

i

;


i
Etot ¼

all qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Xjp~ i j2 þ m2i ;(4)i

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Mtot ¼ E2tot  P2tot ;(5)

where p~ i is the momentum of each Cherenkov ring, and miis the mass of a particle (, e ,  ,  ). The meson massis reconstructed in a similar way by summing up the

(5)
Note

Peþ

M0
M0

momenta and energies of secondary particles from themeson decay. Although our particle identification algorithm can only classify a Cherenkov ring into a showertype ring (e or ) or a non shower-type ring ( or  ),the invariant mass reconstruction in some modes requires
the ability to distinguish e from  or  from  . For
example, for the 0 invariant mass reconstruction in the
p ! eþ 0 mode search, we should identify each
Cherenkov ring as originating from a positron or a -ray.
However, that cannot be done in a large water Cherenkov
detector. In these cases, the invariant mass was calculated
for all possible combinations of particle type assignment.
Then, the best combination in which the reconstructedmass is the closest to the expected nucleon (or meson)
mass, is selected. All of the studied nucleon decay modes
are two-body decays with back-to-back kinematics, andhave isotropic event signatures, which is the most significant difference from typical atmospheric neutrino events.
Therefore, the event selection by total momentum and total
invariant mass is a powerful tool to eliminate the atmospheric neutrino background as can be found in Fig. 6. The
total momentum cut threshold is set to be 250 MeV=c formost searches considering the Fermi motion of boundnucleons. To keep the background rates low enough (below
0.5 events in the total exposure), a tighter total momentum
cut with a threshold of 150ðor 200Þ MeV=c is applied insome relatively high-background mode searches.

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TABLE III. Efficiency of cut on number of rings for nucleon
decay MC for SK-I and SK-II. Numbers in parentheses are
efficiencies for free proton decay events. These efficiencies
include the efficiency for the FC data reduction and the fiducial
volume cut.
Mode

Nring

p ! eþ 0
p ! þ 0
p ! eþ  (2)
p ! þ  (2)
p ! eþ  (30 )p ! þ  (30 )p ! eþ 0
p ! þ 0
p ! eþ ! (0 )
p ! þ ! (0 )
p ! eþ ! (3)
p ! þ ! (3)n ! e þ 
n !  þ 
n ! eþ  
n ! þ 

2 or 32 or 33
3
4 or 5
4 or 53
3
3 or 42 or 34322
43Efficiency %
SK-I
SK-II
73
74
44
44
19
22
26
12
58
61
19
27
49
49
9
17

(98)
(98)
(92)
(91)
(76)
(82)
(50)
(26)
(93)
(97)
(27)
(41)

(98)
(98)
(89)
(89)
(76)
(81)
(47)
(25)
(89)
(96)
(26)
(39)

74
74
45
44
21
21
26
11
59
61
19
26
49
49
9
17

2. p ! lþ 0 mode search
In the proton decay of p ! eþ 0 (p ! þ 0 ), a neutral pion and a positron (muon) are back-to-back and havethe same momentum of 459ð453Þ MeV=c in the proton rest
frame. The neutral pion immediately decays into two
-rays. Figure 7 shows the event signature of a typical
proton decay MC event for p ! eþ 0 . One shower-typering from the positron and two shower-type rings from the0 are clearly seen in this figure.
The two -rays from the 0 decay are back-to-back inthe 0 rest frame. They are Lorentz-boosted by the 0
104

SK-I atm ν MC

Number of Events

SK-II atm ν MC
SK-I data
SK-II data

103

102
1

2

3

4

5

Number of Rings

FIG. 5 (color online). Number of rings distribution for atmospheric neutrino MC and data. The number of MC events arenormalized to the observed data by the number of single-ringe-like events (also in other figures unless otherwise noted).

momentum of 450 MeV=c, so the momentum of one of
the two -rays in the laboratory frame can be very low
depending on the direction of the Lorentz boost. In such acase, it sometimes happens that only one ring from 0decay is identified. For free proton decays of p ! eþ 0 ,the fraction of two-ring and three-ring events identified
was 39% and 60%, respectively.
If all three rings were found, the 0 invariant mass,
which is reconstructed by two of the three rings, wasrequired to be between 85 and 185 MeV=c. The reconstructed 0 invariant mass distribution for the proton
decay MC is shown in Fig. 8. For free proton decay eventsof p ! eþ 0 , the mean of the reconstructed 0 invariant
mass is 137 MeV=c2 , and its resolution is 20 MeV=c2 .
The final criterion of total invariant mass and momentum selects the events which are consistent with the momentum and mass of a parent proton. Figure 9 shows the
distribution of the total invariant mass. For free proton
decay events, the total invariant mass was well reconstructed. The resolution of the total invariant mass
distribution is 28:2ð36:2Þ MeV=c2 in SK-I (SK-II). The
resolution of the total momentum is 29:8ð32:5Þ MeV=c.
The total momentum and invariant mass cut was wide
enough for free proton decay events. The total momentum
and total invariant mass distributions of the proton decay
MC and the atmospheric neutrino MC are clearly different
from each other, as shown in Fig. 10. This criterion reduces
the atmospheric neutrino background by more than 3orders of magnitude, as shown in Fig. 6.
The detection efficiency for p ! eþ 0 was estimated to
be 44.6 (43.5)% in SK-I (SK-II). The inefficiency is mainly
due to nuclear interaction effects of pions in 16 O. For free
proton decay events, high efficiencies of 87% (86%) wereachieved for p ! eþ 0 . As for the p ! þ 0 mode
search, differences in the selection criteria from the p !
eþ 0 mode are the requirement of one non shower-typering and one Michel electron. The detection efficiency for aMichel electron from the decay of  was approximately
80%. This is the reason for the detection efficiency difference between p ! eþ 0 and p ! þ 0 . The detection
efficiency for the p ! þ 0 mode was estimated to be
35.5% (34.7%) in SK-I (SK-II).
The background events for p ! eþ 0 and p ! þ 0were estimated to be 0.31 and 0.34 events in total for SK-I
and SK-II, respectively. The background rates for p !
eþ 0 in SK-I and SK-II are 2.1 and 2:2 events=ðmegaton yearsÞ, respectively. Therefore, low-background observations with high efficiency were achieved for these modes in
the Super-Kamiokande detector, both in the SK-I and
SK-II periods. The background for p ! eþ 0 was also
estimated from the experimental data of the K2K beamand 1-kiloton water Cherenkov detector [37]. The numberof expected background events estimated from the K2K
þ0:06
data is 0:23þ0:06
0:05 ðstatÞ0:07 ðsysÞ events for the exposure of
SK-I plus SK-II, which is consistent with the estimate from112001-8

SEARCH FOR NUCLEON DECAY INTO . . . . I AND IIPHYSICAL REVIEW D 85, 112001 (2012)

FIG. 6 (color online). Number of events and detection efficiency at each event selection step: (FV) fiducial volume, (1) number of
Cherenkov rings, (2) PID, (3) meson invariant mass, (4) number of Michel electrons and (5) total invariant mass and total momentum.
The plot shows three nucleon decay mode searches: the mode with highest efficiency (p ! eþ 0 ), the mode with the greatest numberof rings (p ! eþ  ( ! 30 )) and the mode using PID with both Cherenkov ring pattern and opening angle (p ! þ 0 ). The
number of observed events and the estimated background rates agree with each other. Also, the searches in SK-I and SK-II arecompared.

our MC. The background estimate was also compared witha different neutrino interaction MC, NUANCE [38]. The
number of background events estimated by NUANCE was
0:27  0:10 events (in SK-I þ SK-II), which is also
consistent with our primary estimate. These results are
summarized in Table IV with the results of all the otherstudied modes.

However, the momentum of the two -rays in the  meson
rest frame is 274 MeV=c, which is much larger than that in
p ! eþ 0 and p ! þ 0 . The opening angle between
the two -rays from the  meson decay is about 132 degrees in the laboratory frame. Therefore, three Cherenkov

3. p ! lþ  mode search
The  meson has three dominant decay modes; wesearch for two of the three modes:  ! 2 (Br ¼ 39%)and  ! 30 (Br ¼ 33%).
The mass of  meson is 548 MeV=c2 . Because its massis larger than the 0 mass, the generated charged leptonand  meson have smaller momentum, 300 MeV=c in
the proton rest frame, compared with the momentumof generated particles in the p ! lþ 0 modes. For thep ! þ  mode, PID with Cherenkov ring pattern andopening angle was used to improve the PID for a low
momentum  ring. This is common for both meson decay
modes of p ! þ .
Figure 11 shows the total momentum and total invariant
mass distributions of the p ! lþ  modes. Compared withthe p ! lþ 0 modes many fewer events in both the atmospheric neutrino MC and observed data survive theselection criteria except for the total momentum and invariant mass cut. That is because a significant number ofatmospheric neutrino events with 0 production can survive the selection criteria (except for the total momentum
and invariant mass cut) for the p ! lþ 0 modes while thenumber of atmospheric neutrino events with  production
are negligible.
a. p ! lþ ð ! 2Þ mode These modes have very
similar event signatures with p ! eþ 0 and p ! þ 0 .

FIG. 7 (color online). A typical proton decay MC event of
p ! eþ 0 in SK-I. One Cherenkov ring from a positron and two
Cherenkov rings from the two -rays from 0 decay can beobserved on the right and the left of the figure, respectively. The
size of circles indicate the amount of detected charge. The
crosses on the plot show a reconstructed vertex position horizontally and vertically projected on the detector wall. Solid lines
show the reconstructed rings. The reconstruction algorithms
correctly find all rings and identify their particle for this event.

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FIG. 8 (color online). The invariant mass of 0 distributionsfor SK-I proton decay MC (p ! eþ 0 ), atmospheric neutrinoMC, and SK-I data. The shaded histogram is the distribution offree proton decay events. The bars and arrows indicate the 0
invariant mass cut threshold.

rings are clearly visible and can easily be separated so thatthe number of Cherenkov rings is required to be three. The
fraction of three-ring events in the free proton decay eventis greater than 90%.
Because only the three-ring events survive the numberof rings cut, an  invariant mass cut was applied to all of

FIG. 9 (color online). The total invariant mass distributions for
proton decay MC (p ! eþ 0 ), atmospheric neutrino MC, andobserved data in SK-I. The shaded histogram is the distributionof free proton decay events. The bars and arrows indicate thetotal invariant mass cut threshold. Only events which satisfy allother selection criteria except this are plotted. The distribution of
atmospheric neutrino MC has the 0 invariant mass peak, whichis consistent with the observed data.

the surviving events. Figure 12 (left panels) shows thereconstructed invariant mass of the  meson for the proton
decay MC in the p ! eþ  mode. The  invariant mass
was well reconstructed.
b. p ! lþ ð ! 30 Þ mode In these proton decay
modes, the  meson decays into three 0 s, and the three0 s immediately decay into six -rays. Therefore, one ringfrom a charged lepton and six rings from the -rays can beobserved in principle. However, our Cherenkov ring counting algorithm is only capable of finding up to five rings.
Consequently, the criterion of the number of rings wasapplied to select events with four or five rings. In SK-I
free proton decay events of the  ! 30 mode of p !
eþ  (p ! þ ), 77% (84%) of the events satisfy thecriterion.
The invariant mass of the  meson was reconstructedusing only three or four shower-type rings, though there
should be 6 rings from the 30 s. This resulted in a worse
invariant mass resolution for the  meson. Therefore, theevent selection window of the  invariant mass was larger
than that in the search via the  ! 2 mode as shown in
Table II.
As shown in Fig. 11, the background rates for p ! eþ (3) were not low enough if the standard event selection
criteria of Ptot < 250 MeV=c was applied. In order to further reduce the background, the tighter total momentum cutof Ptot < 150 MeV=c was applied for the p ! eþ  mode.
4. p ! lþ ! mode searchTwo of the ! meson decay modes were searched for inthis study. One is the ! ! þ  0 mode (Br ¼ 89%),
and the other is the ! ! 0  mode (Br ¼ 9%). The
momentum of a generated charged lepton and an ! mesonis 143ð105Þ MeV=c2 in p ! eþ ! (p ! þ !). For thep ! þ ! mode, the muon momentum is lower than the
Cherenkov threshold, and the muon ring cannot be observed. Therefore, the existence of the muon is indicatedonly by detection of the Michel electron from the muon
decay. The ! meson suffers from nuclear effects in the caseof a decay in an 16 O nucleus. Only 20% of the ! mesons
could escape from the nucleus. This causes the inefficiency
for these two search modes.
a. p ! lþ !ð! ! 0 Þ mode In the ! ! 0  decay
mode, the 0 decays into two -rays, and three showertype rings can be observed from the decays of the ! meson.
The 0 momentum from the ! decay is approximately
380 MeV=c in the ! meson rest frame. For same reason as
in p ! eþ 0 or p ! þ 0 , one of the two rings from the0 decay has a certain probability of not being identified.
Therefore, two or three shower-type rings were required
from the ! meson decay, and one more shower-type rings
from eþ was required only in the case of the p ! eþ !
mode. The fraction of events with 3 or 4 rings (2 or 3 rings)
was 95% (97%) for the SK-I free proton decay of the ! !
0  mode for p ! eþ ! (p ! þ !).

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SEARCH FOR NUCLEON DECAY INTO . . . . I AND IIPHYSICAL REVIEW D 85, 112001 (2012)

FIG. 10 (color online). Total momentum versus total invariant mass distributions, from left to right: SK-I p ! eþ 0 ; SK-II p !
eþ 0 ; SK-I p ! þ 0 ; and SK-II p ! þ 0 , from top to bottom: the proton decay MC; the atmospheric neutrino MC(11:25 megaton  years for each SK-I and SK-II); and the observed data (91:7 kiloton  years in SK-I and 49:2 kiloton  years in
SK-II). These events satisfy the event selection criteria except for the selection by the total momentum and total mass. The boxes infigures indicate the total momentum and mass criteria. The points in the boxes of the atmospheric neutrino MC are shown in a larger
size to show the distributions in the signal box. No candidates were found for either p ! eþ 0 or p ! þ 0 in the data.

The ! invariant mass was reconstructed using all detected rings for the p ! þ ! mode. For the p ! eþ !
mode, the invariant mass was reconstructed by all but oneof the detected rings, which was assumed to be eþ ring.
The ! invariant mass distribution for the proton decay MC
is shown in the right panels of Fig. 12. The lower invariant
mass peak in the proton decay MC was due to the another! meson decay mode of ! ! þ  0 .

Since the muon is invisible for the p ! þ ! mode, thetotal momentum corresponds not to the proton momentum,
but to the ! meson momentum. Thus, the reconstructed
momentum for the free proton decay in SK-I peaked around
100 MeV=c, which can be seen in Fig. 13. In order toeliminate the background sufficiently, tighter total momentum cuts were applied for both modes: Ptot < 150 MeV=c
for p ! eþ ! and Ptot < 200 MeV=c for p ! þ !. The

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TABLE IV. Summary of the nucleon decay searches. Numbers in parentheses in backgrounds are exposure-normalized backgroundrates in ðmegaton  yearsÞ1 . Background errors shown here are statistical errors of finite MC statistics.
Eff. (%)

Background

Candidate

NEUT

NUANCE

Modes

SK-I

SK-II

SK-I

SK-II

SK-I þ II

SK-I

SK-II

p ! eþ 0

44.6
35.5

43.5
34.7

0:20  0:04 (2.1)
0:23  0:04 (2.5)

0:11  0:02 (2.2)
0:11  0:02 (2.2)

0:27  0:10
0:27  0:09

0
0

0
0

18.8
8.1

18.2
7.6

0:19  0:04 (2.1)
0:08  0:03 (0.9)

0:09  0:02 (1.8)
0:08  0:02 (1.7)

0:29  0:10
0:32  0:11

0
0

0
0

12.4
6.1
4.9
1.8

11.7
5.4
4.2
1.5

0:03  0:02 (0.3)
0:30  0:05 (3.3)
0:23  0:05 (2.5)
0:30  0:05 (3.3)

0:01  0:01 (0.2)
0:15  0:03 (2.9)
0:12  0:02 (2.4)
0:12  0:02 (2.5)

0:04  0:04
0:44  0:13
0:34  0:11
0:46  0:12

0
0
0
1

0
2
0
0

2.4
2.5

2.2
2.3

0:10  0:03 (1.1)
0:26  0:05 (2.9)

0:04  0:01 (0.9)
0:13  0:02 (2.6)

0:29  0:10
0:30  0:11

0
1

0
0

2.8
2.7
19.4
16.7
1.8
1.1

2.8
2.4
19.3
15.6
1.6
0.94

0:24  0:05 (2.6)
0:10  0:03 (1.1)
0:16  0:04 (1.7)
0:30  0:05 (3.3)
0:25  0:05 (2.7)
0:19  0:04 (2.1)

0:07  0:02 (1.4)
0:07  0:02 (1.3)
0:11  0:02 (2.2)
0:13  0:02 (2.6)
0:13  0:02 (2.7)
0:10  0:02 (1.9)

0:37  0:11
0:05  0:04
0:37  0:12
0:44  0:12
0:44  0:12
0:69  0:14

0
0
0
1
1
0

0
0
0
0
0
0

p ! þ 0
p ! eþ ( ! 2)( ! 30 )p ! þ ( ! 2)( ! 30 )p ! eþ 0
p ! þ 0
p ! eþ !
(! ! 0 )(! ! 3)p ! þ !
(! ! 0 )(! ! 3)n ! e þ 
n !  þ 
n ! eþ  
n ! þ 

Lifetime Limit( 1033 years) at 90% CL
8.2
6.6
4.2

1.3

0.71
0.16
0.32

0.78

sharp cutoffs in the total invariant mass distributions for p !
þ ! (0 ) in Fig. 13 correspond to the ! invariant masscut. There is no total invariant mass cut applied to this mode.
b. p ! lþ !ð! ! þ  0 Þ mode In this ! decay
mode, the ! decays into two low momentum charged pions
and a neutral pion. Their momenta are about 220 MeV=c.
In order to find the low momentum non shower-type ring,
PID with both a Cherenkov ring pattern and an opening
angle was used for these modes. Because of the strong
interaction of charged pions in water, finding both of thecharged pion rings is difficult. Therefore, we required
finding only one of the two charged pion rings. For the p !
eþ ! (p ! þ !) mode, 4 (3) rings were required to befound in total. The efficiency of the number of rings cut
was 27% (42%) for SK-I free proton decay MC of the p !
eþ ! (p ! þ !), ! ! þ  0 mode.
Since one of the two charged pions was assumed to beinvisible in the selection criteria, the invariant mass of the! and the proton cannot be reconstructed. Instead of the !
mass reconstruction, the reconstructed 0 invariant mass
was required to be consistent with 0 mass. As for the total
invariant mass, the event selection criteria for the total
mass were set to be lower than the normal event selection
criteria, as shown in Fig. 13 and Table II. The selection
windows were determined to reduce the atmospheric neutrino MC, though they were not wide enough to also allow
in the free proton decay events.
For the p ! þ ! mode, both Michel electrons from thedecay of þ and þ were required to be found. Although

2.0
1.0
0.070
0.036

the detection efficiency is decreased by a factor of 2, thiscut reduced the background by an order of magnitude.
In order to reduce the background further, the reconstructed positron momentum was also required to be consistent with the positron momentum for the p ! eþ !
mode. This criterion reduced the background by a factorof 2, while the detection efficiency was decreased by about
20%.
5. p ! lþ 0 mode search
In the proton decay of p ! eþ 0 and p ! þ 0 , themomentum of the charged lepton and  meson, which
depends on the  meson mass with a width of  ¼
149 MeV, is about 170 MeV=c. For p ! þ 0 , themuon momentum can be lower than the Cherenkov threshold. The  meson decays into þ  with a branching ratioof 100%. The two pions suffer from strong interactions
with nucleons in water, and also in the nucleus in the caseof a proton decay in an 16 O nucleus. Accordingly, a probability for finding all three Cherenkov rings from thecharged lepton and the two charged pions is intrinsicallyvery low. However, in order to reduce the background in
the selection by total invariant mass and total momentum,
all three rings were required to be found in order toreconstruct the mass and the momentum of the proton.
The fraction of three-ring events was 50% and 27% for
the free proton decay of p ! eþ 0 and p ! þ 0 , respectively. The lower efficiency for p ! þ 0 was due toproton decay events with an invisible muon.

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FIG. 11 (color online). Total momentum versus total invariant mass distributions of proton decay MC (SK-I þ II combined), theatmospheric neutrino MC (SK-I þ II combined; 11:25 megaton  years for each SK-I and SK-II) and SK-I (91:7 kiloton  years) and
SK-II (49:2 kiloton  years) data, from top to bottom: p ! eþ  (2), p ! þ  (2), p ! eþ  (30 ) and p ! þ  (30 ). The
boxes in figures indicate the total momentum and mass criteria. These events satisfy the event selection criteria for each mode except
for the selection on the total momentum and total mass. Two candidates for p ! þ  (30 ) were found in the SK-II data.

The charged pions from the decay of the  meson have a
low momentum of about 300 MeV=c. Therefore, PID withboth Cherenkov ring pattern and opening angle was used
for both p ! eþ 0 and p ! þ 0 .
The invariant mass of the  meson was reconstructedby two non shower-type rings and required to be between

600 and 900 MeV=c2 , as shown in the center panels of
Fig. 12. Most of the events shown in  meson distributions
were from free proton decay events. This means thatthe events from proton decays in an 16 O nucleus rarely
survived the selection criteria on the number of rings andthe PID.

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FIG. 12 (color online). The meson invariant mass distributions for the proton decay MC (solid lines), the atmospheric neutrino MC(dashed lines) and the observed data (points) in SK-I (top) and SK-II (bottom), from left to right; p ! eþ  mode (2), p ! eþ 0 modeand p ! eþ ! mode (0 ). Free proton decay events are indicated by shaded histograms. All decay branches of the mesons are filled in
the histograms for the proton decay MCs. The other peaks outside of the selection window are events from the other decay branches.

For these mode searches, one extra Michel electron is
expected from the þ decay, in addition to the one Michelelectron from the  decay. The number of Michel electrons
were required to be consistent with this expectation.
The total momentum and total invariant mass distributions for the p ! lþ 0 modes are shown in Fig. 14. The
p ! eþ 0 mode had a relatively higher background rate
than that of p ! þ 0 mode. In order to reduce thebackground, a tighter total momentum cut of Ptot <150 MeV=c was applied for the p ! eþ 0 mode.
6. n ! lþ  mode search
All of the neutrons in an H2 O molecule are bound in a
nucleus. Because of this, all generated charged pions inneutron decay modes suffer from nuclear effects, and detection efficiencies for neutron decay searches tend to be lower
compared with their corresponding proton decay searches.
In the neutron decay of n ! lþ  , the  meson decays
into  0 . The 0 decays into two -rays. Accordingly,
two shower-type rings and one non shower-type ring wererequired from the  meson decay. One more shower-typering from the positron was required for the n ! eþ 
mode search, while one more non shower-type ring fromthe muon was not required for the n ! þ  mode
search. In order to find the low momentum non showertype ring, the PID with both a Cherenkov ring pattern andan opening angle was used for these modes. The fractionof 4-ring (3-ring) events was 9% (23%) for n ! eþ (n ! þ  ).
The invariant mass of the  meson was reconstructedusing two shower-type rings and one non shower-type ringand required to be between 600 and 900 MeV=c2 . In
addition to the  meson mass, a 0 invariant mass cut
was also applied. This additional cut reduced the atmospheric neutrino background by a factor of 2, while the lossof detection efficiency was about 10%.
The total momentum and total invariant mass distributions for the n ! lþ  modes are shown in Fig. 14. The
tighter total momentum cut of Ptot < 150 MeV=c wasapplied to reduce the background for the n ! þ 
mode because the nucleon invariant mass cannot be reconstructed for this mode due to the invisible muon.
7. n ! lþ  mode search
The momentum of the charged lepton and charged pionin this mode is about 460 MeV=c, almost the same as that

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FIG. 13 (color online). Total momentum versus total invariant mass distributions of proton decay MC (SK-I þ II combined), the atmospheric
neutrino MC (SK-I þ II combined; 11:25 megaton  years for each SK-I and SK-II) and SK-I (91:7 kiloton  years) and SK-II (49:2 kiloton years) data, from top to bottom: p ! eþ ! (0 ), p ! þ !(0 ), p ! eþ ! (3) and p ! þ ! (3). These events satisfy the event
selection criteria for each mode except for the selections on the total momentum and total mass. The boxes in the figures indicate the total
momentum and mass criteria. For the p ! þ ! (0 ) mode, the total invariant mass is equivalent to the meson invariant mass because a muonis invisible. The sharp cutoffs in the total invariant mass distribution correspond to the ! invariant mass cut. For the p ! þ ! (3) mode, there
are no such sharp cutoffs because the ! invariant mass cut is not applied to this mode. A candidate for p ! eþ ! (3) was found in the SK-I data.

of p ! lþ 0 . In these modes, a Cherenkov ring from thecharged pion generated from the nucleon decay can beobserved. Approximately 50% of the neutron decay events
in SK-I were 2-ring events from the charged lepton and thecharged pion. There was no event selection on the meson
invariant mass for these modes.
For the total invariant mass reconstruction in the n !
þ  mode, it is necessary to determine which ring was

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FIG. 14 (color online). Total momentum versus total invariant mass distributions of proton decay MC (SK-I þ II combined), theatmospheric neutrino MC (SK-I þ II combined; 11:25 megaton  years for each SK-I and SK-II) and SK-I (91:7 kiloton  years) and
SK-II (49:2 kiloton  years) data, from top to bottom: p ! eþ 0 , p ! þ 0 , n ! eþ  and n ! þ  . These events satisfy theevent selection criteria for each mode except for the selection on total momentum and total mass. The boxes in figures indicate the total
momentum and mass criteria. For the n ! þ  mode, no total invariant mass cut is applied and the sharp cutoffs on the total invariant
mass correspond to the  invariant mass cut threshold. A candidate for each p ! þ 0 and n ! eþ  was found in the SK-I data.

made by the muon or the charged pion. As described
before, the ring combination which falls closest to theneutron mass was selected. This resulted in a narrower
invariant mass distribution for n ! þ  than that for
the n ! eþ  MC, as shown in Fig. 15.

B. Search results in the SK-I and SK-II data
The result of the nucleon decay searches are summarizedin Table IV. The detection efficiencies, expected backgrounds and number of candidate events are shown in thetable. The number of events and detection efficiencies

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FIG. 15 (color online). Total momentum versus total invariant mass distributions of proton decay MC (SK-I þ II combined), theatmospheric neutrino MC (SK-I þ II combined; 11:25 megaton  years for each SK-I and SK-II) and SK-I (91:7 kiloton  years) and
SK-II (49:2 kiloton  years) data, for n ! eþ  (top) and n ! þ  (bottom). These events satisfy the event selection criteria foreach mode except for the selection on the total momentum and total mass. The boxes in the figures indicate the total momentum andmass criteria. A candidate for n ! þ  was found in the SK-I data.

at each event selection step are shown in Fig. 6 for thethree typical nucleon decay mode searches. Figure 6 shows
the consistency between the observed data and the atmospheric neutrino background in terms of the number of
events.
Because of the difficulty in detecting charged pions in alarge water Cherenkov detector, the efficiencies for modes
with charged pions are relatively lower. For the modes with
only Cherenkov rings from a charged lepton (e or ) and, high efficiencies were achieved. The highest efficiency
mode is p ! eþ 0 . Its efficiency is 87% for free proton
decay events. Also, the efficiencies for the SK-I free proton
decay events in p ! eþ  (2), p ! eþ  (30 ) andp ! eþ ! (0 ) are 74%, 67% and 83%, respectively.
Nevertheless, the total efficiencies for these modes aremuch lower than p ! eþ 0 due to the lower branchingratios for the meson decay modes.
The detection efficiencies in SK-II are lower than in
SK-I. However, the difference is a only few percent forthe modes with high detection efficiencies (p ! eþ 0 ,p ! eþ , etc.) and less than about 17% even for themodes with low efficiencies as shown in Table IV.
Therefore, nucleon decay searches using SK-II data are comparable to those using SK-I data. The estimated backgroundrates of SK-I and SK-II are also comparable to each other.
Charged current pion production from neutrino interactions was the dominant background source for most of thestudied nucleon decay modes. The breakdown of background events is shown in Table V. Pions producedby neutrino interactions and/or hadronic interactions in
nuclei and/or in water can mimic the event signatures ofnucleon decay signals with a charged lepton. There wasalso a considerable contribution for the p ! lþ 0 mode
background from charged current quasielastic scattering(CCQE). A typical background event from CCQE is shownin Fig. 16. This is because a highly energetic proton(> 1 GeV=c) produced by the interaction and scatteredin water produces a secondary pion. Backgrounds of highring multiplicity modes (four-ring or five-ring events) suchas p ! lþ ð3Þ or p ! lþ !ð3Þ have relatively higher
fractions of multipion production events and has less dependency on whether the interaction is charged current or
neutral current.
The consistency of the neutrino interactions and thenuclear effects was checked by comparing backgroundestimations between our MC and NUANCE [38]. NUANCE
has different models of neutrino interactions and nuclear
effects. The atmospheric neutrino MC generated with
NUANCE used the same atmospheric neutrino flux equivalent to 100 years (2:25 megaton  years exposure) and thesame detector simulation. The results of these two estimates are also shown in Table IV. Estimates obtained with
NUANCE MC were consistent with results from our MC in
most of the modes.

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TABLE V. The breakdown of the neutrino interaction modesof the background events. The breakdowns are calculated bysimply adding background events of the modes decaying into
each meson except for that of p ! eþ 0 .
Mode
CCQE
CC 1-
CC multi-
CC othersNC

p ! eþ 0 N ! lþ  p ! lþ  p ! lþ ! N ! lþ 
28%
32%
19%
2%
19%

21%
51%
14%
6%
9%

5%
20%
24%
13%
37%

4%
25%
29%
7%
35%

9%
45%
14%
4%
28%

In total, six candidate events were found in the SK-I and
SK-II data in the modes; p ! þ  (30 ), p ! þ 0 ,p ! eþ ! (3), n ! þ  and n ! eþ  . As can beseen from Figs. 11 and 13–15, every candidate event wasaround the threshold of the selection window of total momentum and total invariant mass cut. A candidate event for
p ! eþ ! (3) (Fig. 17) has a vertex around the center ofthe detector and the smallest total momentum of all candidates, although there might be a PID misidentification forthis event, which is described in the caption of the figure.
These candidates were found in the five modes. For thep ! þ  (30 ) mode, there were two candidate events.
The probability of observing more than two events from theexpected background was calculated without systematic errors to be 7.5%. For the other modes with a candidate event,probabilities to observe one candidate from the expectations

FIG. 17 (color online). A candidate event for p ! eþ ! (3)in the SK-I data. Reconstructed total momentum and invariant
mass were 137 MeV=c and 796 MeV=c2 , respectively. Solid(dashed) lines correspond to reconstructed rings classified asshower (non shower) type. A Cherenkov ring at the centerbottom of the display was classified as a shower-type ring in
the PID algorithm, but its Cherenkov ring edge looks as sharp asa non shower-type ring.

are about 30% for each. Because the probabilities for observing one (two) or more background events in our sample
are not so small for the 16 decay modes, we cannot take thecandidates as serious evidence of nucleon decay. Moreover,the number of background events in total was 4.7 events.
Consequently, the number of candidates is consistent withthe estimation by the atmospheric neutrino MC. Therefore,
nucleon partial lifetime limits were calculated in Sec. VI D.
C. Systematic errors
Systematic errors for detection efficiencies and background estimations are described in this section. As for the
exposure, the systematic errors of detector size and livetime are less than 1% and negligible.
1. Systematic errors of detection efficiency

FIG. 16 (color online). An example of a background event forthe p ! eþ 0 mode in the atmospheric neutrino MC. An
electron neutrino interacts with a neutron by CCQE and produces an electron and a proton. One ring from the electron andthe other two rings from the decay of a 0 , which is produced bya secondary interaction of the proton in water, mimic a proton
decay signal from p ! eþ 0 . Solid line circles show reconstructed rings.

a. Nuclear effect In most of the modes, meson (, , !)nuclear effects (meson-nucleon interactions in a nucleus)
have large effects on detection efficiencies and can be adominant error source.
b.  nuclear effect The systematic uncertainties of 
nuclear effects were estimated by comparing the nuclear
effect simulation with another simulation result based on
the model used by the IMB experiment [39] because there
are no suitable experimental data which can be used for thesystematic error estimation with enough precision at the
moment. The comparison of the fraction of final states forthe proton decay of p ! eþ 0 in 16 O nuclei is shown in

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0

TABLE VI. Fraction of the final states of  from the proton
decay of p ! eþ 0 in 16 O compared with the simulation used in
the IMB experiment.
Nuclear effect

Our MCIMB

No interaction
Absorption
Charge exchange
Scattered

44%
22%
15%
19%

54%
22%
10%
14%

Table VI. The detection efficiency directly depends on theprobability of the 0 escaping without any scattering.
There is a 10% difference in that probability between thetwo models. This difference corresponds to a 15% difference in the total detection efficiencies of p ! eþ 0 and
p ! þ 0 .
The escape probability difference described above forthe p ! eþ 0 mode is equivalent to 40% differencein the total cross section of the  nuclear effect. Thus,
this difference in the total cross section was used forthe systematic error estimates from  nuclear effects forthe other nucleon decay modes, since detailed results of the
IMB simulation were not available for those modes. As forthe n ! eþ  mode, the effect on the  escape probability from a 40% uncertainty on the  nuclear effect wasestimated by the nucleon decay simulation. This effectcorresponds to a 20% difference in the total detection
efficiency for n ! eþ  . It is greater than that for
p ! eþ 0 because there are no free (unbound) nucleon
decay events for n ! eþ  .
c.  nuclear effect The systematic uncertainty of 
nuclear effects was estimated in Sec. III A 2 by comparing
the experimental  photoproduction cross section with thesimulated cross section. The estimated error for the
-nucleon cross section in 16 O nuclei was a factor of 2.
Table VII shows the effects of the systematic uncertainties of the cross section on the fraction of  meson final
states from a proton decay in 16 O. The events in which no 
meson escapes from a nucleus hardly passed the selection
criteria. The efficiency for the events in which the  meson
was scattered in the nucleus was less than 1=4 of theefficiency for the events without any interactions in a
nucleus. Therefore, effects on the detection efficiency
could be estimated almost entirely by the change of theescape probability with no interaction in a nucleus. The

TABLE VII. Fraction of the final states of  meson from theproton decay of p ! lþ  in 16 O.
 nuclear effectp ! lþ   12

2

No interaction
ScatteredNo  survived

56%
6%
38%

73%
4%
23%

43%
5%
53%

estimated errors corresponded to a 20% error in total
detection efficiencies for p ! eþ  and p ! þ .
d. ! nuclear effect The systematic uncertainty of !
nuclear effects was a factor of 3, which was estimated by
the comparison of the !-nucleon cross section for thetheoretical calculation and the extracted data from the !
photoproduction experiment as described in Sec. III A 3.
The effect of the factor of 3 uncertainty of the crosssection has a large effect on the fraction of ! meson final
states from p ! eþ ! and p ! þ ! in an 16 O nucleus, as
shown in Table VIII. However, these effects correspond to
only a 20% error on the total detection efficiency, since
the fraction of free proton decay events, which do not
suffer from nuclear effects, in the total surviving eventswas 40–60% for the p ! eþ ! and p ! þ ! search.
e. Hadron propagation in water In some of the nucleon
decay mode searches, Cherenkov rings from charged pions
were required to be found. Charged pions strongly interact
with nucleons in water. Thus, whether charged pion rings
can be observed or not depends on their hadronic interactions in water.
The uncertainty of the charged pion hadronic interaction
cross section in water was considered to be 10% by comparing the detector simulation with experimental data
[40,41].
Only for the systematic errors on the background, theuncertainty of the pion production probability by highmomentum (> 1 GeV=c) hadrons was also considered.
This error of the production probability was conservatively
set to 100%.
f. Fraction of N-N correlated decay As described inSec. III A, 10% of nucleons in an 16 O nucleus are assumed
to correlate with another nucleon. Such a decay is calculated as a three-body decay. The detection efficiency forthis decay can be very low. The uncertainty for this fraction
was conservatively set to 100%.
g. Fermi motion The total momentum of a bound nucleon decay event corresponds to the Fermi motion of thesource nucleon. The systematic error from the uncertaintyof the Fermi motion was estimated by comparing the
distributions used in the simulation with the Fermi gas
model or by changing the momentum by 20%. If a tighter
total momentum cut is used, the systematic error from theFermi motion can be large.
h. Fiducial volume The systematic errors from the fiducial volume were estimated by the difference in the number
TABLE VIII. Fraction of the final states of the ! meson fromthe proton decay of p ! eþ ! or p ! þ ! in 16 O.
! nuclear effect in 16 O
No interaction
Scattered
Decay in a nucleus!N ! N þ mesonðÞ !Þ

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p ! eþ !   3 p ! þ !   3
19%
2%
53%
26%

11%
2%
35%
52%

17%
1%
56%
25%

10%
1%
37%
51%

H. NISHINO et al.

PHYSICAL REVIEW D 85, 112001 (2012)of events for reconstructed and true vertices of multi-ring
events. The estimated errors were 3% and 2% for SK-I and
SK-II, respectively. This error can directly affect the detection efficiencies, but its magnitude is negligible compared with other systematic errors.
i. Momentum scale The uncertainty of the momentum
scale was estimated to be 1.1% (1.7%) in SK-I (SK-II) by
the quadratic sum of the uncertainties of the absolute
momentum scale and the time variation described inSec. V B. The momentum scale nonuniformity in the detector was within 0:6%. The nonuniformity can cause
momentum imbalance of an event, leading to a 1.2% error
for the total momentum.
The systematic errors on the efficiencies were estimatedby the changing the threshold of the momentum and massin the selection criteria. These two errors have negligible
effects.
j. PID, ring counting and Cherenkov opening angle The
systematic error of the particle identification was estimatedby comparing the likelihood difference (non shower-type
likelihood-shower-type likelihood) distributions of observed data and atmospheric neutrino MC. The ring counting systematic error was also estimated by the same
method. Those likelihood difference distributions of thedata and MC agree well with each other, and systematic
errors from the PID and the ring counting were estimatedto be negligible.
As for the Cherenkov opening angle, the systematic
error of the Cherenkov opening angle was estimated tobe 0.7 (0.5) degrees in SK-I (SK-II) by comparing the
opening angle distributions of the observed data and atmospheric neutrino MC for nonprimary (not most energetic) non shower-type rings in fully contained sub-GeV
events (in which visible energy is below 1.33 GeV).

Charged pion momentum reconstruction largely depends
on the opening angle. Thus, the systematic errors for themodes which need to reconstruct the charged pion momenta can be relatively large.
k. Vertex shift The vertex position was reconstructed at
the beginning of the event reconstruction. The reconstructed vertex can affect all of the following reconstruction algorithms like the ring counting, the PID, themomentum determination, etc.
The systematic error from the uncertainty of the vertex
position was estimated by shifting the reconstructed vertex
by 30 cm along the direction of the most energetic particle
momentum. This was a conservative estimate since thesystematic shift on that direction could cause largest error
on the other event reconstructions. The shift length 30 cm
corresponds to the typical resolution scale for the nucleon
decay events as well as the scale of the uncertainty of thevertex position estimated by comparing different vertex
fitting algorithms.
l. Summary of the systematic errors of detection efficiencies Table IX summarizes the results of the systematic
error estimation for detection efficiencies of all modes.
The systematic errors for detection efficiencies were about
20–30% except for the much large error of the n ! lþ 
mode.
Systematic uncertainties of nuclear effects are thedominant error sources for most of the modes. For the n !
eþ  and n ! þ  modes, the systematic errors fromthe pion nuclear effects are very large because both of thepions from the  meson decay were required to escapefrom the nucleus. Positive and negative errors were individually estimated especially for these two modes. On theother hand, p ! eþ 0 and p ! þ 0 has a comparably
smaller error since most of the surviving events in these

TABLE IX. Systematic errors for detection efficiencies. The errors of SK-I and SK-II were separately estimated and averaged by the
livetime.
Mode
p ! eþ 0

p ! þ 0
p ! eþ  (2)
p ! þ  (2)
p ! eþ  (30 )p ! þ  (30 )p ! eþ 0
p ! þ 0
p ! eþ ! (0 )
p ! þ ! (0 )
p ! eþ ! (þ  0 )p ! þ ! (þ  0 )n ! e þ 
n !  þ 
n ! eþ  
n ! þ 

Meson
nuclear effectHadron propagationin waterN-N correlated
decay

Fermi
momentum

Detector
performances

Total

15%
15%
20%
18%
15%
20%
8%
9%
21%
23%
19%
19%
20%
24%
þ51% 23%
þ51% 25%







17%
24%


13%
15%
9%
6%
9%
14%

7%
7%
7%
7%
5%
7%
2%
2%
5%
6%
5%
5%
11%
11%
11%
10%

8%
8%
13%
14%
26%
14%
10%
6%
24%
13%
12%
2%
12%
7%
15%
27%

4%
4%
5%
4%
9%
10%
18%
11%
9%
7%
20%
16%
12%
17%
19%
23%

19%
19%
25%
24%
32%
28%
28%
29%
33%
28%
34%
29%
30%
33%
þ59% 37%
þ65% 47%

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modes are free proton decay events. The uncertainty of
Fermi motion can be a dominant error source especially inmodes using a tight total momentum cut like p ! eþ 
(30 ). Another important error is the reconstruction biases
from the Cherenkov opening angle reconstruction andthe vertex shift. These biases mostly contribute errors forthe modes which require charged pion momentum
reconstruction.
These dominant errors are mostly common in SK-I and
SK-II. There are no significant differences between thesystematic errors of SK-I and SK-II.
2. Systematic errors of background estimation
For the background estimations from atmospheric neutrinos, the uncertainties of atmospheric neutrino flux andneutrino cross sections were considered. The systematic
uncertainties of pion nuclear effects, hadron propagation inwater and the detector performance were also considered
as well as the detection efficiencies.
Even with the large statistics of the atmospheric neutrinoMC, only a few tens of events can survive the nucleon
decay event selection criteria. In order to reduce statisticalerrors for the systematic error estimation of the background, systematic errors were estimated by averaging
the estimations of SK-I and SK-II because they werebasically common as described in the error estimation forthe detection efficiencies. Moreover, for the modes withthe same meson decay modes, systematic errors from theuncertainties of pion nuclear effects and hadron interactions in water were estimated by averaging the estimationsof different charged lepton modes.
Almost the same systematic uncertainties as the atmospheric neutrino oscillation analysis in the Super-Kamiokande
experiment were considered for the errors from the neutrino
TABLE X.
Mode
p ! eþ 0

p ! þ 0
p ! eþ  (2)
p ! þ  (2)
p ! eþ  (30 )p ! þ  (30 )p ! eþ 0
p ! þ 0
p ! eþ ! (0 )
p ! þ ! (0 )
p ! eþ ! (þ  0 )p ! þ ! (þ  0 )n ! e þ 
n !  þ 
n ! eþ  
n ! þ 

flux and the neutrino interaction. The details of the source of
the uncertainties are given in [36,42]. The systematic errors
from the neutrino flux were estimated to be 6–8%, and mostly
due to the uncertainty of the energy spectrum. These errors are
negligible compared with the other much larger errors. The
systematic errors from the neutrino interactions were also
estimated to be negligible, 8–16%.
The estimated systematic errors for the backgrounds areshown in Table X. The systematic errors for the backgrounds ranged from about 40–70%. One of the dominanterrors comes from the uncertainty of the pion-nucleon crosssection and the pion production probability in water. The
errors from the detector and event reconstruction performances also have non-negligible contributions. The numberof background events is very sensitive to the error of energy
and momentum, since surviving background events areusually distributed around the threshold of the selection
window of momentum and invariant mass. Therefore, thesystematic error from the energy scale stability, which was
negligible for the detection efficiencies, was estimated to beabout 10–20%. The systematic shift of the reconstructedvertex can cause errors in the Cherenkov opening angle andopening angles between two particles, which are importantfor momentum and mass reconstruction. For the same reason as energy scale, the systematic error from the vertex
shift was larger than that for the detection efficiency, andestimated to be about 10–50%.
D. Lifetime limit
The observed data in SK-I and SK-II are consistent withthe atmospheric neutrino MC. Consequently, lower limits
on the nucleon partial lifetime were calculated.
The partial lifetime limit for each mode is derived from
Bayes’ theorem which incorporates systematic errors.

Systematic errors for background estimates.

Neutrino
flux

Neutrino crosssectionPion nuclear
effectHadron propagationin water

Detector
performances

Total

8%
8%
8%
8%
8%
8%
6%
8%
8%
8%
7%
7%
8%
8%
8%
6%

8%
8%
11%
14%
15%
11%
13%
15%
14%
10%
14%
11%
15%
16%
14%
16%

8%

36%

5%

36%

18%

67%

14%

33%

13%

41%

8%

53%

8%

36%

12%

18%

22%
43%
26%
28%
13%
20%
33%
23%
37%
28%
28%
29%
46%
36%
54%
27%

44%
58%
47%
49%
76%
73%
51%
46%
59%
53%
63%
63%
61%
55%
60%
39%

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H. NISHINO et al.

PHYSICAL REVIEW D 85, 112001 (2012)

Because the nucleon decay search is a counting experiment, the probability to detect n events is given by Poisson
statistics as follows:P ðnj

bÞ ¼

eð

þbÞ

ð
n!

þ bÞn

;

31

10
years , which is sufficiently larger than the limits
by the previous experiments.
By integrating Eq. (9) using the priors, the confidence
level can be calculated as

(6)
CL ¼

where  is the true decay rate, is the true exposure, isthe true detection efficiency, b is the true number ofbackground events, and PðAjBÞ is the conditional probability of A, given that proposition B is true.
Applying Bayes’ theorem allows us to write:P ðbjnÞ ¼

1
Pðnj
A

bÞPð

bÞ;

(7)

where A is the constant to normalize Pð bjnÞ. Because
the decay rate, the detection efficiency, the exposure andthe background are independent, Pð bÞ can be separated
into constituentsP ð

1bjnÞ ¼ PðnjA

Z limit0PðjnÞd:(12)

Lifetime limits are obtained by:limit ¼ 1=limit :(13)

The combined result of SK-I and SK-II is also derived
by the method described above. The probability to detect
n1 events in SK-I and n2 events in SK-II is the product of
the two Poisson probabilities
P ðn1 ;n2 j 1 1 b1 2 2 b2 Þ ¼ Pðn1 j 1 1 b1 ÞPðn2 j 2 2 b2 Þ:(14)bÞPðÞPð ÞPð ÞPðbÞ:(8)

The probability density function of  can be defined as
ZZZPðjnÞ ¼
Pð bjnÞd d db
1 ZZZ eð þbÞ ð þ bÞn¼
An!
 PðÞPð ÞPð ÞPðbÞd d db;

We apply Bayes’ theorem assuming that the decay rate,
the exposure, the detection efficiency and the backgroundare independent:1Pðn1 ; n2 j 1 1 b1 2 2 b2 ÞA PðÞPð 1 ; 2 ÞPð 1 ; 2 ÞPðb1 ; b2 Þ:(15)Pð 1 1 b1 2 2 b2 jn1 ; n2 Þ ¼(9)

where PðÞ, Pð Þ, Pð Þ and PðÞ are the prior probability
distributions, in which systematic uncertainties can beincorporated.
The priors for the exposure, the detection efficiency andthe background are assumed to be truncated Gaussian
distributions defined as


2

0Þ
exp  ðxx
ðx > 0Þ22xPðxÞ /
0ðx  0Þðx ¼ ; ; bÞ;1

Most of the dominant systematic uncertainties like thenuclear effects and hadron propagation in water are common between SK-I and SK-II. Therefore, the systematic
errors of SK-I and SK-II are assumed to be fully correlatedwith each other, which gives conservative lifetime limits
for this method. Then, the priors for the exposure, thedetection efficiency and the background of SK-I and
SK-II are expressed asPðx1 ; x2 Þ ¼ Pð x Þ / exp (10)where 0 ( ), 0 ( ) and b (b ) are the estimates(systematic errors) of the detection efficiency, the exposureand the background, respectively. If the systematic error
for the detection efficiency is assumed to be asymmetric,
the prior Pð Þ is an asymmetric Gaussian.
The prior for the decay rate is assumed to be uniform.
This is implicitly assumed when calculating limits bysimple Poisson statistics without systematic errors

1 ð0 <  < cut ÞP ðÞ ¼
(11)
0 ð  0 or   cut Þ;
where cut is the upper limit of the decay rate for the
calculation of the normalization constant A in order toavoid divergence. The upper limit cut is set to be

2
x

2

ðx ¼ ; ; bÞ;;(16)

where x is a correlated error factor for SK-I and SK-II
defined as follows:x ¼

ðx1  x01 Þ ðx2  x02 Þ
¼
;
x1
x2
ðx ¼ ; ; bÞ:

(17)

0i ,
0i and b0i are the estimated exposure, detection
efficiency and background for SK-I and SK-II, respectively. The statistical error of the background MC is
ignored because of the much larger systematic errors.
Finally the probability density function can be expressed
as112001-22

SEARCH FOR NUCLEON DECAY INTO . . . . I AND IIPHYSICAL REVIEW D 85, 112001 (2012)

1 ZZZ eð 1 1 þb1 Þ ð 1 1 þ b1 Þn1Pðjn1 ; n2 Þ ¼
A
n1 !


eð 2 2 þb2 Þ ð 2 2 þ b2 Þn2n2 !

 PðÞPð

ÞPðÞPð b Þddd b : (18)The confidence level and lifetime limit are calculated byintegrating this probability density function as in Eqs. (12)and (13).
For a mode with two different meson decay modes like
 ! 2 and  ! 30 , the efficiencies and the backgrounds were simply added because such different meson
decay mode searches are independent. The systematic
errors on the detection efficiencies and the backgrounds
were also simply added assuming 100% correlation.
The nucleon partial lifetime limits at 90% confidence
level were obtained and summarized in Table IV and also
shown in Fig. 18.
VII. CONCLUSION
Nucleon decays into a charged antilepton (eþ and þ )plus a light meson (0 ,  , , 0 ,  and !) weresearched for in 91.7 and 49:2 kiloton  year exposures of
the SK-I and SK-II data, respectively.
Performances for nucleon decay searches were compared
between SK-I and SK-II. The observation in the SK-II
period had similar performance to that in the SK-I period
even though the photocathode coverage was half of SK-I.

FIG. 18 (color online). Explored ranges and lower limits (at90% confidence level) of nucleon partial lifetime with the resultsof the previous experiments; IMB-3 [4], KAMIOKANDE-I þ II
[5] and FREJUS [43].

No evidence for proton decays via the p ! eþ 0 mode
was found, though this mode has the highest detection
efficiency and is the dominant proton decay mode invarious GUT models. Six candidate events were found in
the SK-I and SK-II data for the five largest-backgroundmodes. The total expected background from atmospheric
neutrinos was 4.7 events. The number and features ofcandidate events are consistent with the background estimate by the atmospheric neutrino MC.
Nucleon partial lifetime limits were calculated based on
Bayes’ theorem. The lower limit on the partial lifetime ofthe proton via the p ! eþ 0 mode was calculated to be
8:2  1033 years at 90% confidence level.
As for the p ! eþ 0 and p ! þ 0 modes, we haveapplied the same set of cuts to an increased exposure of theSuper-Kamiokande detector and found no candidates. The
new exposure includes running periods of SK-III and
SK-IV. SK-III has restored photocoverage of 11 100
PMTs, but with the acrylic shields introduced for SK-II.
The SK-IV running includes new electronics. The same
proton decay signal and atmospheric neutrino Monte Carlo
methods were used to estimate the signal efficiency andbackground. We found for SK-III the efficiency for p !
eþ 0 to be 45.2% and the efficiency for p ! þ 0 to be
36.3%, with background rates of 1:9 events=megaton year and 2:5 events=megaton  year, respectively. For
SK-IV we found the efficiency for p ! eþ 0 to be 45.0%
and the efficiency for p ! þ 0 to be 43.9%, withbackground rates of 1:7 events=megaton  year and3:6 events=megaton  year respectively. These numbers
are consistent with the efficiencies and background rates
presented in this paper, with the exception that the increased
efficiency for p ! þ 0 in SK-IV is attributed to anincreased efficiency for muon-decay electron finding due
to the improved electronics of SK-IV. The distributions of
total invariant mass and total momentum are substantiallysimilar to those for SK-I and SK-II presented in Fig. 10. As aresult of finding no candidates, we also report an updated
lifetime limit for 219.7 kt-years of SK-I, II, III, and IV
exposure, finding =B > 1:29  1034 years for p ! eþ 0and =B > 1:08  1034 years for p ! þ 0 at 90% CL.
The obtained lower partial lifetime limits via the othermodes except for n ! eþ  and n ! þ  are also more
stringent than the previous limits by IMB-3 or
KAMIOKANDE-I þ II. They range from 1:6  1032 to
6:6  1033 years. The obtained lifetime limits for the n !
eþ  and n ! þ  modes are 7:0  1031 and 3:6 1031 years, respectively. They are less stringent than the
IMB-3 result. For the case of the n ! eþ  mode, thesignal efficiency and estimated background in IMB-3 are
49% (without uncertainty) and 6:3  102 events=megaton 
year, respectively, with the cuts optimized to obtain the best
lifetime limit expectation. On the other hand, we appliedtighter selection criteria to reduce the huge backgrounds to
2:7 events=megaton  year, resulting in a smaller signal

112001-23

H. NISHINO et al.

PHYSICAL REVIEW D 85, 112001 (2012)

efficiency with an assigned uncertainty of 1:7þ1:0
0:7 %. The

smaller efficiency and determined uncertainty are the main
reasons why the obtained limit is less stringent than IMB-3.
The same applies to the n ! þ  mode.
This systematic study does not rule out specific GUT
models, such as SUSY SU(5), SO(10) and so on, but canconstrain parameters relevant to nucleon decay mediatedby a superheavy gauge boson.
ACKNOWLEDGMENTS
We gratefully acknowledge the cooperation of the
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Kamiokande experiment has been built and operated
from funding by the Japanese Ministry of Education,
Culture, Sports, Science and Technology, the UnitedStates Department of Energy, and the U.S. National
Science Foundation. Some of us have been supported
by funds from the Korean Research Foundation underGrant No. BK21, the National Research Foundation of
Korea under Grant No. NRF-20110024009, the State
Committee for Scientific Research in Poland under Grant
No. 1757/B/H03/2008/35, the Japan Society for the
Promotion of Science, and the National Natural Science
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