PHYSICAL REVIEW D 101, 052011 (2020)

Search for proton decay into three charged leptons in 0.37 megaton-years
exposure of the Super-Kamiokande
M. Tanaka ,43 K. Abe,1,42 C. Bronner,1 Y. Hayato,1,42 M. Ikeda,1 S. Imaizumi,1 H. Ito,1 J. Kameda,1,42 Y. Kataoka,1
Y. Kato,1 Y. Kishimoto,1,42 Ll. Marti,1 M. Miura,1,42 S. Moriyama,1,42 T. Mochizuki,1 M. Nakahata,1,42 Y. Nakajima,1,42
S. Nakayama,1,42 T. Okada,1 K. Okamoto,1 A. Orii,1 G. Pronost,1 H. Sekiya,1,42 M. Shiozawa,1,42 Y. Sonoda,1 A. Takeda,1,42
A. Takenaka,1 H. Tanaka,1 T. Yano,1 R. Akutsu,2 T. Kajita,2,42 K. Okumura,2,42 R. Wang,2 J. Xia,2 D. Bravo-Berguño,3
L. Labarga,3 P. Fernandez,3 F. d. M. Blaszczyk,4 E. Kearns,4,42 J. L. Raaf,4 J. L. Stone,4,42 L. Wan,4 T. Wester,4 J. Bian,5N. J. Griskevich,5 W. R. Kropp,5 S. Locke,5 S. Mine,5 M. B. Smy,5,42 H. W. Sobel,5,42 V. Takhistov,5,* P. Weatherly,5 J. Hill,6J. Y. Kim,7 I. T. Lim,7 R. G. Park,7 B. Bodur,8 K. Scholberg,8,42 C. W. Walter,8,42 A. Coffani,9 O. Drapier,9 S. El Hedri,9M. Gonin,9 Th. A. Mueller,9 P. Paganini,9 T. Ishizuka,10 T. Nakamura,11 J. S. Jang,12 J. G. Learned,13 S. Matsuno,13
R. P. Litchfield,14 A. A. Sztuc,14 Y. Uchida,14 V. Berardi,15 M. G. Catanesi,15 E. Radicioni,15 N. F. Calabria,16 G. De Rosa,16
G. Collazuol,17 F. Iacob,17 L. Ludovici,18 Y. Nishimura,20 S. Cao,21 M. Friend,21 T. Hasegawa,21 T. Ishida,21 T. Kobayashi,21T. Nakadaira,21 K. Nakamura,21,42 Y. Oyama,21 K. Sakashita,21 T. Sekiguchi,21 T. Tsukamoto,21 M. Hasegawa,22 Y. Isobe,22
H. Miyabe,22 Y. Nakano,22 T. Shiozawa,22 T. Sugimoto,22 A. T. Suzuki,22 Y. Takeuchi,22,42 A. Ali,23 Y. Ashida,23 S. Hirota,23
M. Jiang,23 T. Kikawa,23 M. Mori,23 KE. Nakamura,23 T. Nakaya,23,42 R. A. Wendell,23,42 L. H. V. Anthony,24
N. McCauley,24 P. Mehta,24 A. Pritchard,24 K. M. Tsui,24 Y. Fukuda,25 Y. Itow,26,27 T. Niwa,26 M. Taani,26,† M. Tsukada,26
P. Mijakowski,28 K. Frankiewicz,28 C. K. Jung,29 C. Vilela,29 M. J. Wilking,29 C. Yanagisawa,29,‡ D. Fukuda,30 M. Harada,30
K. Hagiwara,30 T. Horai,30 H. Ishino,30 S. Ito,30 Y. Koshio,30,42 M. Sakuda,30 Y. Takahira,30 C. Xu,30 Y. Kuno,31 D. Barrow,32
L. Cook,32,42 C. Simpson,32,42 D. Wark,32,37 F. Nova,33 T. Boschi,19,§ F. Di Lodovico,19 S. Molina Sedgwick,19,§
S. Zsoldos,19 S. B. Kim,34 J. Y. Yang,34 M. Thiesse,35 L. Thompson,35 H. Okazawa,36 Y. Choi,38 K. Nishijima,39
M. Koshiba,40 M. Yokoyama,41,42 A. Goldsack,42,32 K. Martens,42 B. Quilain,42 Y. Suzuki,42 M. R. Vagins,42,5 M. Kuze,43
T. Yoshida,43 M. Ishitsuka,44 R. Matsumoto,44 K. Ohta,44 J. F. Martin,45 C. M. Nantais,45 H. A. Tanaka,45 T. Towstego,45
M. Hartz,46 A. Konaka,46 P. de Perio,46 N. W. Prouse,46 S. Chen,47 B. D. Xu,47 B. Richards,48 B. Jamieson,49 J. Walker,49
A. Minamino,50 K. Okamoto,50 and G. Pintaudi50(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, Massachusetts 02215, 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
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, F-91120 Palaiseau, France
10
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
11
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
12
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
13
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
14
Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
15
Dipartimento Interuniversitario di Fisica, INFN Sezione di Bari and Università e Politecnico di Bari,
I-70125 Bari, Italy
16
Dipartimento di Fisica, INFN Sezione di Napoli and Università di Napoli, I-80126 Napoli, Italy
17
Dipartimento di Fisica, INFN Sezione di Padova and Università di Padova, I-35131 Padova, Italy
18
INFN Sezione di Roma and Università di Roma “La Sapienza”, I-00185 Roma, Italy
19
Department of Physics, King’s College London, London WC2R 2LS, United Kingdom
20
Department of Physics, Keio University, Yokohama, Kanagawa 223-8522, Japan
21
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
22
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
23
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan

2470-0010=2020=101(5)=052011(12)052011-1

Published by the American Physical Society

M. TANAKA et al.

PHYS. REV. D 101, 052011 (2020)
24

Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
26
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan
27
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University,
Nagoya, Aichi 464-8602, Japan
28
National Centre For Nuclear Research, 02-093 Warsaw, Poland
29
Department of Physics and Astronomy, State University of New York at Stony Brook,
New York 11794-3800, USA
30
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
31
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
32
Department of Physics, Oxford University, Oxford OX1 3PU, United Kingdom
33
Rutherford Appleton Laboratory, Harwell, Oxford OX11 0QX, United Kingdom
34
Department of Physics, Seoul National University, Seoul 151-742, Korea
35
Department of Physics and Astronomy, University of Sheffield, S3 7RH Sheffield, United Kingdom
36
Department of Informatics in Social Welfare, Shizuoka University of Welfare,
Yaizu, Shizuoka 425-8611, Japan
37
STFC, Rutherford Appleton Laboratory, Harwell, Oxford and Daresbury Laboratory,
Warrington OX11 0QX, United Kingdom
38
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
39
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
40
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
41
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
42
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
43
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
44
Department of Physics, Faculty of Science and Technology, Tokyo University of Science,
Noda, Chiba 278-8510, Japan
45
Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
46
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T2A3, Canada
47
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
48
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
49
Department of Physics, University of Winnipeg, Manitoba R3J 3L8, Canada
50
Faculty of Engineering, Yokohama National University, Yokohama, Kanagawa 240-8501, Japan
25(Received 30 January 2020; accepted 28 February 2020; published 25 March 2020)
A search for proton decay into three charged leptons has been performed by using 0.37 Mton · years ofdata collected in Super-Kamiokande. All possible combinations of electrons, muons, and their antiparticles
consistent with charge conservation were considered as decay modes. No significant excess of events has
been found over the background, and lower limits on the proton lifetime divided by the branching ratio
have been obtained. The limits range between 9.2 × 1033 and 3.4 × 1034 years at 90% confidence level,
improving by more than an order of magnitude upon limits from previous experiments. A first limit has
been set for the p → μ− eþ eþ mode.
DOI: 10.1103/PhysRevD.101.052011*

Also at Department of Physics and Astronomy, UCLA,
California 90095-1547, USA.
†
Also at School of Physics and Astronomy, University of
Edinburgh, Edinburgh EH9 3FD, United Kingdom.
‡
Also at BMCC/CUNY, Science Department, New York,New York, USA.
§
Present address: Queen Mary University of London, London
E1 4NS, United Kingdom.
Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
and DOI. Funded by SCOAP3.

I. INTRODUCTION
The Standard Model of elementary particles describes
strong, weak, and electromagnetic interactions based ongauge symmetries. Grand unified theories (GUTs) [1] canunify three interactions in the Standard Model in a single
gauge group with one coupling constant. In most GUTs,
grand unification is predicted typically at 1015–16 GeV
which is unreachable by accelerators, whereas the effectsof the grand unification might be detected through rare
phenomena beyond the Standard Model. The most promising such phenomenon is violation of baryon number, and052011-2

SEARCH FOR PROTON DECAY INTO THREE CHARGED …
the most sought after signature is proton decay [2]. The
Super-Kamiokande (SK) experiment has been leading thesearch for proton decay and has set the most stringent limits
on the lifetime for various channels predicted by GUT
models. For example, the p → eþ π 0 and p → ν̄K þ arefavored decay modes in nonsupersymmetric and TeV-scale
supersymmetric GUT models, respectively, yet no significant signal was observed, excluding proton lifetimes up to1034 years [3,4]. The simplest unification model, minimal
SU(5) [5], has been ruled out by SK and earlier experiments. Other nucleon decay channels motivated by unification, such as the charged antilepton plus meson
channels were searched for in SK recently; no proton
decay signal was found [6].
However, baryon number may be violated irrespective of
GUTs and is expected in many scenarios beyond theStandard Model [7]. If the usual lower dimensional
operators responsible for p → eþ π 0 etc. are suppressed,then different proton decay channels can dominate fromhigher dimensional operators. This can naturally occur
when considering lepton flavor symmetries [8]. In this case,trilepton nucleon decay channels such as p → μ− eþ eþ or
p → e− μþ μþ can be dominant. As they are generated from
effective dimension d ¼ 10 operators, these processes
probe scales of around 100 TeV. A minimal model forthis based on leptoquarks has been put forward in Ref. [8],which also suggested that such processes could be connected to the recent anomalies observed in B-meson
decays.
Some of these decay modes were already searched for by
the Irvine-Michigan-Brookhaven-3 (IMB-3) [9] andHarvard-Purdue-Wisconsin (HPW) [10] experiments. The
data were consistent with the expected background in bothexperiments and no significant signal was confirmed.
Lifetime limits were set to be 1030 –1032 years for eachdecay mode. SK can significantly extend the experimental
search of the previous experiments. Lifetime limits on thesemodes theoretically derived from published searches inother channels are reported in Ref. [11]. Although thederived limits are typically much more restrictive, they arecalculated for a minimal effective Lagrangian whose origin
is at the GUT scale. Therefore, a positive result from oursearches would indicate beyond-the-Standard-Model physics at lower energy scales.
II. THE SUPER-KAMIOKANDE EXPERIMENT
SK is the largest pure water Cherenkov detector, locatedat the Kamioka mine in Gifu prefecture, Japan. The SK
detector consists of a stainless steel tank (39.3 m diameter,
41.4 m height), 50 kton of ultrapure water, and photomultiplier tubes (PMTs). In order to reduce cosmic ray
muon background, the detector is located 1000 m under the
peak of Mt. Ikenoyama (2700 m water equivalent). The
water tank is optically separated into two concentric
cylindrical volumes by the support frames equipped with

PHYS. REV. D 101, 052011 (2020)

inward-facing 20-inch and outward-facing 8-inch PMTs.
The inner volume is 33.8 m in diameter and 36.2 m inheight and is called the inner detector (ID). The ID contains
32 kton of water and monitored by 11,129 inward facing
PMTs (about half for certain period as explained later).
Outside of the ID is a 2 m thick water outer detector (OD).
The OD is monitored by outward-facing 1885 PMTs andmainly serves as an active cosmic ray muon veto as well asa shield against gamma rays from surrounding rock. Thereare 20- and 8-inch PMTs uniformly mounted on the ID and
OD surfaces, respectively. The details of SK detector aredescribed elsewhere [12,13].
The analysis in this paper uses data taken with four
different detector configurations. SK-I started in 1996 andstopped in 2001 for maintenance. SK-II was operated from2002 to 2005 with about half the number of ID PMTs
compared to SK-I due to the accident during the maintenance work after SK-I. In order to avoid further such
accidents, the PMTs were protected by covers made of fiber
reinforced plastic and acrylic for the photocathode startingfrom SK-II. SK-III started in 2006 and stopped in 2008.
The number of PMTs in SK-III was recovered to almost thesame number as SK-I. Readout electronics and dataacquisition system were upgraded for the SK-IV period.
SK-IV continued from 2008 and ended for the upgrade of
SK in May 2018. Photo coverage of the ID is 19% in SK-II
and 40% in other periods.
In this analysis, all the detected particles must be fully
contained in the ID with the reconstructed vertex inside thefiducial volume (FV). Such events are selected by preselection cuts [3,4,6]. The FV is defined as the volume 2 minside the top, bottom, and barrel walls of the ID andcorresponds to 22.5 kton mass. Contamination of nonneutrino background events due to cosmic muons is
negligible after the preselection cuts. Data around 1 msof the expected neutrino beam arrival timing from the Japan
Proton Accelerator Research Complex, which has a repetition rate of 2.48 s, have been removed. All the available
data from SK-I to SK-IV are used in this analysis. We use
the data of 372.6 kton · years in total by summing up 91.7,
49.2, 31.9, and 199.8 kton · years of SK-I, II, III, and IV
data, respectively.
III. SIMULATION
H2 O molecules are the sources of proton decay in SK
searches, with two protons from hydrogen and eight
protons from oxygen. In the simulation, only a uniform
phase space is assumed for kinematics of outgoing charged
leptons and any additional correlations are not taken into
account. The protons in hydrogen (free protons) have an
initial mass and momentum of 938.27 MeV=c2 and
0 MeV=c, respectively. On the other hand, the protons
in oxygen (bound protons) interact with other nucleons andhave some initial momentum. In the simulation, three
nuclear effects are taken into account: nuclear binding

052011-3

M. TANAKA et al.

PHYS. REV. D 101, 052011 (2020)

energies in 16O, Fermi motion, and correlated decay. Twonuclear binding energies (p state and s state) are accounted
for with Gaussian spreads and are subtracted from theinitial proton mass [6]. Fermi motion is estimated based onelectron-12C scattering data [14]. The bound proton sometimes correlates with the surrounding nucleons during its
decay. This effect is predicted to occur with 10% probability and produces a broad distribution at lower mass inproton mass distribution [15].
For the background, only atmospheric neutrino eventsare considered since other non-neutrino backgrounds are
negligibly small. The simulation of this sample consists ofthree steps: neutrino production in the atmosphere (neutrino flux prediction), neutrino interaction with water, andparticle tracking in the detector. The flux of atmospheric
neutrinos is calculated by the model of Honda et al.
[16,17]. The interactions of atmospheric neutrinos withhydrogen or oxygen nuclei in water are simulated by the
NEUT program [18]. This simulation covers a wide
neutrino energy range from several tens of MeV tohundreds of TeV. Hadrons generated by neutrino interactions in the oxygen nucleus often cause secondaryinteractions within the nucleus. The interactions of pions,
kaons, etas, and nucleons in the target nucleus are simulated in NEUT by using a cascade model [18,19].
Simulated data samples equivalent to 500 years of detector
exposure are generated for each SK period.
The particle propagation, Cherenkov radiation, propagation of Cherenkov photons in water and PMTs, andelectronics response are simulated by a GEANT3 based
package [20] with custom modifications for use in SK, suchas pion interactions in water and wavelength-dependent
water transparency.
The simulation scheme for the signal sample is the same
as for the other recent SK nucleon decay searches [3,4,6],
and the latest SK oscillation analysis [21] for backgroundsample. The oscillation parameters are taken from the latest
atmospheric neutrino oscillation analysis [21].
IV. EVENT RECONSTRUCTION
Events with charged particles are reconstructed byusing charge and time information of the hit PMTs.
A reconstruction scheme consists of vertex fitting, ringcounting, particle identification (PID), momentum
reconstruction, Michel electron search, and neutron tagging.
The reconstruction method is almost the same as the oneused in other recent nucleon decay searches [3,4,6] oroscillation studies [21] in SK. Some updates for charge
separation and neutron tagging improve the sensitivity ofthis search.
In the first step, the vertex is reconstructed by assumingthat Cherenkov light comes from one point at the sametime. Then the ring edge and the direction of the ring are
estimated. Finally, the vertex is reconstructed more

precisely by assuming that photons are emitted along the
track of the charged particle.
Cherenkov rings are then reconstructed by using thepattern recognition algorithm known as the Hough transformation [22]. Ring candidates are evaluated by a likelihood method to determine if they are true or fake. In casemore than one ring (multiring) is identified, the contribution of each ring to the detected photoelectrons in each
PMT is estimated. The opening angle of the ring can becalculated from the reconstructed vertex position and theedge of the ring. The final stage of ring counting uses aring’s angle relative to other rings and visible energy todiscard the candidate rings mostly caused by multiple
Coulomb scattering of charged particles.
Reconstructed rings can be classified as electronke(e like) or muonlike (μ like) by using the pattern of
PMT hits. Cherenkov rings of muons tend to have clear
ring edges. In contrast, Cherenkov rings of electrons tend to
be relatively diffuse due to electromagnetic showers andscattering. Expected PMT charge patterns for electrons andmuons are compared with observed hit patterns using alikelihood function. Information about the opening angle isincluded in the likelihood function. With the emission of
Cherenkov rings, gamma rays are usually identified as elike and charged pions as μ like.
The momentum of the charged particle is reconstructedfrom the total number of photoelectrons in a 70 degree conearound the ring, which is corrected by using a conversion
table depending on the particle type. We correct for time
drift of the gain, which varies according to the year of PMT
manufacture. For the multiring case, the expected charge
distribution for each ring is calculated. Then the momentum is assigned to each ring according to the fraction of
expected charge. For this charge separation algorithm, theexpected charge in the backward direction of a μ-like ring
was tuned to reproduce the data. The precision of total mass
reconstruction was improved with this tuning, especiallyfor the p → μþ μþ μ− events. The energy scale of thedetector is checked precisely by using Michel electrons,
stopping muons and neutral pion samples [21].
Michel electrons are tagged by searching for PMT hit
clusters after the primary event. Since about 20% of μ− iscaptured by nuclei and do not emit a decay electron, thetagging efficiency for μ− is lower than that for μþ.
Free neutrons traveling in water are thermalized andcaptured by oxygen or hydrogen nuclei. Neutrons are
predominantly captured by the interaction nþp → dþγ(2.2 MeV). This 2.2 MeV gamma ray signal is searched for
to identify the neutron (neutron tagging). The capture
signal occurs a few hundred microseconds after the initial
neutrino interaction signal, and the tagging was possible
only with the improved electronics introduced in SK-IV.
The performance of the neutron tagging was recently
improved by lowering the neutron tagging threshold (themaximum number of hit PMTs within a 10 ns sliding time

052011-4

SEARCH FOR PROTON DECAY INTO THREE CHARGED …
window) thanks to an additional cut on the continuous darknoise hits after one initial dark noise pulse and newparameters in the neural network. The tagging efficiency
was improved from 22% [23] to 25%.
V. EVENT SELECTION
The following selection criteria are applied to separate
proton decay signals from atmospheric neutrino background events. The selection criteria resemble those ofother recent SK nucleon decay searches [3,6]. The same
selections are applied to the data and MC simulation (bothproton decay signal and atmospheric neutrino background).
C1: There must be three reconstructed Cherenkov rings.
C2: PID of Cherenkov rings must be consistent with the
decay mode. For example, there must be one e-likering and two μ-like rings for the p → eþ μþ μ− and p →e− μþ μþ decay modes. SK cannot tell the charge of the
final state lepton, so that cuts and backgrounds for thep → μþ eþ e− and p → μ− eþ eþ (p → eþ μþ μ− andp → e− μþ μþ ) are essentially the same.
C3: Numbers of decay electrons should be 0 for thep → eþ eþ e− , 1 for the p → μþ eþ e− (p → μ− eþ eþ ),2 for the p → eþ μþ μ− (p → e− μþ μþ ), and two or
three for the p → μþ μþ μ− decay modes.
C4: Total mass (M tot ) and momentum (Ptot ) of three-ring
events should satisfy 800 < M tot < 1050 MeV=c2 andPtot < 250 MeV=c. In the p → μþ eþ e− (p → μ− eþ eþ )mode, one additional cut is used. The invariant mass of
two e-like rings events should be above 185 MeV=c2 .
C5: There should be no tagged neutron (only for SK-IV).
These cuts are applied to reduce atmospheric neutrino
background, mainly deep inelastic scattering (DIS), basedon the kinematics of the outgoing charged particles. Signal
selection efficiencies of the C1 cut are lower for decay
modes with more muons as shown in Fig. 1. This is due tothe higher Cherenkov threshold for muons compared to thatfor electrons. More than 90% of atmospheric neutrino
background events are rejected by requiring three rings.
The C3 cut requires a number of Michel electrons
depending on the number of muons in the final state.
For the p → μþ μþ μ− mode, two or three decay electrons
are required to keep a good signal efficiency. The signal
efficiency of this cut depends on the charge and number ofmuons as the tagging efficiency of Michel electrons for μþ
is higher than that for μ−. For example, efficiency for p →μþ eþ e− is higher than that for the p → μ− eþ eþ .
After the C3 cut is applied, the main background for thep → μþ eþ e− mode is νμ charged-current (CC) π 0 production events, in which a π 0 decays to two gamma rays and is
identified as two e-like rings. Such background can be
reduced by requiring the invariant total mass of two e-likerings to be different from the π 0 mass (C4 cut for one-muonmode). CC π 0 production events are the dominant background to the p → eþ eþ e− as well (incoming neutrino is νe

PHYS. REV. D 101, 052011 (2020)in this case). However, since the background rejection is
not beneficial to the sensitivity, a cut on the invariant
mass for two e-like rings is not applied for the p →eþ eþ e− mode.
Total mass and momentum cuts (C4) are the mosteffective cut in this analysis. They require that the kinematics of three charged particles is consistent with thatfrom proton decay signals, i.e., their invariant mass should
be consistent with the proton mass and the total momentum
should be below the upper limit of Fermi motion of protons
in oxygen nuclei (the momentum of the proton is zero forfree protons). The lower and higher tails of the proton massand momentum distributions become larger due to effectsof correlated decay.
The probability for a neutron to be emitted by deexcitation of a nucleus after proton decay is estimated to bea few percent [24]. On the other hand, neutrons are often
emitted in the background process, dominated by DIS
interactions of atmospheric neutrinos in water. By applying
the C5 cut, about half of the background events are rejected
while more than 90% of the signal events are kept.
The number of events (data), the signal efficiency, andthe expected background along with the event rates after
selection for each proton decay mode are shown in Fig. 1.
Scatter plots of total mass and momentum for signal andbackground MC are shown in Fig. 2. Two signal boxes aredefined: a lower signal box (Ptot < 100 MeV=c) and an
upper signal box (100 < Ptot < 250 MeV=c). The lower
signal box is almost background free and is dominated byfree protons, while the proton bound in the oxygen nucleus
is dominant in the upper signal box. Signal efficiency andexpected background events after all selections are summarized in Table I. Fractions of each neutrino interaction
mode in the remaining background events are summarizedin Table II. The dominant background is single or multipion
production events for all decay modes.
VI. SYSTEMATIC UNCERTAINTIESDominant systematic uncertainties for the signal efficiency are associated with the uncertainties in correlated
decay and Fermi motion models. Since the mechanism ofcorrelated decay is not well understood, variation of thesignal efficiency was evaluated with 0% and 20% probabilities of correlated decay compared to our nominal
estimate of 10%, and the spread was taken as the uncertainty. In the simulation of the signal, Fermi motion issimulated based on the electron-12C scattering experiment[14]. On the other hand, the Fermi motion model for the
background sample is based on the Fermi gas model. Thismodel difference is considered as a source of systematic
uncertainty.
For the background, systematic uncertainties on theneutrino flux and cross section models are taken into
account in the estimated background rates. These uncertainties are estimated by an event-by-event weighting

052011-5

M. TANAKA et al.

PHYS. REV. D 101, 052011 (2020)
p→e+e+e-

70
60
50
40

C2

C3

C4

60
50
40

C5

70
60
50
40
30

C1

C2

C3

C4

C5

103

102

102

102

10

Events103

Events

10
1

1

10-1

10-1

10-1

C2

C3

C4

10-2

C5

C2

C3

C4

10-2

C5

Efficiency[%]

70
60
50
40
30

90

90

80

80

70
60
50
40
30

C2

C3

C4

C2

C3

C4

C5

C5

30
C1

C2

C3

C4

C5

C1

102

102

102

Events

10

10
1
10-1

10
1

10-2

C2

C3

C4

C5

C2

C3

C4

C5

3

10-1

C5

p→μ+μ+μ-

40

10

C4

C1

50

10

C3

C5

60

3

C2

C4

70

3

10-2 C1

C3

p→e μ μ

80

C1

C2

- + +

p→e+μ+μ-90

C1

Efficiency[%]

C1

C1

10

1

EventsEvents

70

80

103

10-2

Efficiency[%]

80

30
C1

p→μ-e+e+

90

Efficiency[%]80

30

Eventsp→μ+e+e-

90

Efficiency[%]

Efficiency[%]

90

10
1
10-1

C1

C2

C3

C4

C5

10-2 C1

FIG. 1. Signal efficiency (top, blue dots), data (bottom, black dots), and expected background events (bottom, red line) at each cut stepin each mode. In upper column, from left to right for the p → eþ eþ e− , p → μþ eþ e− , and p → μ− eþ eþ modes, respectively. In lower
column, from left to right for the p → eþ μþ μ− , p → e− μþ μþ , and p → μþ μþ μ− modes, respectively. The background MC isnormalized by live time. SK-I to SK-IV are combined in signal MC, background MC, and data. Note that both the data and backgroundMC plots for the p → μþ eþ e− and p → μ− eþ eþ modes are the same, since SK cannot identify the charge sign of the leptons. For thesame reason, the data and background MC plots are the same for the p → eþ μþ μ− and p → e− μþ μþ modes as well.

method based on the neutrino oscillation analysis in SK[21]. A pion generated by a neutrino interaction can interact
with a nucleon in oxygen (final state interaction, FSI). It isalso possible to interact with other nuclei in water after
escaping the original nucleus (secondary interaction, SI).

FSI/SI is simulated by a pion cascade model and theiruncertainties are taken into account.
Systematic uncertainties for the detector performanceand reconstruction are taken into account for both signal
and background. In order to estimate these uncertainties,

052011-6

Total momentum [MeV/c]

SEARCH FOR PROTON DECAY INTO THREE CHARGED …
1000
900
800
700
600
500
400
300
200
100
0

PHYS. REV. D 101, 052011 (2020)

p→e+e+e-

0

200

400

600

800 1000 1200

200

400

600

800

1000 1200

200

400

600

800

1000 1200

200

400

600

800

1000 1200

200

400

600

800

1000 1200

200

400

600

800

1000 1200

Total momentum [MeV/c]

Total mass [MeV/c2]
1000
900
800
700
600
500
400
300
200
100
0

p→μ+e+e-

0

200

400

600

800 1000 1200

200

400

600

800

1000 1200
2

Total momentum [MeV/c]

Total mass [MeV/c ]p→e-μ+μ+

1000
900
800
700
600
500
400
300
200
100
0

0

200

400

600

800 1000 1200

200

400

600

800

1000 1200

Total momentum [MeV/c]

Total mass [MeV/c2]
1000
900
800
700
600
500
400
300
200
100
0

p→μ+μ+μ-

0

200

400

600

800 1000 1200

200

400

600

800

1000 1200
2

Total mass [MeV/c ]FIG. 2. Two-dimensional plots of total mass and momentum for signal (left), background (center), and measured data (right) after theselections C1–C3 and C5 are applied. From the top to the bottom, for the p → eþ eþ e− , p → μþ eþ e− , p → e− μþ μþ , and p → μþ μþ μ−modes, respectively. Light blue shows free proton and dark blue shows bound proton in the signal plot. Two black squares show thelower and upper signal boxes. The dot size is enlarged in the signal box only for background. SK-I to SK-IV are combined in signal MC,
background MC (4 × 500 years), and data. For the p → μ− eþ eþ mode, the number of signal MC points is lower than that of p →μþ eþ e− by 19%, due to the different effective lifetimes (and therefore different decay electron production probabilities) of the μ− and μþin water. Similarly, the signal MC for p → eþ μþ μ− has 20% fewer events than that for the p → e− μþ μþ mode. As in Fig. 1, the data andbackground MC figures are the same for modes that differ only by the charge sign of the leptons.

052011-7

M. TANAKA et al.

PHYS. REV. D 101, 052011 (2020)

TABLE I. Summary of signal efficiency, expected background events, and data candidates for each decay mode and each data taking
period (SK-I to SK-IV). The error values correspond to the statistical uncertainty of the MC sample. Lower and upper stand for
Ptot < 100 MeV=c and 100 < Ptot < 250 MeV=c, respectively. The data events remaining in the p → eþ μþ μ− and p → e− μþ μþmodes are the same event.
Efficiency (%)
Modes
p → eþ eþ e−(Lower)(Upper)p → μþ eþ e−(Lower)(Upper)p → μ− eþ eþ(Lower)(Upper)p → eþ μþ μ−(Lower)(Upper)p → e− μþ μþ(Lower)(Upper)p → μþ μþ μ−(Lower)(Upper)Background (events)

Candidate (events)

I

II

III

IV

I

II

III

IV

I

II

III

IV

22.7
43.9

19.8
40.4

23.1
44.3

22.4
41.1

<0.01
0.19  0.04

<0.01
0.10  0.02

<0.01
0.05  0.01

<0.01
0.24  0.07

0
0

0
0

0
0

0
0

15.0
27.1

13.5
26.0

16.3
27.3

17.6
30.3

0.02  0.01
0.13  0.03

0.02  0.01
0.10  0.02

0.01  0.00
0.05  0.01

<0.01
0.17  0.05

0
0

0
0

0
0

0
0

11.9
20.8

11.1
19.8

12.6
22.3

14.9
25.9

0.02  0.01
0.13  0.03

0.02  0.01
0.10  0.02

0.01  0.00
0.05  0.01

<0.01
0.17  0.05

0
0

0
0

0
0

0
0

9.2
15.8

8.1
14.1

9.1
16.2

11.7
20.9

<0.01
0.09  0.02

<0.01
0.07  0.02

<0.01
0.03  0.01

<0.01
0.08  0.03

0
0

0
0

0
0

0
1

11.1
19.9

10.9
18.2

11.9
20.0

14.4
24.2

<0.01
0.09  0.02

<0.01
0.07  0.02

<0.01
0.03  0.01

<0.01
0.08  0.03

0
0

0
0

0
0

0
1

10.8
19.9

10.4
17.2

12.0
20.4

12.2
20.4

<0.01
0.10  0.03

<0.01
0.05  0.01

<0.01
0.03  0.01

<0.01
0.22  0.06

0
1

0
0

0
0

0
0

TABLE II. The fraction [%] from each background interaction mode remaining in the signal box for each proton
decay channel. CC, NC, and QE stand for charged-current, neutral-current, and quasielastic neutrino interactions,
respectively.

CCQE
CC single π
CC multi π
CC othersNC

p→eþ eþ e−p→μþ eþ e−(p→μ− eþ eþ )p→eþ μþ μ−(p→e− μþ μþ )p→μþ μþ μ−

13
41
12
13
21

7
32
27
12
21

10
34
42
5
9

21
58
13
4
4

control sample data and MC are compared for each sourceof systematic uncertainties. We consider uncertainties for
FV, detector nonuniformity, energy scale, ring counting,
PID, decay electron tagging, and neutron tagging.
Systematic uncertainty for the detector exposure is negligible. We assigned a 1% error for the detector exposure to
be conservative.
Systematic uncertainties for the signal and backgroundare summarized in Tables III and IV, respectively. The
dominant uncertainties for the background due to theevent reconstruction are energy scale and detector nonuniformity. Uncertainties of the energy scale [21] aretaken into account for all the charge-related reconstruction
parameters. The effect of detector nonuniformity of theenergy scale [21] is taken into account for the total
momentum reconstruction.

The dominant error for p → μþ μþ μ− (Table III) comesfrom uncertainty of the decay electron tagging. Since thenumber of candidate events with three μ-like rings and twoor three decay electrons (selections for the p → μþ μþ μ− ) issmaller than for the other modes, the statistical error of theatmospheric neutrino control sample data used to estimate
the systematic error is larger.
VII. RESULT
No events are found in the signal box region for thep → eþ eþ e− and p → μþ eþ e− (p → μ− eþ eþ ) modes.
One event is observed in the upper signal box for boththe p → eþ μþ μ− (p → e− μþ μþ ) and p → μþ μþ μ− modes(all the event displays in [25]). Observed candidates are
summarized in Tables I and V. Figure 1 shows the052011-8

SEARCH FOR PROTON DECAY INTO THREE CHARGED …

Total mass and momentum distributions are shown in Fig. 2
as two-dimensional plots and in Fig. 3 as histograms. Dataand background MC distributions agree well in each decay
channel.
The candidate for the p → eþ μþ μ− (p → e− μþ μþ )modes is observed in the upper signal box of the SK-IV
period. Reconstructed proton mass and momentum for thiscandidate are 882 MeV=c2 and 160 MeV=c, respectively.
Another candidate for the p → μþ μþ μ− mode is found in
the upper signal box of the SK-I period. There are two
decay electrons, and the total mass and momentum are
835 MeV=c2 and 170 MeV=c, respectively. These eventswere visually inspected and they appear not to be misreconstruction events.
The expected background events in the p → eþ μþ μ−(p → e− μþ μþ ) mode is 0.27  0.04 ðstatÞ events.
Assuming a Poisson distribution of mean 0.27, the probability to observe ≥ 1 events is 18.4%. Considering the
expected background events in the p → μþ μþ μ− to be
0.40  0.07 ðstatÞ events, the probability of observing ≥ 1
events is 25.8%.

TABLE III. Summary of systematic uncertainty [%] for thesignal averaged over the live time of each period. Lower andupper stand for Ptot < 100 MeV=c and 100 < Ptot < 250 MeV=c,
respectively.
Modes

Correlated
decay

Fermi
momentum

Detector andreconstruction

Total

4.0
9.3

10.4
3.1

5.9
4.4

12.6
10.8

3.9
9.4

10.3
3.4

8.1
7.5

13.7
12.6

3.9
9.6

10.3
3.0

8.1
7.6

13.7
12.5

3.7
9.5

10.1
3.5

8.3
7.2

13.6
12.7

3.7
8.8

9.4
5.6

8.0
7.2

13.1
12.9

3.8
9.7

10.5
6.5

18.9
18.6

22.1
22.1

p → eþ e þ e −(Lower)(Upper)p → μþ eþ e−(Lower)(Upper)p → μ− eþ eþ(Lower)(Upper)p → eþ μþ μ−(Lower)(Upper)p → e− μþ μþ(Lower)(Upper)p → μþ μþ μ−(Lower)(Upper)

PHYS. REV. D 101, 052011 (2020)

VIII. PARTIAL LIFETIME LIMITThe observed events are consistent with expectedbackgrounds; therefore, lower proton lifetime limits at
90% confidence level (CL) with respect to each proton
decay mode are calculated by using a Bayesian method[26,27]. The limit calculation is the same as for recent
nucleon decay analyses [3,4,6]. We have eight signal

comparisons of the number of observed events to theestimated background along the event selection for each
proton decay mode. The observed numbers of events ateach cut step are consistent with the expected background.

TABLE IV. Summary of systematic uncertainty [%] for the background averaged over the live time of each period.
Modes

Neutrino
flux

Neutrino

Pion FSI/SI

Detector andreconstruction

Total

7.0
7.3
8.2
8.3

14.1
16.9
23.6
16.6

1.9
1.9
3.3
1.8

32.4
19.3
19.6
32.4

36.1
26.7
32.0
37.4

þ þ −

p→e e ep → μþ eþ e− (p → μ− eþ eþ )p → eþ μþ μ− (p → e− μþ μþ )p → μþ μþ μ−TABLE V. Summary of expected background events with statistical errors, number of candidates, Poisson
probabilities to observe events greater than or equal to the number of data candidates, and estimated partial lifetime
lower limits.

Modes

Background(events)

Candidate(events)

Probability(%)

Lifetime limit(×1034 years)
at 90% CL

p → eþ eþ e−p → μþ eþ e−p → μ− eþ eþ
p → eþ μþ μ−
p → e− μþ μþ
p → μþ μþ μ−0.58  0.08
0.50  0.06
0.50  0.06
0.27  0.04
0.27  0.04
0.40  0.07

0
0
0
1
1
1

…
…
…
18.4
18.4
25.8

3.4
2.3
1.9
0.92
1.1
1.0

052011-9

M. TANAKA et al.

PHYS. REV. D 101, 052011 (2020)
2

Number of events

10p→e+e+e-

10
1
-1

10

10-2
10-3
10-4
0

200

400

600

800

1000

1200

100 200 300 400 500 600 700 800 900 1000

Total mass [MeV/c2]

Number of events

102

Total momentum [MeV/c]

p→μ+e+e-

10
1
-1

10

10-2
10-3
10-4
0

200

400

600

800

1000

1200

100 200 300 400 500 600 700 800 900 1000

Total mass [MeV/c2]

Number of events

102

Total momentum [MeV/c]

p→e-μ+μ+

10
1
10-1
10-2
10-3
10-4
0

200

400

600

800

1000

1200

100 200 300 400 500 600 700 800 900 1000

Total mass [MeV/c2]

Number of events

102

Total momentum [MeV/c]

p→μ+μ+μ-

10
1
10-1
10-2
10-3
10-4
0

200

400

600

800

1000

1200

100 200 300 400 500 600 700 800 900 1000

Total mass [MeV/c2]

Total momentum [MeV/c]

FIG. 3. Data (black dots) and background (red line) comparison for total mass (left) and momentum (right) after the selections C1–C3
and C5 are applied. The shape of the signal (free proton only) distribution is shown by the blue line (filled cyan histogram). Additionally,a Ptot < 250 MeV=c cut is applied on the total mass plot and an 800 < M tot < 1050 MeV=c2 cut is applied on the total momentum plot.
From the top to the bottom, the p → eþ eþ e− , p → μþ eþ e− , p → e− μþ μþ , and p → μþ μþ μ− modes are shown, respectively. Dottedblack lines show the boundary of the signal box. SK-I to SK-IV are combined in signal, background MC, and data. Background MC isnormalized by atmospheric neutrino flux, oscillation probability, and live time. Signal MC is normalized to the partial proton lifetime
limit calculated in Sec. VIII. The number of signal MC events for the p → μ− eþ eþ mode is lower than that of p → μþ eþ e− by 19%, due
to the different effective lifetimes (and therefore different decay electron production probabilities) of the μ− and μþ in water. Similarly,
the signal MC for p → eþ μþ μ− has 20% fewer events than that for the p → e− μþ μþ mode. As in Fig. 1, the data and background MC
figures are the same for modes that differ only by the charge sign of the leptons.

052011-10

SEARCH FOR PROTON DECAY INTO THREE CHARGED …

PHYS. REV. D 101, 052011 (2020)

Finally, the lower limit of partial proton lifetime is calculated
according to
τ=B ¼

1
:
Γlimitð3Þ

Here B is the branching ratio of each proton decay mode. By
using these functions, the partial lifetime limits at 90% CL
for each mode of proton decay into three charged leptons arecalculated as summarized in Table V.
IX. CONCLUSION

FIG. 4. Estimated partial lifetime lower limit for each mode of
proton decay into three charged leptons by this analysis (redhistogram), IMB-3 (star) [9], and HPW (circle) [10] experiments.
The p → μ− eþ eþ channel was not searched for by IMB-3 and
HPW experiments.

regions (four periods × two boxes) for each decay mode.
The probability density function (PDF) is defined for eachregion as below.
PðΓjni Þ ¼

1
Ai

ZZZ

e−ðΓλi ϵi þbi Þ ðΓλi ϵi þ bi Þni
ni !

× PðΓÞPðλi ÞPðϵi ÞPðbi Þdϵi dλi dbi :ð1ÞHere, i is the index of each signal region, Ai is a normalization factor, Γ is the decay rate, ni is the observed events, λi
is the exposure, ϵi is the signal efficiency, and bi is the
expected background events. PðΓÞ represents the probability distribution for the decay rate, assumed to be uniform.
Pðλi Þ and Pðϵi Þ are the probabilities for the exposure andsignal efficiency, respectively, described by a Gaussian.
Pðbi Þ is the probability for the expected background definedby the convolution of Gaussian and Poisson distributions.
All PDFs are combined and the upper limits of the decay rateΓlimit at 90% CL are estimated as follows:
Z Γ

limit

Γ¼0

8
Y
i¼1

PðΓjni ÞdΓ ¼ 0.9:

ð2Þ

Proton decay into three charged leptons was searched forby using 0.37 Mton · years of data collected by SK. The
observed data were consistent with the atmospheric neutrino background prediction and no clear indication of
proton decay was observed. According to the observation,
the model [8] for these decay modes at an energy scale
below 100 TeV was excluded by this analysis. The lower
partial lifetime limits at 90% CL were calculated for eachmode as summarized in Table V. Compared with theprevious limits by IMB-3 and HPW experiments, each
limit was improved by 15–1800 times in this analysis asshown in Fig. 4. A first limit has been set for the p →μ− eþ eþ mode.
ACKNOWLEDGMENTS
We gratefully acknowledge the cooperation of the Kamioka
Mining and Smelting Company. The Super-Kamiokande
experiment has been built and operated from funding by
the Japanese Ministry of Education, Culture, Sports, Scienceand Technology, the U. S. Department of Energy, and theU. S. National Science Foundation. Some of us have been
supported by funds from the National Research Foundation of
Korea Grant No. NRF-2009-0083526 (KNRC) funded by the
Ministry of Science, ICT, and Future Planning and the Ministryof Education (Grants No. 2018R1D1A3B07050696 andNo. 2018R1D1A1B07049158), the Japan Society for
the Promotion of Science, the National Natural Science
Foundation of China under Grant No. 11235006, theSpanish Ministry of Science, Universities and Innovation(Grant No. PGC2018-099388-B-I00), the Natural Sciencesand Engineering Research Council (NSERC) of Canada,
the Scinet and Westgrid consortia of Compute Canada, theNational Science Centre, Poland (2015/18/E/ST2/00758), the
Science and Technology Facilities Council and GridPPP,
United Kingdom, the European Union’s H2020-MSCARISE-2018 JENNIFER2 Grant No. 822070, and H2020MSCA-RISE-2019 SK2HK Grant No. 872549.

052011-11

M. TANAKA et al.

PHYS. REV. D 101, 052011 (2020)[1] H. Georgi and S. L. Glashow, Unity of All Elementary
Particle Forces, Phys. Rev. Lett. 32, 438 (1974).
[2] K. S. Babu, E. Kearns et al., Working group report: Baryon
number violation, arXiv:1311.5285.
[3] K. Abe et al., Search for proton decay via p → eþ π 0 and
p → μþ π 0 in 0.31 megaton · years exposure of the SuperKamiokande water Cherenkov detector, Phys. Rev. D 95,
012004 (2017).
[4] K. Abe et al., Search for proton decay via p → νK þ using
260 kiloton · years data of Super-Kamiokande, Phys. Rev. D
90, 072005 (2014).
[5] P. Langacker, Grand unification and the standard model,
Phys. Rep. 72, 185 (1981).
[6] K. Abe et al., Search for nucleon decay into charged
antilepton plus meson in 0.316 megaton · years exposureof the Super-Kamiokande water Cherenkov detector, Phys.
Rev. D 96, 012003 (2017).
[7] P. Nath and P. F. Perez, Proton stability in grand unified
theories, in strings and in branes, Phys. Rep. 441, 191 (2007).
[8] T. Hambye and J. Heeck, Proton Decay into Charged
Leptons, Phys. Rev. Lett. 120, 171801 (2018).
[9] C. McGrew et al., Search for nucleon decay using the
IMB-3 detector, Phys. Rev. D 59, 052004 (1999).
[10] T. J. Philips et al., A search for nucleon decay with multiple
muon decays, Phys. Lett. B 224, 348 (1989).
[11] S. Girmohanta and R. Shrock, Improved lower bounds onpartial lifetimes for nucleon decay modes, Phys. Rev. D 100,
115025 (2019).
[12] Y. Fukuda et al., The Super-Kamiokande detector, Nucl.
Instrum. Methods Phys. Res., Sect. A 501, 418 (2003).
[13] K. Abe et al. (Super-Kamiokande Collaboration), Calibration of the Super-Kamiokande detector, Nucl. Instrum.
Methods Phys. Res., Sect. A 737, 253 (2014).
[14] K. Nakamura, S. Hiramatsu, T. Kamae, H. Muramatsu, N.
Izutsu, and Y. Watase, The reaction C-12ðe; e0 pÞ at 700-MeV
and DWIA analysis, Nucl. Phys. A268, 381 (1976).

[15] T. Yamazaki and Y. Akaishi, Nuclear medium effects oninvariant mass spectra of hadron decaying in nuclei, Phys.
Lett. B 453, 1 (1999).
[16] M. Honda, T. Kajita, K. Kasahara, S. Midorikawa, and T.
Sanuki, Calculation of atmospheric neutrino flux using theinteraction model calibrated with atmospheric muon data,
Phys. Rev. D 75, 043006 (2007).
[17] M. Honda, T. Kajita, K. Kasahara, and S. Midorikawa,
Improvement of low energy atmospheric neutrino flux
calculation using the JAM nuclear interaction model, Phys.
Rev. D 83, 123001 (2011).
[18] Y. Hayato, A neutrino interaction simulation programlibrary NEUT, Acta Phys. Pol. B 40, 2477 (2009).
[19] P. de Perio, NEUT pion FSI, AIP Conf. Proc. 1405, 223(2011).
[20] R. Brun et al. (GEANT3 Collaboration), CERN-DD-EE-84-1,
1987.
[21] K. Abe et al., Atmospheric neutrino oscillation analysis withexternal constraints in Super-Kamiokande I-IV, Phys. Rev.
D 97, 072001 (2018).
[22] E. R. Davies, Compute & Machine Vision: Theory,
Algorithm, Practicalities (Academic Press, San Diego,
1997).
[23] H. Zhang et al. (Super-Kamiokande Collaboration),
Supernova relic neutrino search with neutron tagging at
Super-Kamiokande-IV, Astropart. Phys. 60, 41 (2015).
[24] H. Ejiri, Nuclear deexcitations of nucleon holes associatedwith nucleon decays in nuclei, Phys. Rev. C 48, 1442
(1993).
[25] See Supplemental Material at http://link.aps.org/supplemental/
10.1103/PhysRevD.101.052011 for graphical event displaysof the candidate events.
[26] C. Amsler et al. (Particle Data Group), Review of particle
physics, Phys. Lett. B 667, 1 (2008).
[27] B. P. Roe and M. B. Woodroofe, Setting confidence belts,
Phys. Rev. D 63, 013009 (2000).

052011-12