PHYSICAL REVIEW D 96, 012003 (2017)

Search for nucleon decay into charged antilepton plus meson
in 0.316 megaton · years exposure of the Super-Kamiokande
water Cherenkov detector
K. Abe,1,38 C. Bronner,1 G. Pronost,1 Y. Hayato,1,38 M. Ikeda,1 K. Iyogi,1 J. Kameda,1,38 Y. Kato,1 Y. Kishimoto,1,38
Ll. Marti,1 M. Miura,1,38 S. Moriyama,1,38 M. Nakahata,1,38 Y. Nakano,1 S. Nakayama,1,38 Y. Okajima,1 A. Orii,1
H. Sekiya,1,38 M. Shiozawa,1,38 Y. Sonoda,1 A. Takeda,1,38 A. Takenaka,1 H. Tanaka,1 S. Tasaka,1 T. Tomura,1,38 R. Akutsu,2T. Kajita,2,38 K. Kaneyuki,2,38,* Y. Nishimura,2 K. Okumura,2,38 K. M. Tsui,2 L. Labarga,3 P. Fernandez,3F. d. M. Blaszczyk,4 J. Gustafson,4 C. Kachulis,4 E. Kearns,4,38 J. L. Raaf,4 J. L. Stone,4,38 L. R. Sulak,4 S. Berkman,5
S. Tobayama,5 M. Goldhaber,6,* M. Elnimr,7 W. R. Kropp,7 S. Mine,7 S. Locke,7 P. Weatherly,7 M. B. Smy,7,38
H. W. Sobel,7,38 V. Takhistov,7,† K. S. Ganezer,8 J. Hill,8 J. Y. Kim,9 I. T. Lim,9 R. G. Park,9 A. Himmel,10 Z. Li,10
E. O’Sullivan,10 K. Scholberg,10,38 C. W. Walter,10,38 T. Ishizuka,11 T. Nakamura,12 J. S. Jang,13 K. Choi,14 J. G. Learned,14
S. Matsuno,14 S. N. Smith,14 J. Amey,15 R. P. Litchfield,15 W. Y. Ma,15 Y. Uchida,15 M. O. Wascko,15 S. Cao,16 M. Friend,16
T. Hasegawa,16 T. Ishida,16 T. Ishii,16 T. Kobayashi,16 T. Nakadaira,16 K. Nakamura,16,38 Y. Oyama,16 K. Sakashita,16
T. Sekiguchi,16 T. Tsukamoto,16 KE. Abe,17 M. Hasegawa,17 A. T. Suzuki,17 Y. Takeuchi,17,38 T. Yano,17 T. Hayashino,18
T. Hiraki,18 S. Hirota,18 K. Huang,18 M. Jiang,18 KE. Nakamura,18 T. Nakaya,18,38 B. Quilain,18 N. D. Patel,18
R. A. Wendell,18,38 L. H. V. Anthony,19 N. McCauley,19 A. Pritchard,19 Y. Fukuda,20 Y. Itow,21,22 M. Murase,21 F. Muto,21
P. Mijakowski,23 K. Frankiewicz,23 C. K. Jung,24 X. Li,24 J. L. Palomino,24 G. Santucci,24 C. Vilela,24 M. J. Wilking,24
C. Yanagisawa,24,‡ S. Ito,25 D. Fukuda,25 H. Ishino,25 A. Kibayashi,25 Y. Koshio,25,38 H. Nagata,25 M. Sakuda,25 C. Xu,25
Y. Kuno,26 D. Wark,27,33 F. Di Lodovico,28 B. Richards,28 R. Tacik,29,40 S. B. Kim,30 A. Cole,31 L. Thompson,31
H. Okazawa,32 Y. Choi,34 K. Ito,35 K. Nishijima,35 M. Koshiba,36 Y. Totsuka,36,* Y. Suda,37 M. Yokoyama,37,38
R. G. Calland,38 M. Hartz,38 K. Martens,38 C. Shimpson,38,27 Y. Suzuki,38 M. R. Vagins,38,7 J. F. Martin,39 C. M. Nantais,39
H. A. Tanaka,39 A. Konaka,40 S. Chen,41 L. Wan,41 Y. Zhang,41 A. Minamino,42 and R. J. Wilkes43(The Super-Kamiokande Collaboration)
1

Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo,
Kamioka, Gifu 506-1205, Japan
2
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo,
Kashiwa, Chiba 277-8582, Japan3
Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain
4
Department of Physics, Boston University, Boston, MA 02215, USA
5
Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T1Z4, Canada
6
Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA
7
Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA
8
Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USA
9
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
10
Department of Physics, Duke University, Durham NC 27708, USA
11
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
12
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
13
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
14
Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA
15
Department of Physics, Imperial College London, London, SW7 2AZ, United Kingdom
16High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan17
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan18
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
19
Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom
20
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
21
Institute for Space-Earth Enviromental Research, Nagoya University,
Nagoya, Aichi 464-8602, Japan
22
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University,
Nagoya, Aichi 464-8602, Japan
23
National Centre For Nuclear Research, 00-681 Warsaw, Poland
24
Department of Physics and Astronomy, State University of New York at Stony Brook,
NY 11794-3800, USA
25
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
26
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
27
Department of Physics, Oxford University, Oxford, OX1 3PU, United Kingdom

2470-0010=2017=96(1)=012003(18)012003-1© 2017 American Physical Society

K. ABE et al.

PHYSICAL REVIEW D 96, 012003 (2017)28

School of Physics and Astronomy, Queen Mary University of London, London, E1 4NS, United Kingdom
Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, SK, S4SOA2, Canada
30
Department of Physics, Seoul National University, Seoul 151-742, Korea
31
Department of Physics and Astronomy, University of Sheffield, S10 2TN, Sheffield, United Kingdom
32
Department of Informatics in Social Welfare, Shizuoka University of Welfare,
Yaizu, Shizuoka, 425-8611, Japan
33
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory,
Warrington, OX11 0QX, United Kingdom
34
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
35
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
36
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
37
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
38
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes
for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8583, Japan
39
Department of Physics, University of Toronto, ON, M5S 1A7, Canada
40
TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T2A3, Canada
41
Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
42
Faculty of Engineering, Yokohama National University, Yokohama, 240-8501, Japan
43
Department of Physics, University of Washington, Seattle, WA 98195-1560, USA(Received 23 May 2017; published 24 July 2017)29

We have searched for proton decays into a charged antilepton (eþ , μþ ) plus a meson (η, ρ0 , ω) andfor neutron decays into a charged antilepton (eþ , μþ ) plus a meson (π − , ρ− ) using Super-Kamiokande
I-IV data, corresponding to 0.316 megaton · years of exposure. This measurement updates the previous
published result by using 2.26 times more data and improved analysis methods. No significant evidence fornucleon decay is observed and lower limits on the partial lifetime of the nucleon are obtained. The limits
range from 3 × 1031 to 1 × 1034 years at 90% confidence level, depending on the decay mode.
DOI: 10.1103/PhysRevD.96.012003

I. INTRODUCTION
A. Grand unification theories
The standard model of particle physics, based on the
SUð3Þc × SUð2ÞL × Uð1ÞY gauge symmetry, seems to be an
incomplete description of nature’s structure of matter andforces. The standard model fails to include massive neutrinos
or provide a satisfying explanation for charge quantization or
the convergence of gauge couplings at high energy scales.
These issues are addressed in grand unified theories (GUTs),
which embed the standard model in a single unifying gauge
group such as SU(5) [1] or SO(10) [2]. While numerous
specific realizations of GUTs exist (see [3] for review), as auniversal feature they predict nucleon decay, and therefore,baryon number violation. The gauge coupling unification
scale is around 1015–16 GeV, which is unreachable withaccelerators but can be explored by virtual processes thatinduce nucleon decay with lifetimes of 1032–35 years. The
lower end of this lifetime range may yield observable event
rates in long exposures of a large water Cherenkov detector
such as Super-Kamiokande (SK).
*

Deceased.
Also at Department of Physics and Astronomy, UCLA, CA
90095-1547, USA.
‡
Also at BMCC/CUNY, Science Department, New York,New York, USA.
†The two benchmark nucleon decay modes p → eþ π 0
and p → ν̄K þ are favored channels [4] in nonsupersymmetric GUTs and TeV-scale supersymmetric GUTs,
respectively. However, depending on the model, thebranching ratios for nucleon decay channels vary anddifferent decay modes can dominate or be comparable
to the favored channels. For example, in SU(5) the rate
for n → eþ π − is twice that of p → eþ π 0 [5]; however, thelatter mode has a stronger experimental signature. It isconceivable that rates for channels with heavy nonstrange
mesons (η, ρ, ω) are comparable in magnitude to thosewith pions [6]. In the lifetime limit where the expectation
for any single channel is one event or less, searching in
multiple decay modes enhances the chance that one
observes any nucleon decay at all. Finally, observing
proton decay from a nonstandard channel in the absenceof a signal from p → eþ π 0 might hint at some exotic
scenario.
In this work, we describe nucleon decay searches forwhich the final state is comprised of two particles: acharged antilepton, eþ or μþ, and a nonstrange meson.
These nucleon decays violate baryon number, B, butconserve baryon number minus lepton number, B − L.
This paper, in combination with our recent publication
searching for p → eþ π 0 and p → μþ π 0 [7], has covered allsuch two-body decay modes.

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PHYSICAL REVIEW D 96, 012003 (2017)

B. The Super-Kamiokande experiment
Super-Kamiokande is a large water Cherenkov detector
located in the Kamioka mine under about 1 km rockoverburden (2.7 km water equivalent) at the Ikenoyama
mountain in Japan [8]. It is composed of a 39.3 m diameterby 41.4 m high vertical cylinder lined with 50-cm photomultiplier tubes (PMTs) facing the inner volume. The SKexperiment has been collecting data since 1996 in four
different experimental phases denoted as SK-I to SK-IV.
The inner detector photo coverage is around 40% in SK-I,
SK-III, and SK-IV but was 19% in SK-II. New front-end
electronics called QBEE [9] were implemented in SK-IV,
which enabled deadtime-free data acquisition of a wide
time window of PMT hit information. This enabled neutron
capture to be included in SK-IV analyses. The SK detector
has been extensively tuned and calibrated [8].
Due to its large fiducial volume (22.5 kilotons, corresponding to about 7.5 × 1033 protons and 6.0 × 1033
neutrons), excellent event reconstruction performance[10] as well as long stable detector operation, SK has
sensitivity to nucleon decay generally exceeding pastexperiments by an order of magnitude or more. Decays
into a charged antilepton and a meson are particularly well
suited for water Cherenkov detector searches since both thelepton and the meson or their decay particles are above theCherenkov threshold and are visible in most cases.
The search for nucleon decay into a charged antilepton
plus a meson using data from SK-I and SK-II(0.141 megaton · years) has been published previously[11]. Among those nucleon decay modes, the p →ðeþ ; μþ Þπ 0 searches have been updated recently withadditional data from SK-III and SK-IV along with several
analysis improvements [7]. No evidence has been observed
for any nucleon decays, and the corresponding lifetime
limits were set for these channels.
In this work, we update the searches for proton decay
into a charged antilepton (eþ , μþ ) plus a meson (η, ρ0 , ω)and neutron decay into a charged antilepton (eþ , μþ ) plus ameson (π − , ρ− ) using the latest data set from SK-I to SK-IV,
an exposure of 0.316 megaton · years.
C. Analysis improvements
This paper incorporates several major improvements inthe analysis over the previously published results [11].
These improvements have already been implemented for
p → eþ π 0 and p → μþ π 0 and recently published [7].
For some channels, the signal region in the reconstructed
total momentum and invariant mass distribution parameters
is separated into two distinct subregions (“boxes”), according
to the total momentum. This permits a statistical separation ofbound and free proton decays for channels that have goodinvariant mass and momentum resolution. For this paper,
the channels that benefit are the p → lþ η, η → 2γ searches(lþ ¼ eþ , μþ ). The majority of the free proton decays havetotal momentum in the lower-momentum box, where thenumber of expected atmospheric neutrino background eventsis negligibly small. The two-box momentum separation is
implemented for these channels in all data sets from SK-I to
SK-IV. For more details see Sec. IVA.
Atmospheric neutrino background is often accompaniedby neutron production whereas it is expected that nucleon
decay seldom releases a free neutron [12]. For SK-IV
analysis, a neutron capture reconstruction algorithm [13]is included, which allows us to reduce the atmospheric
neutrino background rate. The neutron tagging is available,
only for SK-IV, thanks to a triggerless readout scheme thatrecords every hit in a wide time window. Following a
primary event, we search over 435 μs for coincident hits
near the vertex from the 2.2 MeV gamma ray from neutron
capture on hydrogen, which occurs with a mean capture
time of 200 μs in water. Description of the neutron
simulation and the tagging algorithm can be found in
Ref. [7]. In this analysis, the number of expected SK-IV
background events is reduced using neutron tagging
by 30–90% depending on the nucleon decay modes. A
full summary of the resulting background for each SK
period can be found in Table I.
The systematic uncertainties of the pion interactions in
the oxygen nuclei and water have been reevaluated since
the previous analysis of Ref. [11]. See Sec. VA for moredetails.
The new two-box strategy and neutron tagging provide
better discovery reach. For example, the 3-σ discovery
potential in the proton lifetime for p → eþ η search isestimated to be about 12% higher than the previous singlebox analysis without neutron tagging for the exposure usedin this analysis.
II. SIMULATION
A. Nucleon decay
Nucleon decay Monte Carlo (MC) samples are generated
to determine the search strategy and to estimate the signal
efficiencies. The MC simulation includes: initial nucleon
decay kinematics, meson interactions in the oxygen
nucleus for bound nucleon decays, hadron propagationin water, propagation of particles, and Cherenkov lightemission, absorption, and scattering. The initial nucleon
decay kinematics are identical to those in Ref. [11], while
updated pion interactions and particle and Cherenkov light
simulations in water are adopted from Ref. [7].
In the case of nucleon decay within the oxygen nucleus,
the effects due to Fermi momentum, correlation with othernucleons [14] (correlated nucleon decay), nuclear binding
energy, and meson-nucleon interactions are all taken into
account [11]. The effective mass of the decayed neutron for
n → eþ π − MC is shown in Fig. 1. Unlike for the proton
decay, there is no sharp peak at the neutron mass
(940 MeV=c2 ) because all the neutrons in a H2 O molecule
are bound in a nucleus and there is no free neutron decay.

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PHYSICAL REVIEW D 96, 012003 (2017)
1p

10

π- 12
6 C

400

10

350

2

300
σ (mb)

events1s10Reactive (TunedFSI)
Reactive (OldFSI)
Quasi-elastic
Absorption
Single CX
π Production

450

3correlated decay

250
200
150
100

1

50

100 200 300 400 500 600 700 800 900 1000
neutron effective mass in 16O (MeV/c2)

0

200

O for

The largest and most energetic peak corresponds to the 1p
state; the 1s state is nearby. The nuclear binding energies
are 39.0 MeV for the 1s state and 15.5 MeV for the 1p state[15]. Correlated neutron decay, which accounts for the
possibility of another nucleon recoiling with the decaying
nucleon, makes the tail in the lower mass region.
The meson-nucleon interactions in an oxygen nucleus are
simulated with the NEUT neutrino interaction simulation[16]. Mesons generated in an oxygen nucleus may interact
with nucleons before they escape from the nucleus. The
position of the nucleon decay in a nucleus is determined by
the Woods-Saxon nuclear density distribution in the simulation. From this position, π, η, and ω mesons are tracked
within the oxygen nucleus. The lifetime of the ρ meson isshort enough (βγcτ ∼ 0.3 fm) that it decays immediately
inside the nucleus into two π mesons. Therefore, the nuclear
effects of the ρ meson itself are not considered in thesimulation, but those of the secondary pions are included.
The pion interaction model in NEUT is a semiclassicalcascade model. The interaction probabilities (mean freepaths) for low-momentum pions are calculated with the
Delta-hole model by Oset et al. [17]. The pion interaction
probabilities for high-momentum pions are extracted fromthe π  -nucleus scattering experimental data. All the pion
interaction probabilities and cross section parameters havebeen tuned with various π  -nucleus scattering data, including C, O, Al, Fe [7], since the previous paper [11]. Figure 2
shows the π − cross sections of the external data and MC
on 12 C [18]. The tuned MC used in this analysis increased
the cross sections with the largest improvement at around
500 MeV=c.
The interactions between the η and nucleons in the
nucleus are considered through a baryon resonance ofNð1535Þ and the corresponding cross section is calculatedby the Breit-Wigner formula. Since pions can be generated
by the decay of the resonance, nuclear effects for them areconsidered. Figure 3 shows the fractions of the meson
interactions in the oxygen nucleus in the p → eþ η MC.

400
600
800
1000 1200
π- Initial Momentum (MeV/c)

1400

1600

FIG. 2. The π − interaction cross section on 12 C as a function of
momentum. Open circles indicate existing data [18]; dashed andsolid lines show before and after the tune, respectively. The colors
correspond to the total cross section and exclusive channels: total(black), quasielastic scattering (green), absorption (red), charge
exchange “CX” (blue), and π production (light blue). “FSI”
stands for final state interaction.

The ω meson interactions with a nucleon in an oxygen
nucleus are calculated with a boson exchange model [19].
Uncertainties due to these physics processes are taken
into account within the systematic error estimations on thesignal efficiencies as discussed in Sec. VA.
B. Atmospheric neutrinos
The background for nucleon decay searches comes fromatmospheric neutrino interactions in water. The standard
Super-Kamiokande atmospheric neutrino simulations[16,20–22] are used to estimate the background rate.
1

η scattering
scatt
sc
att
tteringi g
π esc
escape
escap
escap
pe
pe

0.8

fraction

FIG. 1. The effective mass of the decayed neutron inn → eþ π − as simulated by Monte Carlo.

160

π absorption
ab
abso
absor
bso
sorrption
ptiio

0.6

0.4

No interaction
0.2

0
100

200

300

400

500

600

η initial momentum (MeV/c)

FIG. 3. Fraction of meson interactions in the oxygen nucleus inbins of η momentum generated by p → eþ η MC. η’s that exit thenucleus without experiencing any interactions are indicated by the
portion labeled “No interaction.” If at least one of the pions
generated via the baryon resonance of Nð1535Þ is absorbed, it
is called “π absorption.” If none of the pions are absorbed, it iscalled “π escape.”

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PHYSICAL REVIEW D 96, 012003 (2017)

III. DATA REDUCTION
AND RECONSTRUCTION
Data from 91.5, 49.1, 31.8, and 143.8 kiloton · year
exposures, corresponding to the 1489.2, 798.2, 518.1, and2339.4 live days of the experiment during the SK-I, SK-II,
SK-III, and SK-IV phases, are used. Several stages of
reduction are applied to suppress the cosmic ray muon
background and prepare samples for the physics analyses.
The reduction algorithms are identical to those used foratmospheric neutrino analyses and nucleon decay
searches [24].
Fully contained (FC) events are selected by requiring avertex inside of the 22.5 kiloton fiducial volume (2 m awayfrom the inner detector wall), visible energy greater than
30 MeV, and no hit-PMT clusters in the outer detector.
Event reconstruction algorithms are applied to all of the
FC events to determine the event vertex location, find
Cherenkov ring directions, assign a particle identificationof showering or nonshowering to each ring, assign particle
momentum to each ring, and identify muon decay electrons
that follow the primary event by microseconds. The samereconstruction algorithms are applied to both the observed
data and the MCs. The algorithms are the same as foratmospheric neutrino analyses, with the details of theiralgorithms described in [10].
One of the most important event reconstructions fornucleon decay searches is the energy scale because we
distinguish the nucleon decay events from the atmospheric
neutrino background events using their invariant mass andmomentum. The energy scale uncertainty is estimated bytaking the absolute scale difference between control sample

140

SK-IV

120
100

eventsThe model includes an atmospheric neutrino flux calculation, neutrino oscillation, and a detailed model ofneutrino-nucleus interaction cross sections. The meson
interactions in the oxygen nucleus are treated similarly
for the nucleon decay and the atmospheric neutrino MC.
Simulated data samples equivalent to around 500 years ofdetector exposure are generated for each SK period. The
detector simulation, including Cherenkov light production,
scattering, absorption, and detector response, is identical
for the nucleon decay signal MC and the atmospheric
neutrino background MC.
Uncertainties of the neutrino flux, neutrino cross sections, pion-nuclear interactions as well as hadron propagation in water are all taken into account in the systematic
error estimates on the number of the expected background
events as discussed in Sec. VA.
The neutrino and the pion interactions in the atmospheric
neutrino background for the p → eþ π 0 search in SK wereexperimentally validated using an accelerator neutrino
beam and a 1-kiloton water Cherenkov detector [23].
The dynamics of pion production and interactions relevant
for the nucleon decay searches for the SK-type water
Cherenkov detector have been verified.

80
60
40
20
0

0

50

100

150

200

250

300

2

π mass (MeV/c )FIG. 4. Reconstructed invariant mass distribution of the atmospheric-neutrino-induced π 0 events in the observed data (black dot)
and the atmospheric neutrino MC samples (red histogram) used in
the absolute energy scale error estimation in SK-IV. MC events arenormalized by the live time of the observed data (1631 days).

data and MC as well as the time variation of control sample
data for each SK period. For the four SK periods, theenergy scale uncertainties are 1.1%, 1.7%, 2.7%, and 2.1%
for SK-I, SK-II, SK-III, and SK-IV, respectively. The
uncertainties from SK-I to SK-III are same as in a previous
publication [25] and details of the energy reconstruction
and the error estimation can be found there. Figure 4 shows
the reconstructed π 0 mass distributions used in the absoluteenergy scale error estimation of SK-IV. Good agreement
is observed between data and MC in reconstruction of theπ 0 mass. Zenith angle-dependent nonuniformities of theenergy scale are 0.6%, 0.6%, 1.3%, and 0.7% for SK-I,
SK-II, SK-III, and SK-IV, respectively. These energy scaleerrors are used in the systematic error estimations describedin Sec. VA.
The reconstructed total momentum, Ptot , the total energy
Etot , and the invariant mass Mtot are defined asX all ⃗pi ;ð1Þ
Ptot ¼ 
iEtot ¼

all qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Xj ⃗pi j2 þ m2i ;ð2Þi

Mtot ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
E2tot − P2tot ;ð3Þ

where ⃗pi is the momentum of each Cherenkov ring and miis the mass of a particle.
The meson mass is reconstructed in a similar way bysumming up the momenta and energies of the secondary
particles from the meson decay. Under the assumption of aparticular meson decay, the meson mass is calculated for all
possible combinations of particle type assignment and thebest combination in which the reconstructed mass is theclosest to the expected mass is selected.

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PHYSICAL REVIEW D 96, 012003 (2017)++p→e η(2γ)
500

SK-I

0

events (arbitrary)

SK-II

0

SK-III

SK-I

0
200

A. p → l + η search
The η meson, with a mass of 548 MeV=c2 and a lifetimeof 5 × 10−19 seconds, has three dominant decay modes.
Two of them, η → 2γ (branching ratio ¼ 39%) and η → 3π 0(branching ratio ¼ 33%), are analyzed. The η → π þ π − π 0(branching ratio ¼ 23%) is not used because the branchingratio is smaller and the signal selection efficiency isworse [11].

SK-II

0
200

SK-III

100

250
0
500

200

data for each nucleon decay search and each SK period,
are summarized in Table I.

100

250

500

p→e η(3π )

100

250

500

0

SK-IV

0
200

250

100

0
0

0
200 400 600 800 1000 0

SK-IV

1. η → 2γ search

200 400 600 800 10002

η mass (MeV/c )FIG. 5. The reconstructed η mass distributions for p → eþ η
MC events for η → 2γ search (left) and η → 3π 0 (right) search foreach SK period. The histograms show all simulated p → eþ η
events. For the left plots the eta meson is reconstructed under theassumption of η → 2γ, and for the right plots the eta meson isreconstructed under the assumption of η → 3π 0 . The hatchedhistograms show, for free proton decays, the true η → 2γ events(left) and true η → 3π 0 events (right). The event selections(A1–A2) of Sec. IVA are applied. The inside of the two verticalgreen lines corresponds to the signal region.

For example, Fig. 5 shows the reconstructed η mass
distributions for the p → eþ η MC events for each SK
period. The η mass is reconstructed well. The open
histogram contains all the relevant η decay channels
associated with the signal MC. For example, the broad
peak between 200–400 MeV=c2 in the left plots is from all
the η decays except for η → 2γ. The mass resolution isobserved to be worse for the 3π 0 search since there are
six true gamma rays in the final state, but only up to four orfive Cherenkov rings are reconstructed; the ring-counting
algorithm terminates at five rings. For both meson decay
searches, there is no significant difference in the mass
reconstruction among the four SK periods. Details of thecomparison of event reconstructions between SK-I and
SK-II are found in the previous publication [11].
IV. EVENT SELECTION
The event selections were already optimized in theprevious analysis [11] for each nucleon decay mode to
maximize the lifetime sensitivity and are exactly the samein this analysis except when the two-box total momentum
separation and the SK-IV neutron tagging are used.
The event selections for each nucleon decay (lþ ¼ eþ ,þμ ) search are described in the following subsections.
The signal selection efficiency and the number of expected
atmospheric neutrino backgrounds, as well as the observed

The following event selection is used:(A1) the number of Cherenkov rings is three,(A2) all the rings are shower-type rings for p → eþ η andone of the rings is a nonshower-type ring for p → μþ η,(A3) the invariant mass is between 480 and 620 MeV=c2 ,(A4) the number of Michel electrons is 0 for p → eþ η or 1
for p → μþ η,(A5) the total momentum is less than 250 MeV=c and theinvariant mass is between 800 and 1050 MeV=c2 ,(A6) the total momentum is greater than or (A7) less than
100 MeV=c (total momentum separation),(A8) the number of neutrons is 0 for the upper or (A9)lower total momentum region in SK-IV.
After the selections (A1–A5), the total momentum separation (A6–A7) into two search boxes is implemented since
the following three extra criteria are satisfied in the lowermomentum signal box: (1) the expected number of the
background events is negligibly small (≪0.1 events foreach SK period), (2) the signal efficiency is sufficiently high(>1%), (3) most of the free proton decays are in this region.
The signal selection efficiency and the number of
expected background events at each event selection step
are shown in Fig. 6. The event selection by total momentum
and invariant mass at selection (A5) significantly reduces
the atmospheric neutrino background. The total expected
number of the background is further reduced and becomes
negligibly small, ∼0.03 (<0.01) integrated over all the SK
periods for p → eþ η (p → μþ η) search (see Table I for
detail), in the lower signal box at selection (A7). The signal
efficiency is still sufficiently high (>1%) in the lower box.
The total mass and total momentum distributions areshown in Figs. 7 and 8. Most of the free protons decay inthe lower box (total momentum < 100 MeV=c) for theη → 2γ searches shown in the upper-left two plots, and thedata and the atmospheric neutrino MC agree with eachother in all the lower plots in Fig. 8.
2. η → 3π0 search
The following event selection is used:(B1) the number of Cherenkov rings is four or five,

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10p→e η(2γ)

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A1 A2 A3 A4 A5 A6 A7 A8 A9 A1 A2 A3 A4 A5 A6 A7 A8 A9 B1 B2 B3 B4 B5 B6 B1 B2 B3 B4 B5 B6event selection

FIG. 6. The signal efficiencies (upper) and the number of expected backgrounds (lower, red histogram) and data candidates (lower,
black dots) for p → eþ η (η → 2γ), p → μþ η (η → 2γ), p → eþ η (η → 3π 0 ), and p → μþ η (η → 3π 0 ) searches from left to right. The
results from SK-I to SK-IV are combined. The event selection is defined in the text.

total momentum (MeV/c)

+

1000
800
600
400
200
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500

500

1000 0+0p→e η(3π )1000 05001000 0

+

0

500

1000

p→μ η(3π )total mass (MeV/c2)

FIG. 7. Total invariant mass and total momentum for p → lþ η MC (top, cyan for free proton and blue for bound proton), atmospheric
neutrino background MC corresponding to about 2000 years live time of SK (middle), and data (bottom) for p → eþ η (η → 2γ),
p → μþ η (η → 2γ), p → eþ η (η → 3π 0 ), and p → μþ η (η → 3π 0 ) searches from left to right. All the event selections except (A5–A7)
and (B5) in Sec. IVA are applied. The results from SK-I to SK-IV are combined. The signal box is shown as a green box. For thep → lþ η (2γ) searches, the total momentum is separated at the horizontal dashed line in the signal box.

(B2) all the rings are shower-type rings for p → eþ η andone of the rings is a nonshower-type ring for p → μþ η,(B3) the η mass is between 400 and 700 MeV=c2 ,(B4) the number of Michel electrons is 0 for p → eþ η and
1 for p → μþ η,(B5) the total momentum is less than 150 MeV=c for p →eþ η and less than 250 MeV=c for p → μþ η; the total
invariant mass is between 800 and 1050 MeV=c2 ,(B6) the number of neutrons is 0 in SK-IV.
The signal selection efficiency and the number of
expected background events at each event selection step

are shown in Fig. 6. The total mass and total momentum
distributions are shown in Figs. 7 and 8. Unlike the η → 2γ
mode, a significant fraction of the events have reconstructed total momentum greater than 100 MeV=c evenfor free proton decay. Therefore, we do not implement thetwo-box total momentum separation.
After the full event selection in the p → μþ η searchhas been applied, there are two data candidates remaining,
one in SK-II and another in SK-IV. The total number of
expected background events integrated over all the meson
decay modes and all SK periods is 0.85. The Poisson

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0

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FIG. 8. Total momentum for p → lþ η MC (upper, open histogram for bounded protons and shaded histogram for free protons),
atmospheric neutrino MC (lower, red histogram), and data (lower, black circles) for p → eþ η (η → 2γ), p → μþ η (η → 2γ), p → eþ η
(η → 3π 0 ), and p → μþ η (η → 3π 0 ) searches from left to right. All the event selections except (A5–A7) and (B5) in Sec. IVA are
applied. The atmospheric neutrino MC is normalized to data by area. Results from SK-I to SK-IV are combined. The signal region
corresponds to the left side from the vertical green solid line. The vertical dashed line for p → lþ η (2γ) corresponds to the total
momentum separation cut value. Total momenta for the p → μþ η (η → 3π 0 ) data candidates are 188 MeV=c and 239 MeV=c.

selection step. The total invariant mass and momentum
distributions are shown in Figs. 10 and 11.
There are two data candidates in SK-IV for the p →eþ ρ0 search and one candidate in SK-I for the p → μþ ρ0search. The SK-I event was also selected in the analysis of
the previous publication. The total number of expectedbackground events is 0.64 for p → eþ ρ0 and 1.30 for
p → μþ ρ0 searches.
+ 0

10efficiency (%)

probability to observe two or more events is 20.9%, assummarized in Table III.
The data candidate found in SK-II using the current
analysis was also found in the previously publishedanalysis. The previous work also found an additional data
candidate in SK-II. In that event, a faint nonshowerlike
ring reconstructed in the previous analysis is not reconstructed in this work, excluding it from the selection
criteria. Event reconstruction improvements, such as tuning of the backward charge within the charge separation
algorithm among Cherenkov rings, can cause suchchanges in the ring counting outcome on an event-byevent basis.
B. p → l + ρ0

p→μ ρ

10

1
4
10

eventsThe ρ0 meson, with a mass of 775 MeV=c2 and a widthof 149 MeV, decays immediately into π þ π − with abranching ratio of nearly 100%.
The following event selection is used for this search:(C1) the number of Cherenkov rings is three,(C2) one of the rings is a shower-type ring for p → eþ ρ0
and all the rings are nonshower-type rings forp → μþ ρ0 ,(C3) the ρ0 mass is between 600 and 900 MeV=c2 ,(C4) the number of Michel electrons is 0 or 1 forp → eþ ρ0 and 1 or 2 for p → μþ ρ0,(C5) the total momentum is less than 150 MeV=c for
p → eþ ρ0 and less than 250 MeV=c for p → μþ ρ0 ;the total invariant mass is between 800 and
1050 MeV=c2 ,(C6) the number of neutrons is 0 in SK-IV.
Figure 9 shows the signal selection efficiency and thenumber of expected background events at each event

+ 0

p→e ρ

2

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1
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C1

C2

C3

C4

C5

C6

C1

C2

C3

C4

C5

C6

event selection

FIG. 9. The signal efficiencies (upper) and the number of
expected backgrounds (lower, red histogram) and data candidates(lower, black dots) for p → eþ ρ0 (left) and p → μþ ρ0 (right)
searches. The results from SK-I to SK-IV are combined. The
event selection is defined in the text.

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C. p → l + ω
The ω meson has a mass of 783 MeV=c2 and immediately decays due to a width of 8.5 MeV. Two decay
modes are analyzed: one is the ω → π þ π − π 0 mode
(branching ratio ¼ 89%), and the other is the ω → π 0 γ
mode (branching ratio ¼ 8%).

800
600

total momentum (MeV/c)

400
200
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1. ω → π0 γ search

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400
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1000
800
600
400
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0

250

500

750 1000 0

250

500

750 1000

total mass (MeV/c2)

FIG. 10. Total invariant mass and total momentum for
p → lþ ρ0 MC (top, cyan for free proton and blue for boundproton), atmospheric neutrino background MC corresponding toabout 2000 years live time of SK (middle), and data (bottom)
for p → eþ ρ0 (left) and p → μþ ρ0 (right) searches. All theevent selections except (C5) in Sec. IV B are applied. The resultsfrom SK-I to SK-IV are combined. The signal box is shown as agreen box.

The following event selection is used for this search:(D1) the number of Cherenkov rings is 3 or 4 for
p → eþ ω and 2 or 3 for p → μþ ω,(D2) all rings are shower-type rings,(D3) the ω mass is between 650 and 900 MeV=c2 ,(D4) the number of Michel electrons is 0 for p → eþ ω
and 1 for p → μþ ω,(D5) the total momentum is less than 150 MeV=c for
p → eþ ω and less than 200 MeV=c for p → μþ ω;
the invariant mass is between 800 and 1050 MeV=c2
for p → eþ ω,(D6) the number of neutrons is 0 in SK-IV.
For the p → μþ ω mode, the muon momentum is lower
than the Cherenkov threshold and the muon ring is notobserved.
Figure 12 shows the signal selection efficiency and thenumber of expected background events at each event
selection step. The total mass and total momentum distributions are shown in Figs. 13 and 14.
2. ω → π + π − π0 search

+ 0

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events

p→e ρ

p→μ ρ

600

150

400

100

200

50

0
6

0
4

4
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2
0
0

200 400 600 800 1000

00200 400 600 800 1000

total momentum (MeV/c)

FIG. 11. Total momentum for p → lþ ρ0 MC (upper, open
histogram for bounded protons and shaded histogram for free
protons), atmospheric neutrino MC (lower, red histogram), anddata (lower, black circles) for p → eþ ρ0 (left) and p → μþ ρ0(right) searches. All the event selections except (C5) in Sec. IV B
are applied. The atmospheric neutrino MC is normalized to databy area. Results from SK-I to SK-IV are combined. The signal
region corresponds to left side from the vertical green line. Total
momenta are 61 MeV=c and 90 MeV=c for the p → eþ ρ0 data
candidates and 179 MeV=c for the p → μþ ρ0 data candidate.

The following event selection is used for this search:(E1) the number of Cherenkov rings is 4 for p → eþ ω
and 3 for p → μþ ω,(E2) one of the rings is a nonshower ring,(E3) the π 0 mass is between 85 and 185 MeV=c2 ,(E4) the number of Michel electrons is 0 or 1 forp → eþ ω and 2 for p → μþ ω,(E5) the total momentum is less than 200 MeV=c, and thetotal invariant mass is between 600 and 800 MeV=c2
for p → eþ ω and between 450 and 700 MeV=c2
for p → μþ ω,(E6) the positron momentum is between 100 and
200 MeV=c for p → eþ ω,(E7) the number of neutrons is 0 in SK-IV.
Due to the strong interaction of the charged pions in water,
finding both charged pion rings is difficult. Therefore, we
require finding only one of the two charged pion rings inthese searches. Since one of the two charged pions is
assumed to be invisible in the selection criteria, the invariant
mass for the ω can not be reconstructed. Instead, we requirethat the reconstructed π 0 invariant mass is consistent with theπ 0 mass. In order to reduce the background even further, thepositron momentum is also required to be consistent withthe expected positron momentum for the p → eþ ω mode.
The positron momentum distribution is shown in Fig. 15.

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p→μ+ω(3π)

10events

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D1 D2 D3 D4 D5 D6 D1 D2 D3 D4 D5 D6 E1 E2 E3 E4 E5 E6 E7 E1 E2 E3 E4 E5 E7event selection

FIG. 12. The signal efficiencies (upper) and the number of expected backgrounds (lower, red histogram) and data candidates (lower,
black dots) for p → eþ ω (ω → π 0 γ), p → μþ ω (ω → π 0 γ), p → eþ ω (ω → 3π), and p → μþ ω (ω → 3π) searches from left to right. The
results from SK-I to SK-IV are combined. The event selection is defined in the text.

total momentum (MeV/c)

+

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p→e ω(π γ)05001000 0+0+p→μ ω(π γ)5001000 0+p→e ω(3π)

p→μ ω(3π)

500

500

1000 01000

2total mass (MeV/c )FIG. 13. Total invariant mass and total momentum for p → lþ ω MC (top, cyan for free proton and blue for bound proton), atmospheric
neutrino background MC corresponding to about 2000 years live time of SK (middle), and data (bottom) for p → eþ ω (ω → π 0 γ),
p → μþ ω (ω → π 0 γ), p → eþ ω (ω → 3π 0 ), and p → μþ ω (ω → 3π 0 ) searches from left to right. All the event selections except (D5)and (E5) in Sec. IV C are applied. The results from SK-I to SK-IV are combined. The signal box is shown as a green box.

There is one data candidate in SK-I for p → eþ ω searchand the number of total expected background events is
1.35. An identical event was selected in the previous
analysis.
D. n → l + π −The following event selection is used for this search:(F1) the number of Cherenkov rings is two,(F2) one of the rings is a shower-type ring for n → eþ π −and all the rings are nonshower-type rings forn → μþ π − ,(F3) the number of Michel electrons is 0 for n → eþ π −and 1 for n → μþ π −,(F4) the total momentum is less than 250 MeV=c,
and the total invariant mass is between 800 and
1050 MeV=c2 ,(F5) the number of neutrons is 0 in SK-IV.
In these modes, a Cherenkov ring from the charged pion
generated from the nucleon decay can be directly observed.
It is not necessary to select the events by a meson invariant
mass for these modes.
Figure 16 shows the signal selection efficiency and thenumber of expected background events at each event

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total momentum (MeV/c)

FIG. 14. Total momentum for p → lþ ω MC (upper, open histogram for bounded protons and shaded histogram for free protons),
atmospheric neutrino MC (lower, red histogram), and data (lower, black circles) for p → eþ ω (ω → π 0 γ), p → μþ ω (ω → π 0 γ),
p → eþ ω (ω → 3π), and p → μþ ω (ω → 3π) searches from left to right. All the event selections except (D5) and (E5) in Sec. IV C are
applied. The atmospheric neutrino MC is normalized to data by area. Results from SK-I to SK-IV are combined. The signal region
corresponds to the left side from the vertical green line. Total momentum for p → eþ ω (ω → 3π) data candidate is 124 MeV=c.

selection step. The total mass and total momentum distributions are shown in Figs. 17 and 18.
There is one data candidate in SK-III in n → μþ π −search and the number of total expected background events
is 0.77.
p→e+ω(3π)
1500

In the previous published analysis, there was one data
candidate in SK-I for the n → μþ π − search. In bothprevious and current analyses, the event vertex is in thefiducial volume, the number of rings is two, both rings arenonshower types, and the number of Michel electrons isone, passing those selection criteria. The invariant mass andmomentum, (M tot , Ptot ) was (809 MeV=c2 , 245 MeV=c) in
the previous analysis but changed slightly to (829 MeV=c2 ,253 MeV=c) in this analysis. The Ptot is near the signal box

1250
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efficiency (%)

events

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positron momentum (MeV/c)

FIG. 15. Positron momentum for p → eþ ω MC (upper, open
histogram for bounded protons and shaded histogram for free
protons), atmospheric neutrino MC (lower, red histogram), anddata (lower, black circles) for p → eþ ω (ω → 3π) search. The
event selections (E1–E4) of Sec. IV C are applied. The atmospheric neutrino MC is normalized to data by area. Results from
SK-I to SK-IV are combined. The inside of the two vertical green
lines corresponds to the signal region.

10

4

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F1

F2

F3

F4

F5

F1

F2

F3

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event selection

FIG. 16. The signal efficiencies (upper) and the number of
expected background events (lower, red histogram) and data
candidates (lower, black dots) for n → eþ π − (left) and n → μþ π −(right) searches. The results from SK-I to SK-IV are combined.
The event selection is defined in the text.

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200 400 600 800 1000

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200
250

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750 1000 0

250

500

750 1000

2

total mass (MeV/c )FIG. 17. Total invariant mass and total momentum forn → lþ π − MC (top), atmospheric neutrino background MC
corresponding to about 2000 years live time of SK (middle),
and data (bottom) for n → eþ π − (left) and n → μþ π − (right)
searches. All the event selections except (F4) in Sec. IV D are
applied. The results from SK-I to SK-IV are combined. The signal
box is shown as a green box.

but above the cut threshold (250 MeV=c) and this event
fails final selection for this analysis.
E. n → l + ρ −The ρ− meson has a mass of 770 MeV=c2 and a width of
150 MeV, immediately decaying into π − π 0 with a branching ratio of nearly 100%.
The following event selection is used for this search:(G1) the number of Cherenkov rings is four for n → eþ ρ−and three for n → μþ ρ−,(G2) one of the rings is a nonshower ring,(G3) the ρ− mass is between 600 and 900 MeV=c2 ,(G4) the π 0 mass is between 85 and 185 MeV=c2 ,(G5) the number of Michel electrons is 0 for n → eþ ρ−
and 1 for n → μþ ρ−,(G6) the total momentum is less than 250 MeV=c forn → eþ ρ− and less than 150 MeV=c for n → μþ ρ− ;the total invariant mass is between 800 and
1050 MeV=c2 for n → eþ ρ−,(G7) the number of neutrons is 0 in SK-IV.
The tighter total momentum cut of Ptot < 150 MeV=c isapplied to reduce the background for the n → μþ ρ− mode
because the nucleon invariant mass cannot be reconstructed
for the mode due to the invisible muon.
Figure 19 shows the signal selection efficiency andthe number of expected background events at each event
selection step. The total mass and total momentum distributions are shown in Figs. 20 and 21.

FIG. 18. Total momentum for n → lþ π − MC (upper), atmospheric neutrino MC (lower, red histogram), and data (lower, black
circles) for n → eþ π − (left) and n → μþ π − (right) searches. All
the event selections except (F4) in Sec. IV D are applied. The
atmospheric neutrino MC is normalized to data by area. Resultsfrom SK-I to SK-IV are combined. The signal region corresponds
to the left side from the vertical green line. Total momentum forn → μþ π − data candidate is 205 MeV=c.

There are four data candidates (one in SK-I, one
in SK-II, and two in SK-III) in the n → eþ ρ− searchand one data candidate in SK-II in the n → μþ ρ− search.
The number of total expected background events is 0.87
for n → eþ ρ− and 0.96 for n → μþ ρ− searches. The
Poisson probability to observe four or more events is
+ -

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n→e ρ

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0

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events

0

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G1 G2 G3 G4 G5 G6 G7 G1 G2 G3 G4 G5 G6 G7

event selection

FIG. 19. The signal efficiencies (upper) and the number of
expected backgrounds (lower, red histogram) and data candidates(lower, black dots) for n → eþ ρ− (left) and n → μþ ρ− (right).
The results from SK-I to SK-IV are combined. The event
selection is defined in the text.

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1.2% for the n → eþ ρ− search. This is the lowest probability among all the nucleon decay searches and moredetails of these four events are described in Sec. V.
The one data candidate in SK-I in the n → eþ ρ− searchin this analysis was also selected in the previous analysis.
There is one SK-II data candidate in both the n → eþ ρ− andn → μþ ρ− searches in this analysis. Both events were notselected in the previous analysis because their total
momentum and mass were near the cut thresholds but
outside of the signal box.

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V. SEARCH RESULTS IN THE SK DATA

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750 1000

total mass (MeV/c2)

FIG. 20. Total invariant mass and total momentum forn → lþ ρ− MC (top), atmospheric neutrino background MC
corresponding to about 2000 years live time of SK (middle),
and data (bottom) for n → eþ ρ− (left) and n → μþ ρ− (right)
searches. All the event selections except (G6) in Sec. IV E are
applied. The results from SK-I to SK-IV are combined. For then → eþ ρ− search, the signal box is shown as a green box. For then → μþ ρ− search, no total mass cut is applied in the analysis andthe sharp cutoffs on the total mass correspond to the ρ− mass cut
threshold.

+ -

n→μ ρ

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150

200
100

events

50

100

0
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0
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200 400 600 800 1000

00200 400 600 800 1000

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FIG. 21. Total momentum for n → lþ ρ− MC (upper), atmospheric neutrino MC (lower, red histogram), and data (lower, black
circles) for n → eþ ρ− (left) and n → μþ ρ− (right) searches. All
the event selections except (G6) in Sec. IV E are applied. The
atmospheric neutrino MC is normalized to data by area. Resultsfrom SK-I to SK-IV are combined. The signal region corresponds
to the left side from the vertical green line. Total momenta ofthe data candidates are 173 MeV=c, 235 MeV=c, 239 MeV=c,
246 MeV=c for n → eþ ρ− search and 129 MeV=c for n → μþ ρ−search.

The signal selection efficiency, the number of the
expected atmospheric neutrino backgrounds, and the number of data candidate events for each SK period aresummarized in Table I.
For all the nucleon decay searches, the data and theatmospheric neutrino background MC agree with eachother in both the event rates along the event selections
and the relevant selection parameter distribution shapes
shown in Sec. IV. There is no significant excess of data
above the background expectation.
Thanks to the improvements of the 2008 electronics
and data acquisition upgrade, the Michel electron tagging
efficiency is higher and hence signal efficiency is improvedin SK-IV, especially for nucleon decay modes including μþ
in the final state. Likwise, the addition of neutron tagging
has reduced the atmospheric neutrino background rate in
SK-IV compared to SK-I-II-III while maintaining similar or
higher signal efficiency.
The classification of background atmospheric neutrino
interactions is shown in Table II. They are consistent withthe previous analysis (Table V in [11]) within the statisticalerrors.
There are 12 data candidates in total (all the event
displays in [26]). Back-to-back Cherenkov rings are visible
and events are reconstructed as expected. All of thecandidate events are near the total mass and momentum
cut thresholds. For the SK-I and SK-II data samples, whichhave been reanalyzed for this paper, event migrations
between the previous and current analysis can be explainedby slight differences in the reconstructed parameters due
to updates of the reconstruction algorithms as well as thedetector calibrations.
The number of expected background events and data
candidates as well as their Poisson probabilities are
summarized in Table III. The number of detected events
is consistent with the expected atmospheric neutrino background for all the searches.
The lowest probability (1.2%) is seen in the n → eþ ρ−
search. The number of events for each event selection
step (Fig. 19) is in agreement with expectation leading
up to the application of the momentum and mass signal
region. In total, there are four data candidates. Their total
invariant mass (MeV=c2 ) and total momentum (MeV=c)

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K. ABE et al.

PHYSICAL REVIEW D 96, 012003 (2017)

TABLE I. Summary of the signal efficiencies, the number of expected background events, and the number of data candidates for 91.5,
49.1, 31.8, and 143.8 kiloton · year exposure during SK-I, SK-II, SK-III, and SK-IV. For the p → lþ η, η → 2γ searches, “upper” and“lower” stand for 100 < Ptot < 250 MeV=c and Ptot < 100 MeV=c, respectively. Errors in the background events are statistical fromfinite MC statistics (about 500 years for each SK period). The number of expected background events scaled to 1 megaton · year are
shown in parentheses.
Modes

I

Efficiency (%)
II III IV

Background (events)
II
III

I

Candidate (events)
I
II
III
IV

IV

p → eþ η(2γ, upper) 11.0 10.9 10.7 9.8 0.170.04ð1.8Þ 0.100.02ð2.0Þ 0.050.01ð1.5Þ 0.130.04ð0.92Þ
(2γ, lower) 7.9 6.7 8.2 7.5 0.010.01ð0.09Þ 0.010.01ð0.18Þ 0.0030.003ð0.09Þ 0.010.01ð0.09Þ
(3π 0 )
8.0 8.2 7.6 7.7 0.150.03ð1.6Þ 0.060.02ð1.1Þ 0.060.01ð2.0Þ 0.030.02ð0.19Þ

0
0
0

0
0
0

0
0
0

0
0
0

p → μþ η(2γ, upper)(2γ, lower)(3π 0 )
p → eþ ρ 0
p → μþ ρ0

7.3
5.8
6.9
3.8
1.9

8.4 0.050.02ð0.54Þ 0.020.01ð0.31Þ
7.0
0þ0.006ð0Þ
0þ0.004ð0Þ
7.9 0.340.05ð3.7Þ 0.130.02ð2.7Þ
3.8 0.290.05ð3.2Þ 0.130.02ð2.6Þ
1.9 0.410.05ð4.4Þ 0.210.03ð4.4Þ

0.010.01ð0.28Þ
0þ0.003ð0Þ
0.120.02ð3.7Þ
0.050.01ð1.4Þ
0.130.02ð4.0Þ

0.030.01ð0.17Þ
0þ0.008ð0Þ
0.160.04ð1.1Þ
0.170.04ð1.2Þ
0.550.07ð3.8Þ

0
0
0
0
1

0
0
1
0
0

0
0
0
0
0

0
0
1
2
0

p → eþ ω(π 0 γ)(π þ π − π 0 )2.3 2.5 2.3 2.1 0.160.04ð1.7Þ 0.080.02ð1.6Þ
2.7 2.2 2.6 2.7 0.440.06ð4.8Þ 0.170.03ð3.4Þ

0.060.01ð1.8Þ
0.120.02ð3.9Þ

0.050.03ð0.36Þ
0.270.06ð1.8Þ

0
1

0
0

0
0

0
0

p → μþ ω(π 0 γ)(π þ π − π 0 )n → eþ π −n → μþ π −n → eþ ρ −n → μþ ρ−

2.6 3.0 3.1 3.3 0.180.04ð1.9Þ
3.1 2.6 3.2 4.6 0.190.03ð2.0Þ
12.7 12.2 13.5 12.6 0.170.04ð1.9Þ
11.3 10.7 11.5 13.4 0.290.04ð3.1Þ
1.4 1.1 1.4 1.5 0.360.05ð3.9Þ
1.0 1.0 1.1 1.2 0.340.04ð3.7Þ

0.080.01ð2.4Þ
0.080.01ð2.5Þ
0.070.01ð2.0Þ
0.090.01ð2.9Þ
0.140.02ð4.4Þ
0.140.02ð4.3Þ

0.070.03ð0.71Þ
0.290.05ð2.0Þ
0.120.04ð0.83Þ
0.240.05ð1.7Þ
0.240.06ð1.6Þ
0.340.06ð2.4Þ

0
0
0
0
1
0

0
0
0
0
1
1

0
0
0
1
2
0

0
0
0
0
0
0

6.5
5.6
6.2
3.3
1.3

7.2
6.0
6.9
3.6
2.2

0.100.02ð1.1Þ
0.100.02ð1.1Þ
0.050.01ð1.1Þ
0.150.02ð3.0Þ
0.130.02ð2.7Þ
0.140.02ð2.8Þ

are (884.7, 245.5), (821.5, 239.1), (897.7, 235.4), and(807.8, 173.2), respectively. Every candidate event is near
the threshold of the selection window of the total massand the momentum cut. The total invariant mass andmomentum plots (Figs. 20 and 21) show that the data
distributions agree with the expected atmospheric neutrino
background distributions. Overall, we have concluded thatthe observed data candidates are due to atmospheric
neutrino backgrounds.
The estimated signal efficiencies for n → lþ π − with the
charged pion in the final state are lower in this analysis thanthe previous analysis. For example, the signal efficiency for
TABLE II. The breakdown (percentage contribution) of theneutrino interaction modes of the background events [16].
The breakdowns are calculated by adding background events ofthe modes decaying into each meson from SK-I to SK-IV in total.
Mode
CCQE
CC 1-πCC multi-π
CC othersNC

p → l þ η p → l þ ρ p → l þ ω n → lþ π n → lþ ρ
4
27
21
23
25

9
59
10
1
21

1
27
32
8
32

22
53
11
3
12

4
45
13
3
35

TABLE III. Summary of the nucleon decay searches. The
number of events are summed from SK-I to SK-IV and for all
the meson decay modes for each nucleon decay search. The
events in the total signal box are shown for the p → lþ η search.
The number of the expected atmospheric background events,
along with systematic errors (see Table V for more details), isshown in the second column. The Poisson probability to observe
events greater than or equal to the number of data candidates,
without considering the systematic uncertainty in the background, is shown in the fourth column.

Modes

Lifetime Limit
Background Candidate Probability (×1033 years)(events)(events)(%)
at 90% CL

p→eþ η
p→μþ η
p→eþ ρ0p→μþ ρ0p→eþ ω
p→μþ ω
n→eþ π −n→μþ π −n→eþ ρ−n→μþ ρ−0.78  0.30
0.85  0.23
0.64  0.17
1.30  0.33
1.35  0.43
1.09  0.52
0.41  0.13
0.77  0.20
0.87  0.26
0.96  0.28

0
2
2
1
1
0
0
1
4
1


20.9
13.5
72.7
74.1


53.7
1.2
61.7

10.
4.7
0.72
0.57
1.6
2.8
5.3
3.5
0.03
0.06

8.6

12

15.7



total

012003-14

SEARCH FOR NUCLEON DECAY INTO CHARGED …

PHYSICAL REVIEW D 96, 012003 (2017)þ −the n → e π search in SK-I decreased from 19.4% to12.7%. This is due to the improved pion interaction model
which better matches external data. As shown in Fig. 2, thecross sections for all the interactions are increased around
500 MeV=c. The larger cross sections reduce the numberof the visible Cherenkov rings, with reduction of theestimated signal efficiency mainly coming from the corresponding event selection.
A. Systematic errors
The total systematic errors in the signal efficiency andthe number of expected background events are summarizedin Tables IV and V. The systematic error sources consistof uncertainties of physics models in the nucleon decay
MC, the atmospheric neutrino background MC, and event
reconstruction performance. The systematic error estimation methods are the same as in the previous analysis, withseveral improvements that allow us to significantly reduce
the errors.
Table IV shows the systematic errors in the signal
efficiencies for each systematic error source. The dominantsystematic errors come from uncertainties of the meson
interactions in the oxygen nucleus (meson nuclear effect).
The meson nuclear effect errors are smaller in the lower
signal box for p → lþ η and η → 2γ searches thanks to thelarge fraction of the free proton decays.
In this analysis, the systematic uncertainties of pion
interactions are evaluated by varying the tuning parameters of the interaction models within 1σ uncertaintiesof π  -nucleus experimental data. This method provides
a more reliable evaluation of systematic uncertainties
of the pion interactions compared to the previous paper[11], especially for higher-momentum ð≥500 MeV=cÞ
pions. This method leads to relatively smaller systematic
uncertainties of the pion interactions in signal and atmospheric neutrino background events than the previous
analysis.
In the previous analysis [11] the uncertainty in Fermi
momentum distribution was estimated by artificially rescaling the distribution by 20%. While being simple, this is arather crude procedure. In this work, we improve andprovide a more precise uncertainty estimate by directlycomparing the momentum distributions, simulated using aspectral function fit to the 12 C electron scattering data [15],to the simulated atmospheric background momentum distribution from NEUT, which uses a relativistic Fermi gas
model. The difference between the two is taken as asystematic error.
Uncertainties associated with event reconstruction are
implemented as detector performance errors. The error
sources include: vertex position, number of Cherenkov
rings, particle identification (e=μ separation), the number ofMichel electrons, and the energy scale. In the previous
study, the error estimate was overly conservative andincluded an additional contribution from the effects ofartificially shifting the vertex by 30 cm. We do not adopt
such a contribution in this work.
Table V shows the systematic errors in the number of
expected background events for each systematic error
source. After the event selection, the raw number of theremaining expected background events is either zero or one
in the lower signal box for p → lþ η, η → 2γ searches.
Therefore, the systematic errors are estimated in the totalbox (Ptot < 250 MeV=c) and assumed to be the same both

TABLE IV. Summary of systematic errors (percentage contribution) on signal efficiencies for each error source. The errors from SK-I
to SK-IV are averaged by the live time. For p → lþ η, η → 2γ searches, “upper” and “lower” stand for 100 < Ptot < 250 MeV=c andPtot < 100 MeV=c, respectively.
Modes
p → eþ η (2γ, upper)

p → eþ η (2γ, lower)
p → eþ η (3π 0 )p → μþ η (2γ, upper)p → μþ η (2γ, lower)p → μþ η (3π 0 )p → eþ ρ 0
p → μþ ρ0
p → eþ ω (π 0 γ)
p → eþ ω (π þ π − π 0 )p → μþ ω (π 0 γ)
p → μþ ω (π þ π − π 0 )n → eþ π −n → μþ π −n → eþ ρ −n → μþ ρ−

Meson nuclear
effectHadron propagationin waterN-N correlated
decay

Fermi
momentum

Detector
performances

Total

26
9
12
27
11
17
9
10
14
14
14
24
13
15
60
48







13
9

6

5
7
7
3
5

8
3
4
9
3
6
1
1
3
3
1
2
11
10
9
3

9
13
15
10
12
2
4
2
14
0.4
2
1
1
3
5
12

2
2
4
3
3
5
6
10
4
7
3
4
4
4
5
8

29
16
20
30
17
19
17
17
20
17
14
25
19
20
61
50

012003-15

K. ABE et al.

PHYSICAL REVIEW D 96, 012003 (2017)

TABLE V. Summary of systematic errors (percentage contribution) on the number of expected background events for each error
source. The errors from SK-I to SK-IV are averaged by the live time. For p → lþ η, η → 2γ searches, “upper” and “lower” stand for
100 < Ptot < 250 MeV=c and Ptot < 100 MeV=c, respectively.
Modes
p → eþ η (2γ, upper)
p → eþ η (2γ, lower)
p → eþ η (3π 0 )p → μþ η (2γ, upper)p → μþ η (2γ, lower)p → μþ η (3π 0 )p → eþ ρ 0
p → μþ ρ0
p → eþ ω (π 0 γ)
p → eþ ω (π þ π − π 0 )p → μþ ω (π 0 γ)
p → μþ ω (π þ π − π 0 )n → eþ π −n → μþ π −n → eþ ρ −n → μþ ρ−

Neutrino
flux

Neutrino
cross section

Pion nuclear
effectHadron propagationin water

Detector
performances

Total

8
8
8
9
9
8
4
7
8
6
8
8
7
8
7
5

15
15
12
15
15
12
18
16
15
15
13
10
17
16
16
20

12
12
34
14
14
9
10
5
21
7
18
22
6
3
15
15

5
5
17
8
8
13
7
11
5
14
8
46
10
6
16
4

21
21
30
28
28
12
15
14
32
17
28
16
24
17
11
14

30
30
51
37
37
25
27
25
42
28
37
55
32
26
30
29

in the upper and lower boxes. With the improved error
estimation method, the systematic errors in the mostdominant systematic error source in the previous analysis,
hadron propagation in water, are reduced by a factor ofthree to five in this analysis.
B. Lifetime limit
All of the observed events are consistent with the
expected backgrounds and nucleon lifetime limits arecalculated as in [7,11] using the Bayes method to incorporate systematic uncertainty. The limits are calculated by
combining different search methods as well as different SK
periods for each nucleon decay search. All of the nucleon
decay searches except p → lþ η have four measurements
corresponding to four SK periods. As in the previous
analysis, the signal efficiencies and the backgrounds areadded for p → lþ ω mode with two different meson decay
modes ω → π 0 γ and ω → π þ π − π 0 . There are 12 measurements for p → lþ η searches corresponding to three methods per each of the four SK periods, where the threemethods come from upper and lower signal boxes forη → 2γ search and one signal box for η → 3π 0 search.
The conditional probability distribution for each nucleon
decay rate is expressed as
ZZZPðΓjni Þ ¼e−ðΓλi ϵi þbi Þ ðΓλi ϵi þ bi Þni
ni !

× PðΓÞPðλi ÞPðϵi ÞPðbi Þdλi dϵi dbi ;ð4Þ

where ni is the number of data candidate events in the ithmeasurement, λi is the true detector exposure, ϵi is thetrue selection efficiency, and bi is the true number ofbackground events. The decay rate prior probability
distribution PðΓÞ is 1 for Γ ≥ 0 and otherwise 0. Pðλi Þ,Pðϵi Þ, and Pðbi Þ are the prior probability distributions
for detector exposure, efficiency, and background, respectively, which are assumed to be Gaussian distributions.
The uncertainty on the exposure is assumed to be 1% for
all SK periods.
The upper limit of the nucleon decay rate, Γlimit , isR Γlimit QNPðΓjni ÞdΓ
QNi¼1;
CL ¼ RΓ¼0∞
i¼1 PðΓjni ÞdΓ
Γ¼0

ð5Þ

where N is the number of measurements for each nucleon
decay search and CL is the confidence level taken to be
90%. The partial lower lifetime limit for each nucleon
decay mode is given by
τ=B ¼

1
Γlimit:ð6Þ

The nucleon partial lifetime limits at 90% confidence
level are summarized in Table III. The limits range from3 × 1031 to 1 × 1034 years. Thanks to the addition of SK-III
and SK-IV data and various analysis improvements, thelifetime limits published in this paper are typically higher
than those in the previous analysis by a factor of two to
three, as shown in Fig. 22. However, some channels show
similar or even lower limits due to more observed data
candidates.
Figure 22 compares the updated SK results with the otherexperiments: IMB-3 [27], KAMIOKANDE-I+II [28], and
FREJUS [29]. The updated SK results are better than those

012003-16

SEARCH FOR NUCLEON DECAY INTO CHARGED …

PHYSICAL REVIEW D 96, 012003 (2017)

data [11] has been updated to include improved event
reconstruction algorithms, event selections, systematic
error estimations, and an additional 0.175 megaton · years
of SK-III and SK-IV data. A similar update for thep → lþ π 0 search by Super-Kamiokande has also been
published recently [7].
Using 0.316 megaton · years of data, no significant
excess is found above the expected atmospheric neutrino
background. The number and features of candidate eventsare consistent with the background estimation by theatmospheric neutrino MC. Therefore, partial lifetime limits
are set ranging from 3 × 1031 to 1 × 1034 years at 90% confidence level depending on the nucleon decay mode. The
lifetime limits are summarized in Table III.
Most of the results presented here are world-best limits,and they further constrain the relevant GUT models.

p → e+ π0
p → μ+ π0
p → e+ η
p → μ+ η
p → e+ ρ0

SK I-IVSK I-II
IMB-3
Kam-I+II
FREJUSp→μ ρ+

0

p → e+ ω
p → μ+ ωn → e+ πn → μ+ πn → e+ ρn → μ+ ρ31

10

32

10

33

10

34

10

35

10

ACKNOWLEDGMENTS

Lifetime limit (years)

The survey of nucleon decay into charged antilepton plus
meson by Super-Kamiokande based on only SK-I and SK-II

We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande experiment has been built and operated fromfunding by the Japanese Ministry of Education, Culture,
Sports, Science and Technology, the U.S. Department ofEnergy, and the U.S. National Science Foundation. Someof us have been supported by funds from the National
Research Foundation of Korea NRF-2009-0083526(KNRC) funded by the Ministry of Science, ICT, andFuture Planning, the European Union H2020 RISEGA641540-SKPLUS, the Japan Society for the
Promotion of Science, the National Natural Science
Foundation of China under Grants No. 11235006, theNational Science and Engineering Research Council(NSERC) of Canada, the Scinet and Westgrid consortia
of Compute Canada, and the National Science Centre of
Poland (2015/17/N/ST2/04064, 2015/18/E/ST2/00758).

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