PHYSICAL REVIEW D 102, 112011 (2020)

Search for proton decay via p → e + π0 and p → μ + π0 with an enlarged
fiducial volume in Super-Kamiokande I-IV
A. Takenaka ,1 K. Abe,1,43 C. Bronner,1 Y. Hayato,1,43 M. Ikeda,1 S. Imaizumi,1 H. Ito,1 J. Kameda,1,43 Y. Kataoka,1
Y. Kato,1 Y. Kishimoto,1,43 Ll. Marti,1 M. Miura,1,43 S. Moriyama,1,43 T. Mochizuki,1 Y. Nagao,1 M. Nakahata,1,43
Y. Nakajima,1,43 S. Nakayama,1,43 T. Okada,1 K. Okamoto,1 A. Orii,1 G. Pronost,1 H. Sekiya,1,43 M. Shiozawa,1,43
Y. Sonoda,1 Y. Suzuki,1 A. Takeda,1,43 Y. Takemoto,1 H. Tanaka,1 T. Yano,1 R. Akutsu,2 S. Han,2 T. Kajita,2,43
K. Okumura,2,43 T. Tashiro,2 R. Wang,2 J. Xia,2 D. Bravo-Berguño,3 L. Labarga,3 P. Fernandez,3 B. Zaldivar,3
F. d. M. Blaszczyk,4 E. Kearns,4,43 J. L. Raaf,4 J. L. Stone,4,43 L. Wan,4 T. Wester,4 B. W. Pointon,5 J. Bian,6
N. J. Griskevich,6 W. R. Kropp,6 S. Locke,6 S. Mine,6 M. B. Smy,6,43 H. W. Sobel,6,43 V. Takhistov,6,† P. Weatherly,6
K. S. Ganezer,7,* J. Hill,7 J. Y. Kim,8 I. T. Lim,8 R. G. Park,8 B. Bodur,9 K. Scholberg,9,43 C. W. Walter,9,43 A. Coffani,10
O. Drapier,10 S. El Hedri,10 A. Giampaolo,10 M. Gonin,10 Th. A. Mueller,10 P. Paganini,10 B. Quilain,10 T. Ishizuka,11T. Nakamura,12 J. S. Jang,13 J. G. Learned,14 S. Matsuno,14 L. H. V. Anthony,15 R. P. Litchfield,15 A. A. Sztuc,15
Y. Uchida,15 V. Berardi,16 M. G. Catanesi,16 E. Radicioni,16 N. F. Calabria,17 L. N. Machado,17 G. De Rosa,17
G. Collazuol,18 F. Iacob,18 M. Lamoureux,18 N. Ospina,18 L. Ludovici,19 Y. Nishimura,21 S. Cao,22 M. Friend,22
T. Hasegawa,22 T. Ishida,22 M. Jakkapu,22 T. Kobayashi,22 T. Matsubara,22 T. Nakadaira,22 K. Nakamura,22,43 Y. Oyama,22
K. Sakashita,22 T. Sekiguchi,22 T. Tsukamoto,22 M. Hasegawa,23 Y. Isobe,23 H. Miyabe,23 Y. Nakano,23 T. Shiozawa,23
T. Sugimoto,23 A. T. Suzuki,23 Y. Takeuchi,23,43 S. Yamamoto,23 A. Ali,24 Y. Ashida,24 J. Feng,24 S. Hirota,24
A. K. Ichikawa,24 M. Jiang,24 T. Kikawa,24 M. Mori,24 KE. Nakamura,24 T. Nakaya,24,43 R. A. Wendell,24,43 K. Yasutome,24
N. McCauley,25 P. Mehta,25 A. Pritchard,25 K. M. Tsui,25 Y. Fukuda,26 Y. Itow,27,28 H. Menjo,27 T. Niwa,27 K. Sato,27
M. Taani,27,‡ M. Tsukada,27 P. Mijakowski,29 K. Frankiewicz,29 C. K. Jung,30 G. Santucci,30 C. Vilela,30 M. J. Wilking,30
C. Yanagisawa,30,§ D. Fukuda,31 M. Harada,31 K. Hagiwara,31 T. Horai,31 H. Ishino,31 S. Ito,31 Y. Koshio,31,43 W. Ma,31
N. Piplani,31 S. Sakai,31 M. Sakuda,31 Y. Takahira,31 C. Xu,31 Y. Kuno,32 G. Barr,33 D. Barrow,33 L. Cook,33,43
C. Simpson,33,43 D. Wark,33,38 F. Nova,34 T. Boschi,20,∥ F. Di Lodovico,20 S. Molina Sedgwick,20,∥ S. Zsoldos,20 J. Y. Yang,35
S. J. Jenkins,36 J. M. McElwee,36 M. D. Thiesse,36 L. F. Thompson,36 H. Okazawa,37 Y. Choi,39 S. B. Kim,39 I. Yu,39
K. Nishijima,40 M. Koshiba,41 K. Iwamoto,42 N. Ogawa,42 M. Yokoyama,42,43 A. Goldsack,43,33 K. Martens,43
M. R. Vagins,43,6 M. Kuze,44 M. Tanaka,44 T. Yoshida,44 M. Inomoto,45 M. Ishitsuka,45 R. Matsumoto,45 K. Ohta,45
M. Shinoki,45 J. F. Martin,46 C. M. Nantais,46 H. A. Tanaka,46 T. Towstego,46 M. Hartz,47 A. Konaka,47 P. de Perio,47
N. W. Prouse,47 S. Chen,48 B. D. Xu,48 M. Posiadala-Zezula,49 B. Richards,50 B. Jamieson,51 J. Walker,51 A. Minamino,52
K. Okamoto,52 G. Pintaudi,52 and R. Sasaki52(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, British Columbia Institute of Technology,
Burnaby, British Columbia V5G 3H2, Canada
6
Department of Physics and Astronomy, University of California,
Irvine, Irvine, California 92697-4575, USA
7
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
8
Institute for Universe and Elementary Particles, Chonnam National University, Gwangju 61186, Korea
9
Department of Physics, Duke University, Durham North Carolina 27708, USA
10
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, F-91120 Palaiseau, France
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, Hawaii 96822, USA
15
Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
16
Dipartimento Interuniversitario di Fisica, INFN Sezione di Bari and Università e Politecnico di Bari,
I-70125 Bari, Italy
17
Dipartimento di Fisica, INFN Sezione di Napoli and Università di Napoli, I-80126 Napoli, Italy

2470-0010=2020=102(11)=112011(16)112011-1

Published by the American Physical Society

A. TAKENAKA et al.

PHYS. REV. D 102, 112011 (2020)

18

Dipartimento di Fisica, INFN Sezione di Padova and Università di Padova, I-35131 Padova, Italy
19
INFN Sezione di Roma and Università di Roma “La Sapienza”, I-00185 Roma, Italy
20
Department of Physics, King’s College London, London WC2R 2LS, United Kingdom
21
Department of Physics, Keio University, Yokohama, Kanagawa 223-8522, Japan
22
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
23
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
24
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
25
Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom
26
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
27
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan
28
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University,
Nagoya, Aichi 464-8602, Japan
29
National Centre For Nuclear Research, 02-093 Warsaw, Poland
30
Department of Physics and Astronomy, State University of New York at Stony Brook,
New York 11794-3800, USA
31
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
32
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
33
Department of Physics, Oxford University, Oxford OX1 3PU, United Kingdom
34
Rutherford Appleton Laboratory, Harwell, Oxford OX11 0QX, United Kingdom
35
Department of Physics, Seoul National University, Seoul 151-742, Korea
36
Department of Physics and Astronomy, University of Sheffield, S3 7RH Sheffield, United Kingdom
37
Department of Informatics in Social Welfare, Shizuoka University of Welfare,
Yaizu, Shizuoka 425-8611, Japan
38
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory,
Warrington OX11 0QX, United Kingdom
39
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
40
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
41
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
42
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
43
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
44
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
45
Department of Physics, Faculty of Science and Technology, Tokyo University of Science,
Noda, Chiba 278-8510, Japan46
Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
47
TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T2A3, Canada
48
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
49
Faculty of Physics, University of Warsaw, Warsaw 02-093, Poland
50
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
51
Department of Physics, University of Winnipeg, MB R3J 3L8, Canada
52
Department of Physics, Yokohama National University, Yokohama, Kanagawa 240-8501, Japan(Received 1 November 2020; accepted 10 November 2020; published 22 December 2020)
We have searched for proton decay via p → eþ π 0 and p → μþ π 0 modes with the enlarged fiducial
volume data of Super-Kamiokande from April 1996 to May 2018, which corresponds to 450 kton · years
exposure. We have accumulated about 25% more livetime and enlarged the fiducial volume of the SuperKamiokande detector from 22.5 kton to 27.2 kton for this analysis, so that 144 kton · years of data,
including 78 kton · years of additional fiducial volume data, has been newly analyzed. No candidates havebeen found for p → eþ π 0 and one candidate remains for p → μþ π 0 in the conventional 22.5 kton fiducial*

Deceased.
Also at Department of Physics and Astronomy, UCLA, Los Angeles, 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 10007, 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.

112011-2

SEARCH FOR PROTON DECAY VIA p → eþ π 0 …

PHYS. REV. D 102, 112011 (2020)

volume and it is consistent with the atmospheric neutrino background prediction. We set lower limits on thepartial lifetime for each of these modes: τ=Bðp → eþ π 0 Þ > 2.4 × 1034 years and τ=Bðp → μþ π 0 Þ >1.6 × 1034 years at 90% confidence level.
DOI: 10.1103/PhysRevD.102.112011

I. INTRODUCTION
Grand unified theories (GUTs) [1] extend the Standard
Model gauge symmetry to larger symmetry groups andprovide explanations for the quantization of electric charge
and predict the convergence of the electromagnetic, weak,
and strong interaction couplings at energies around∼1016 GeV [2]. There are a variety of proposed GUT
models based on different gauge groups, such as SU(5) [1],SO(10) [3], E6 [4], some with and some without incorporating supersymmetry. These models offer dark mattercandidates [5], neutrino mass generation mechanisms[6], and insight into the strong CP problem [7], making
them a promising target for many searches for physics
beyond the Standard Model. Furthermore, by incorporating
quarks and leptons into common multiplets, GUTs generically predict transitions between the two which result inbaryon-number-violating proton decays, whose observation would provide strong support for such models.
While the p → eþ π 0 mode is favored by many GUT
models, the “flipped SU(5)” ones [8] predict a higher
branching fraction in the p → μþ π 0 channel. Since recent
theoretical studies [9,10] show that the preferred models of
GUTs may be revealed by the first signs of proton decay, it
is important to search for both modes. Both modes produce
back-to-back event topologies in which all final stateparticles are visible making it possible to cleanly separate
a proton decay signal from atmospheric neutrino backgrounds in water Cherenkov detectors. Moreover, free
protons (hydrogen nuclei) in their water provide enhanced
background rejection capabilities since a decay thereinwould be free from the effects of the Fermi motion andintranuclear scattering processes that alter the final stateparticles from decays within 16O.
These decay modes have been the target of several
experimental searches, but there have been no positive
observations so far [11]. Prior to the present work the moststringent constraints come from 306 kton · years of SuperKamiokande data: τ=Bðp → eþ π 0 Þ > 1.6 × 1034 years andτ=Bðp → μþ π 0 Þ > 7.7 × 1033 years at 90% confidence
level [12]. Since then the detector has accumulated about
25% more live days of data and its fiducial volume has beenenlarged from 22.5 kton to 27.2 kton resulting in a roughly
50% larger exposure of 450 kton · years. This paper
describes a search for these two proton decay modes using
this updated dataset and is organized as follows. A
summary of the Super-Kamiokande detector and its event
reconstruction is presented in Sec. II before describing

analysis improvements that enabled the fiducial volume to
be enlarged in Sec. III. Section IV details the simulation of
proton decay and atmospheric neutrino events and Secs. V
and VI describe the proton decay search sensitivity andresults. As no proton decay signal has been found, lifetime
limits are calculated in Sec. VII before concluding in
Sec. VIII.
II. THE SUPER-KAMIOKANDE DETECTOR
Super-Kamiokande (SK) is located about 1,000 m(2,700 meters water equivalent) under Mt. Ikenoyama in
Gifu Prefecture, Japan. The detector is an upright cylindrical vessel, 39.3 m in diameter and 41.4 m in height, andis filled with 50 kton of ultrapure water that is opticallyseparated into two regions, an inner detector (ID) andan outer detector (OD). The ID has a diameter of 33.8 m
and a height of 36.2 m that is viewed by more than 11,000
inward-facing 50-cm photomultiplier tubes (PMTs)
mounted on a steel structure offset from the tank outerwall by 2 m and forming the boundary with the OD.
The OD is composed of 20-cm PMTs installed behind
the ID PMTs and facing outward. Reflective Tyvek lines
the walls of the OD and wavelength shifting plates aremounted on its PMTs in order to achieve more efficient
light collection and improve the rejection of external
backgrounds. Detailed descriptions of the detector andits calibration can be found in [13,14].
The SK data are divided into four phases representing
different configurations of the detector, SK-I, -II, -III,and -IV. The SK-I period began in April 1996 and ended
in July 2001 with a photocathode coverage of 40%. In
November 2001, a chain reaction implosion destroyed
more than half of the PMTs, such that SK-II was operated
from October 2002 to October 2005, using 5,182 ID PMTs
with 19% photocathode coverage. Since SK-II the ID
PMTs have been covered in fiber-reinforced plastic caseswith an acrylic window to prevent similar accidents.
New ID PMTs were installed thereafter and SK-III started
in July 2006 with 40% of photocathode coverage. In
September 2008 the front-end electronics [15] and dataacquisition system were upgraded to start the SK-IV
period, which continued until May 2018. These systems
improve the efficiency for tagging Michel electrons andthe faint 2.2 MeV gamma ray that accompanies neutron
capture on hydrogen, resulting in 20% higher signal
selection efficiency in the search for p → μþ π 0 decays
and a reduction of atmospheric neutrino backgrounds in

112011-3

A. TAKENAKA et al.

PHYS. REV. D 102, 112011 (2020)

both decay modes considered here by 50% relative to theprevious analysis [12].
Charged particles above the Cherenkov threshold inside
the ID are reconstructed using PMT timing and charge
information. First, a charged particle’s initial vertex isreconstructed by finding the point for which the distributionof time-of-flight corrected PMT times has the sharpest
peak. This is done by maximizing the estimator,
goodness ¼

X
i



1
ðt0i − t0 Þ2;exp −σ 2i ðqi Þ
2 × ðhσi × 1.5Þ2ð1Þ

where σ i is the timing resolution of the ith PMT tabulated
as a function of observed charge, hσi is the average timing
resolution for hit PMTs, and t0i is the ith PMT’s residual
time for an assumed vertex position. In the residual time
calculation, the track length of the charged particle is taken
into account only for the most energetic one since this isprior to the Cherenkov ring counting algorithm described
below. Here 1.5 is a tuning parameter that has been chosen
to optimize performance and t0 is chosen so that the
goodness is maximal at each tested vertex position. The
vertex position is the point with the highest goodness.
After reconstructing the vertex position, the number of
Cherenkov rings projected on the ID wall is determinedusing a ring pattern recognition algorithm based on the
Hough transformation [16]. The PMT charge distribution
is corrected for the water’s attenuation length and PMT
acceptance before being transformed into the Hough space.
Ring centers, corresponding to particle directions, and ring
opening angles, corresponding to Cherenkov angles, manifest as peaks in the resulting distribution.
Each identified Cherenkov ring is identified as either
showering (e-like) particle (e ; γ) or nonshowering (μ-like)particle (μ ; π  ) based on the pattern of hit PMTs in thering. Rings from electrons and gamma rays tend to havediffuse edges due to the overlap of many Cherenkov rings
produced by the particles in their electromagnetic showers.
On the other hand, muon and pion rings tend to have crisp
edges since they do not shower due to their larger masses.
The expected charge distribution is calculated for eachparticle assumption and compared to the observation usingXχ2 ∝ −
log10 Pðqi ; qexp
ð2Þi Þ;
θi <ð1.5×θc Þ

where qi is the ith PMT’s observed charge, qexp
is thei
expected charge for that PMT for either the electron ormuon assumption, and P is the probability of observing qi
given an expectation of qexp
i . For both the electron andmuon assumptions, the summation is performed for PMTs
whose angle to the ring direction (θi ) is within 1.5 times thereconstructed Cherenkov opening angle (θc ). The particle
type with the smallest χ 2 is assigned to each reconstructed
ring. For multiring events such as those from p → eþ π 0

and p → μþ π 0 decays, the observed charge at each PMT isseparated into the contribution from each Cherenkov ringusing the expected charge distribution. In this step, thecontributions from light scattering in the water and reflection on the PMT surfaces are calculated and subtracted
from the total charge associated with each ring in order toestimate their momenta. The relationship between the total
observed charge within a 70 degree half opening angle fromthe particle direction and particle momentum is based onMonte Carlo (MC) simulation and is tabulated in advancefor each particle taking into account corrections for water
attenuation length and PMT acceptance. A more detailed
description of the event reconstruction algorithm can befound in [17]. The performance of the reconstruction on
proton decay events is discussed in the next section.
Neutrons emitted from a primary event thermalize inwater and are eventually captured by hydrogen, resulting in
the emission of a 2.2 MeV gamma ray. Such gamma rays
are tagged by searching for clusters of at least five hit ID
PMTs in a sliding 10 nsec window scanned between
18 μ sec and 535 μ sec after the primary event trigger.
This search time region is set to avoid effects from PMT
after-pulsing which occurs between 12 and 18 μ sec after
the primary PMT hit. A dedicated neural network that has
been trained using simulated atmospheric neutrino eventsand random trigger data representing mostly PMT darknoise is applied to each cluster to identify it as either aneutron signal or background. The total neutron tagging
efficiency is estimated to be 25.2  2.3% using atmospheric neutrino MC and calibration data from an AmBe
neutron source. The estimated false-positive rate of thealgorithm is 0.018 neutron-candidates per primary event.
A detailed description of the neural net and recent update of
the algorithm can be found in [18,19].
III. ENLARGING THE FIDUCIAL VOLUMEThis analysis uses events termed “fully contained” (FC)whose interaction vertex has been reconstructed within the
ID and which have no cluster of hits in the OD and whichpass other selection criteria [20]. The detector’s fiducial
volume is defined using the distance between the nearest ID
wall and the event’s reconstructed vertex (dwall) without
reconstructed particle direction dependence. In the previous
analysis [12] this region was defined as the region more than
200 cm from the wall (200 cm < dwall) which corresponds
to 22.5 kton of fiducial mass. In order to further improve theproton decay search sensitivity, the following studies havebeen conducted for the present analysis to enlarge thefiducial volume boundary from 200 cm to 100 cm, thereby
increasing the water mass to 27.2 kton. In the following, theterm “conventional” fiducial volume refers to the region withdwall greater than 200 cm and “additional” fiducial volume
refers to the region with dwall between 100 cm and 200 cm.
Terms used to represent different detector regions are
summarized in Table I.

112011-4

SEARCH FOR PROTON DECAY VIA p → eþ π 0 …

Term
Conventional
Additional
Enlarged
Outsidedwall

Water mass

200 cm < dwall
100 < dwall ≤ 200 cm
100 cm < dwall
50 < dwall ≤ 100 cm

22.5 kton
4.7 kton
27.2 kton
2.6 kton

Non-neutrino background events originating from outside of the conventional fiducial volume, such as cosmicray muons or noise events from erroneous discharges in a
PMT’s dynode (“flasher” events), typically have reconstructed vertices on the wall (dwall around 0 cm) but due tothe limited vertex resolution, some may be reconstructedwithin the fiducial volume. All FC events with reconstructed vertices more than 50 cm from the wall were eyescanned using a graphical event display tool to estimate thecontamination from such backgrounds. Since the enlarged
fiducial volume boundary is closer to the wall, thesebackgrounds occur more frequently and have been identified by this scanning. No event has been rejected based on
the scanning results but several changes have been made to
the existing FC event selection [20] to remove them.
First, to reject cosmic-ray muons that pass though cablebundles running through the OD without leaving sufficient
light to trigger its PMTs before entering the ID, plastic
scintillator-based veto counters are placed above the four
bundles located closest to the ID. In previous analyses,
events with both a signal in a veto counter and a vertex lessthan 4 m from the top of the cable bundle have been
rejected. In order to more accurately identify such entering
particles, an independent algorithm dedicated to muonvertex reconstruction that forces the vertex (entering point)
to be reconstructed on the ID wall is used. In the present
work, events leaving sufficiently large charge in a vetocounter are also removed regardless of their vertex position.
The veto counters were installed in the middle of SK-I,
Apr. 1997 and the cut associated with them is applied to thedata since then. In addition, events whose reconstructed
direction is downward-going (cosθz > 0.6, where cosθz ¼ 1
is vertically downward-going) and whose vertex is less than
2.5 m from any of the 12 ports housing a cable bundle areremoved. Here again the dedicated vertex algorithm isused. The above two changes eliminate cosmic-ray muons
passing through the cable bundles.
Events are also removed if their vertex goodness as
defined in Equation (1) is less than 0.77 and if they havemore than 7000 ID PMT hits with more than 70000
photoelectrons deposited therein (corresponding to about
7 GeV of energy deposition in the detector) and more than
5 OD PMT hits around their entrance point. This cut
eliminates high energy cosmic-ray muons that have been
misreconstructed inside the fiducial volume. In order toreject Michel electrons from cosmic-ray muons which are
below the Cherenkov threshold and stop in the ID, events

50
45

SK-I to -IV
Cosmic-Ray Muon
No Cherenkov Ring

40
35
30
25
20
15
10
5
0
0

Not Scanned

Terms used to represent detector regions.

Number of External
Background Events [/10 cm]

TABLE I.

PHYS. REV. D 102, 112011 (2020)

Additional
RegionConventional
Region50
100 150 200 250 300 350
Distance to the nearest ID Wall (dwall ) [cm]FIG. 1. Distribution of the distance to the nearest ID wall from thereconstructed vertex (dwall) of non-neutrino background events
remaining in SK-I to -IV. Cosmic-ray muon events (red, vertical
stripe) and no Cherenkov ring events (green, horizontal stripe) are
shown in a stacked histogram. No Cherenkov ring events are
dominated by PMT “flasher” events described in the text.

which have more than 50 (55 in SK-IV) OD hits in a sliding
200 nsec timing window before an ID trigger are removed.
Figure 1 shows the remaining non-neutrino backgrounds
in the SK-I to -IV data as a function of dwall and identified
by the visual scanning after adopting these new criteria.
With the new selection the fraction of non-neutrino backgrounds relative to atmospheric neutrino events is about
0.5% (0.1%) in the additional (conventional) fiducial
volume, tolerably worse than that in the conventional
fiducial volume. However, this fraction increases to
2.0% for dwall between 50 cm and 100 cm from the walland restricts further expansion of the fiducial volume. The
region with dwall between 50 cm and 100 cm is referred to“outside” region in the following. The new selection has
negligible impact on signal efficiency for atmospheric
neutrinos and proton decay.
For events occurring in the region close to the ID wall,the number of hit PMTs is typically small and more
localized than for interactions in the conventional fiducial
volume, and it is easier for particles to escape the ID with
non-negligible momentum. It is the case for both p → eþ π 0
and p → μþ π 0 decays because they produce back-to-back
event topologies and one of the reconstructed rings generally has a small distance to the wall along its direction. As
shown in Eqs. (1) and (2), since the accuracy of the vertex
reconstruction and particle identification depend on thenumber of ID PMT hits, both will degrade with fewer PMT
hits. Furthermore, where the PMT hits are too localized, thereconstruction algorithm may be unable to find or separate
Cherenkov rings from multiple particles. Particles that exit
the ID will have biased reconstructed momenta and make it
impossible to tag any Michel electrons from their decays.
Though these issues are unavoidable, their impact has
been mitigated by the following improvements to theparticle identification calculation. With a lower number

112011-5

A. TAKENAKA et al.

PHYS. REV. D 102, 112011 (2020)

TABLE II. Summary of reconstruction performance in different ID regions using only free proton decay MC events and weighted by
the combined SK-I to -IV livetime. The particle identification (PID) efficiency is the fraction of events which pass the proton decay
signal criterion C3 defined in Sec. V out of all two- and three-ring signal events. Here M π 0 (M tot ) peak is the reconstructed neutral pion
(total) mass distribution’s peak position after applying all selections except C6. The peak is determined using a Gaussian fit. Note that
M π0 peak values are evaluated for only three-ring events. The terms “Conventional,” “Additional,” and “Outside” stand for theconventional (200 cm < dwall), additional fiducial volume (100 < dwall ≤ 200 cm) and outside region (50 < dwall ≤ 100 cm),
respectively. The outside region is not used for the present analysis.
Decay mode Region

Vertex2-ring 3-ring
PID
Michel electron
resolution fraction fraction efficiency tagging efficiency

M π 0 peak
(3-ring)

M tot peak
(2-ring)

M tot peak
(3-ring)p → eþ π 0

Conventional 17.1 cm
Additional
24.1 cm
Outside25.9 cm

39.3%
51.9%
55.9%

58.7%
44.5%
37.6%

95.8%
87.7%
89.6%

N.A.
N.A.
N.A.

135 MeV=c2 910 MeV=c2 933 MeV=c2
134 MeV=c2 898 MeV=c2 927 MeV=c2
125 MeV=c2 828 MeV=c2 852 MeV=c2

p → μþ π 0

Conventional 20.6 cm
Additional
24.8 cm
Outside26.7 cm

36.8%
49.1%
55.3%

62.0%
48.1%
39.8%

96.2%
90.7%
82.6%

88.6%
78.9%
64.8%

135 MeV=c2 917 MeV=c2 936 MeV=c2
132 MeV=c2 917 MeV=c2 941 MeV=c2
125 MeV=c2 905 MeV=c2 925 MeV=c2

difference in reconstructed momenta or masses between
data and MC for several control samples in each SK phase.
For the absolute energy scale, the Michel electron momentum spectrum from stopping cosmic-ray muons, the π 0mass spectrum from neutral current atmospheric neutrino
interactions, and the momentum divided by the range ofcosmic-ray muons with energy deposition in the detector of
more and less than 1.33 GeV are used. Figure 3 shows theabsolute energy scale difference between data and MC foreach of these control samples. For Michel electrons and π 0
events, the event vertices can be reconstructed inside the ID
and are used to estimate the difference between data andMC for each volume of the detector separately. Figure 4
shows the reconstructed π 0 mass distributions for both theconventional and additional fiducial volumes in SK-IV.
Two-ring both e-like atmospheric neutrino events are used2

Number of Events [/10 (MeV/c )](Normalized to Unity)of ID PMT hits, the expected charge calculation [qexpiniEq. (2)] for each PMT becomes more important. Therefore
the expected charge tables have been updated using eventsfrom both within and outside of the conventional fiducial
volume and have been parametrized as a function of the
distance between the event vertex and PMT position as wellas the angle to the particle direction as viewed by the PMT.
By adopting the updated charge tables, the particle misidentification probability in the additional fiducial volume
has been reduced by about 35% for single-ring events andfor proton decay MC events, the signal selection efficiency
for both modes has been improved by about 20% relative toprevious versions. Table II compares the reconstruction
performance among the different ID regions using free
proton decay (p → eþ π 0 and p → μþ π 0 ) MC events toremove the influence of nuclear effects. Though the full
event selection is presented below, note that two-ring events
are included in the analysis to allow for asymmetric π 0
decays in which one of the gamma ray rings may overlay
with that from another particle. The fraction of these eventsnear the ID wall is larger than that in the conventional
fiducial volume due to the increased likelihood of missing athird ring resulting from more localized PMT hits. For thep → μþ π 0 mode, an escaping muon causes a lower Michelelectron tagging efficiency for events close to the ID wall.
Figure 2 shows the reconstructed total mass distribution ofp → eþ π 0 MC events with three reconstructed rings fromfree proton decays. Here all proton decay selection cuts(defined in Sec. V) except the cut on the plotted variable
have been applied. The two distributions outside of theconventional fiducial volume have longer tails in the low
mass region due to particles exiting the ID.
Systematic uncertainties associated with the reconstruction in the additional fiducial volume are estimated separately from those in the conventional fiducial volume.
In this analysis the energy scale uncertainty is the dominanterror from the reconstruction and it is estimated with the

0.14
0.12
0.1

200 cm<dwall

Fitted Peak, Sigma
933 MeV/c2, 27.6 MeV/c2
100<dwall 200 cm
2

0.08
0.06

927 MeV/c , 41.9 MeV/c2
50<dwall 100 cm

852 MeV/c2, 68.4 MeV/c2

0.04
0.02
0

700
800
900
1000
2
Reconstructed Total Mass [MeV/c ]1100

FIG. 2. Reconstructed total mass distribution for free proton
decays via p → eþ π 0 MC events with three rings. The solid cyan
histogram shows events reconstructed in the conventional fiducial
volume (200 cm < dwall), the pink dashed histogram shows thatfor the additional fiducial volume (100 < dwall ≤ 200 cm) andthe black dotted histogram is for the region between dwall of
50 cm and 100 cm. Gaussian fits have been used to determine themass peak and width.

112011-6

SEARCH FOR PROTON DECAY VIA p → eþ π 0 …

PHYS. REV. D 102, 112011 (2020)

6
4
2
SK-I

(MC - Data) / Data [%]

0

SK-II

Michel Electron
Conventional Region
Additional Region-2

Neutral Pion 0 Mass
Conventional Region
Additional Region-4

Sub-GeV Stopping
Multi-GeV Stopping-6
4
2
SK-III

SK-IV

0
-2
-4
-6

10 2

10

3

10 4

10 2

10

3

10 4

Momentum [MeV/c]
FIG. 3. Absolute energy scale difference between data and MC control samples. Vertical error bars denote the statistical uncertainty
and horizontal error bars show the momentum range for each control sample. For the Michel electron and π 0 samples, points withsolid error bars correspond to the conventional fiducial volume and points with dashed error bars correspond to the additional fiducial
volume. Cosmic-ray muon samples are considered for the enlarged fiducial volume. The term “Sub-GeV” (“Multi-GeV”) stands forenergy deposition in the detector of less (more) than 1.33 GeV.

and they confirm good agreement between data and MC.
The absolute scale uncertainty is taken to be the value ofthe most discrepant control sample in each SK phase andfiducial volume. To take the most discrepant control
sample, cosmic-ray muon samples are considered for both
fiducial volumes.
The evolution of the energy scale over time is estimatedusing the variation in the average reconstructed momentumof Michel electrons and the variation in the reconstructedmuon momentum over range. Figure 5 shows the time
variation of Michel electron momentum as a function ofdate. The time variation is defined as the sample standard
deviation of the data value over the run time in each period.
In the end, the total energy scale uncertainty in each SK
phase and fiducial volume is the sum in quadrature of thisvariation with the absolute uncertainty. A zenith-angledependent uncertainty in the energy scale is also estimatedusing Michel electrons. These results are summarized inTable III and confirm that the data and MC agree to within a
few percent in both the conventional and additional fiducial
volumes. These are used as the source of the systematic
uncertainty for the proton decay searches described inSec. VI.

The fiducial volume for the analysis presented below ischosen to be 100 cm < dwall since in this region the nonneutrino background contamination is within 1% and theenergy scale uncertainty is comparable to the conventional
fiducial volume. Moving closer to the ID wall would incurlarger backgrounds and systematic errors that would
degrade the search sensitivity more than the search would
benefit from the increased exposure. This enlarged fiducial
volume is used in all data in this paper and results in an
additional 78 kton · year exposure analyzed here for the
first time. The sensitivity improvement with the larger
fiducial volume is described in Sec. V.
IV. SIMULATIONIn this analysis p → eþ π 0 and p → μþ π 0 MC are used toestimate the signal selection efficiency and atmospheric
neutrino MC is used to estimate the expected number ofbackground events. When generating proton decay events,
the decay is assumed to happen with equal probability
for each proton in the water molecule. Hydrogen nuclei(free protons) are stationary and do not interact with othernucleons, whereas protons in oxygen nuclei (bound112011-7

Number of Events [/10 (MeV/c2)]

A. TAKENAKA et al.

PHYS. REV. D 102, 112011 (2020)
Conventional Region
SK-IV
Data
MC

250
200
150
100

Energy scale uncertainty

50

Region0
Number of Events [/10 (MeV/c2)]

TABLE III. Summary of the energy scale uncertainty andzenith angle dependent non-uniformity of the energy scale forboth the conventional and additional fiducial volumes in unitsof %. The row “(Abs., Var.)” is the breakdown of the energy scale
uncertainty, denoting the absolute energy scale uncertainty (Abs.)
and the time variation of the energy scale (Var.), respectively.

Additional Region
SK-IV
Data
MC

50

Conventional(Abs., Var.)
Additional(Abs., Var.)

40
30
20

Conventional
Additional

10
50

100

150

Reconstructed

0

200

250

300

Mass [MeV/c2]

FIG. 4. Reconstructed π 0 mass distribution of the two-ring bothe-like events in SK-IV. The top plot corresponds to the conventional and the bottom plot corresponds to the additional fiducial
volume. The black dots show the data in SK-IV, and red andgreen histograms show the atmospheric neutrino MC events.
Vertical error bars denote the statistical uncertainty.

protons) are subject to the effects of the Fermi motion,
nuclear binding energy, and correlated momentum effects
with the surrounding nucleons all of which must be
considered during their decays. Furthermore, the interaction of pions with the nuclear medium and the emission of

Deviation from Mean [%]Conventional Region
SK-I

SK-II

SK-III

SK-IV

2
0
-2
-4
4

SK-II

SK-III

SK-IV

3.3(3.1, 0.9)
3.3
(3.1, 0.9)

2.0
(2.0, 0.6)
3.9
(3.9, 0.6)

2.4
(1.6, 1.8)
2.4
(1.6, 1.8)

2.1
(2.1, 0.4)
2.2
(2.1, 0.6)

Zenith angle dependent nonuniformity

0
0

4

SK-I

Additional Region

2
0
-2
-4

2000/01/01

2004/12/31

2009/12/31

2014/12/31

Date

FIG. 5. Time variation of the average momentum of Michelelectrons as a function of date. For each fiducial volume and SK
phase data points are normalized by their mean value. The upper(lower) plot corresponds to the conventional (additional) fiducial
volume. Vertical error bars denote the statistical uncertainty. For
SK-I to -III, each data point corresponds to a one month averageand for SK-IV, each data point corresponds to a 10 day average.

0.6
1.4

1.1
1.5

0.6
1.3

0.5
0.4

gamma rays and neutrons as the residual 15N nucleus
deexcites must also be considered in bound proton decays.
The Fermi momentum of nucleons in 16O is simulated
based on the electron-12C scattering experiment data[21]. For such decays the effect of the nuclear binding
energy is introduced as an effective mass of the proton,
M0P ¼ M P − Eb , where M 0P is the modified proton mass,
MP is the proton rest mass and Eb is the nuclear binding
energy. Here Eb is drawn from a Gaussian distribution witha mean of 39.0 MeV (15.5 MeV) and a standard deviationof 10.2 MeV(3.8 MeV) for S (P) state protons. The ratio of
protons in the S state to those in the P state is taken to be
1∶3 based on the nuclear shell model [22]. Proton decay
kinematics can be distorted by repeated collisions withsurrounding nuclei during their decay, an effect known
as correlated decay, with a predicted probability of about
10% [23]. Neutral pion absorption, scattering, and charge
exchange processes (final state interactions, FSI) are
simulated with the NEUT cascade model [24,25].
Detailed descriptions about π-FSI and its interaction breakdown plot can be found in the last paper [12]. Gamma ray
and neutron emission following a bound proton decay issimulated based on [26], where the latter has a probabilityof less than 10%.
Atmospheric neutrinos are simulated using the HKKM
flux [27] and NEUT [24]. The neutrino interaction model
has been updated since the last paper [12] and a summaryof each interaction mode update can be found in [28].
For this analysis the update to the charged current single π
production model is the most important as it is thedominant background interaction mode. Previously thisinteraction was simulated using the Rein-Sehgal model[29] but updated form factors have been obtained from asimultaneous fit [30] to neutrino scattering data frombubble chamber experiments [31] and are included in
the new model. A comparison of the cross section as afunction of neutrino energy between the previous model

112011-8

SEARCH FOR PROTON DECAY VIA p → eþ π 0 …

PHYS. REV. D 102, 112011 (2020)

Cross Section [10-38 cm2]

1.2
Last Analysis, [12]Current Analysis (NEUT 5.3.6)
ANL Data, [31]
BNL Data, [31]

1
0.8
0.6

p

-

p +

-

n

p 0

n

-

n +

0.4
0.2
0
-1
10

1

10

-1

1

10

-1

1

10

Neutrino Energy [GeV]

FIG. 6. Charged current single π production cross section as a function of neutrino energy. The dotted black line corresponds to themodel used in previous SK proton decay searches, NEUT 5.1.4, and the solid red line shows that for the current analysis, NEUT 5.3.6.

(NEUT 5.1.4) and the current model (NEUT 5.3.6) isshown in Fig. 6. Since neutrinos of about 1 to 3 GeV are thedominant background to proton decay, this change is
expected to reduce the number of background events byabout 15%. At the same time the neutrino-nucleon momentum transfer is reduced in the new model, which subsequently increases the momentum of the produced lepton.
As the search below focuses on a back-to-back event
topology with a low total momentum characteristic ofproton decays, this change in the momentum transfer is
expected to further reduce backgrounds by 15%. In total a
30% reduction of the background is expected with the
new model.
Neutrons play an important role in distinguishingproton decay events from atmospheric neutrino backgrounds. The dominant production process for the latter,
representing 70% of produced neutrons, is via theinteraction of secondary hadrons with water. These
processes are simulated with the CALOR package [32],which uses HETC [33] for hadrons below 10 GeV,FLUKA [34] for hadrons above 10 GeV, and MICAP[35] for neutrons below 20 MeV. Low energy backgroundsources, such as gamma rays from the radioactive decayof nuclei in the detector material, are not simulated in the
MC but have non-negligible impacts on the search for
2.2 MeV gamma rays from neutron capture on hydrogen.
Therefore, PMT information from random trigger data isadded to the MC 18 μ sec after the primary event trigger
to model these backgrounds.
V. SEARCH METHOD
The event selection criteria for the search for p → eþ π 0
and p → μþ π 0 modes are as follows:
C1 Events must pass the updated FC event selection
criteria (see Sec. III) with a vertex within the fiducial
volume.
C2 Events must have two or three reconstructed
Cherenkov rings.

C3 All rings must be reconstructed as showering for
p → eþ π 0 and exactly one ring must be a nonshowering for p → μþ π 0.
C4 There must be no tagged Michel electrons for
p → eþ π 0 and exactly one for p → μþ π 0.
C5 For events with three rings, the reconstructed π 0 mass
must be 85 < Mπ0 < 185 MeV=c2 .
C6 The total reconstructed mass must be 800 < M tot <1050 MeV=c2 .
C7 The total momentum must be Ptot < 250 MeV=c.
C8 For the SK-IV data there must be no tagged neutrons.
For criterion C5 in the p → eþ π 0 mode, the π 0 mass iscalculated with every pair of rings. The pair giving the π 0mass closest to 135 MeV=c2 is considered to be two
gamma rays from the π 0 decay. The signal selection
efficiencies and the expected number of atmospheric
neutrino background events for both the conventional
and additional fiducial volumes are estimated with MC
and are shown at each step of the selection in Fig. 7. The
expected number of atmospheric neutrino background
events is estimated using a 500-year equivalent exposureof atmospheric neutrino MC events for each SK phase(2000 years in total) and is normalized to detector livetimeand the latest SK oscillation result [28]. Signal selection
efficiencies in the additional fiducial volume have been
improved by about 20% based on improvements in theevent reconstruction algorithm described in Sec. III.
However, due to fewer hit PMTs and a higher likelihoodof particles escaping the ID, the efficiencies are still lower
than those in the conventional fiducial volume. This isespecially true for C3, where the PID is degraded due toreduced hits, and C6, where energy is lost due to an
escaping particle, for p → eþ π 0. The situation is similar forp → μþ π 0 , where losses are seen at C3 (PID) and also at
C4 due to the muon exiting the ID.
Two signal regions are defined: a lower total momentum
region (Ptot < 100 MeV=c) and a higher total momentum region (100 ≤ Ptot < 250 MeV=c). The final signal

112011-9

A. TAKENAKA et al.

PHYS. REV. D 102, 112011 (2020)

1050Additional Region

Conventional Region
p e+ 0 MC

p e+ 0 MC

20
N

N

N

10

50

MC

+ 0

p

MC

20

N

N

N

N

N

4

10
Number of Events

Number of Events

+ 0

p

10

103
102

1

Additional Region

Conventional Region

4

10

+ 0

p
2

Signal Selection Efficiency [%]Signal Selection Efficiency [%]p e+ 02

DATA SKI~IV
ATM MCDATA SKI~IV
ATM MC

103
102
10
1

DATA SKI~IV
ATM MCDATA SKI~IV
ATM MC

10-1

10-1

10-2 C1 C2 C3 C4 C5 C6 C7 C8 C1 C2 C3 C4 C5 C6 C7 C8

10-2 C1 C2 C3 C4 C5 C6 C7 C8 C1 C2 C3 C4 C5 C6 C7 C8Event Selection

Event Selection

FIG. 7. The signal selection efficiencies (upper) and the expected number of atmospheric neutrino background events (lower,
histogram) and data candidates (lower, black dots) for p → eþ π 0 (left) and p → μþ π 0 (right). Vertical error bars on the data points
denote the statistical uncertainty. In each plot, the left panel corresponds to the conventional fiducial volume and the right panel to theadditional fiducial volume. Atmospheric neutrino MC is normalized by livetime and includes reweighting to the latest SK oscillation fit[28]. The combined data from SK-I to -IV is shown along with the combined signal and background MC.

selection efficiencies and expected number of atmospheric
neutrino background events are summarized in Table IV.
For the p → eþ π 0 (p → μþ π 0 ) mode, the livetimeweighted total signal selection efficiency and expected
number of background events in the additional fiducial
volume are 25.8% (25.2%) and 0.10 (0.19), respectively,
while in the conventional fiducial volume they are 39.8%(36.3%) and 0.49 (0.74). The expected background rate
for p → eþ π 0 without C8 is 1.83=Mt · years and is consistent with previous estimations by the K2K 1 kton waterþ0.45
Cherenkov detector of 1.63þ0.42−0.33 ðstatÞ −0.51 ðsysÞ=Mt · years[36]. A breakdown of the remaining background events byinteraction mode is shown in Table V. There are no
significant differences in the dominant charged current
single π production backgrounds in the two fiducial
volumes. Although the signal selection efficiencies in the
additional fiducial volume are lower than in the conventional fiducial volume, the enlarged fiducial volume leads
to an increase in the search sensitivity at the 90% C.L. of
about 12%.
Figures 8 and 9 show the two-dimensional total mass andtotal momentum distributions for the signal MC, theatmospheric neutrino MC, and all data from SK-I to -IVafter all the selection cuts have been applied except thecuts on the plotted variables. The lower Ptot signal region
contains mostly decays from free protons and is nearlybackground-free in both fiducial volumes. One-dimensional
distributions of each variable are shown in Fig. 10 after
all the selection cuts except the cut on the plotted variable.

As discussed in Sec. III, the total mass and total momentum
distributions in the additional fiducial volume are wider
than those in the conventional due to the effects of lower
numbers of hit PMTs and particles escaping the ID.
VI. SEARCH RESULTS
Applying the search criteria above to a 450 kton · years
exposure of the data resulted in no signal candidates forthe p → eþ π 0 mode in either the conventional or additional
fiducial volume. A single candidate was found in the p →μþ π 0 search’s upper Ptot part of the conventional fiducial
volume and is the same candidate found in the previous
search [12]. No additional candidates were found in the
additional fiducial volume. The number of data candidates
is not significantly higher than the expected number ofatmospheric neutrino events in either mode, for p → eþ π 00.59 events and for p → μþ π 0 0.94 events in total. For thelatter the Poisson probability to observe 1 event or morewith mean value of 0.94 is 60.9%. The data are consistent
with the atmospheric neutrino MC prediction in and outsideof the signal regions.
Systematic uncertainties for the selection efficiencies andthe expected number of background events are summarizedin Tables VI and VII. Uncertainties in the vertex position,
the number of identified Cherenkov rings, the identified
particle type, the number of tagged Michel electrons,
the energy scale, and the number of tagged neutrons are
considered as uncertainties in the reconstruction and are

112011-10

SEARCH FOR PROTON DECAY VIA p → eþ π 0 …

PHYS. REV. D 102, 112011 (2020)

TABLE IV. Summary of signal selection efficiencies, the expected number of background events and the number of data candidates
for 92.1 (19.3), 49.1 (10.3), 31.9 (6.7) and 199.5 ð41.8Þ kton · years exposures from the conventional (additional) fiducial volume of
SK-I, -II, -III, and -IV. The “Enlarged” row shows results for the enlarged 27.2 kton fiducial volume. Here “Lower” and “Upper” indicate
Ptot < 100 MeV=c and 100 ≤ Ptot < 250 MeV=c, respectively. Errors in the signal selection efficiency and the expected number ofbackground events are the quadratic sum of MC statistical error and systematic errors.
Signal selection efficiency (%)
Search mode Region

I

II

III

Background (events)
IV

I

II

III

Candidate (events)
IV

I

II

III

IV

p → eþ π 0

Conventional (Lower) 19.9  1.9 18.1  1.8 20.3  1.8 19.6  1.6<0.01
0.01  0.01
<0.01
<0.01
(Upper) 21.0  3.5 20.2  3.2 21.1  3.5 19.8  3.3 0.13  0.05 0.11  0.04 0.05  0.02 0.20  0.09
Additional(Lower) 9.6  1.5 8.8  1.4 9.9  1.7 11.0  1.5 0.01  0.01
<0.01
<0.01
<0.01
(Upper) 14.5  2.9 14.9  2.7 16.4  2.8 15.9  2.6 0.02  0.01
<0.01
0.02  0.01 0.05  0.04
Enlarged(Lower) 18.3  1.7 16.6  1.7 18.7  1.7 18.2  1.5 0.01  0.01 0.01  0.01
<0.01
<0.01
(Upper) 20.0  3.3 19.4  3.0 20.3  3.3 19.2  3.1 0.15  0.06 0.11  0.04 0.07  0.03 0.25  0.11

0
0
0
0
0
0

0
0
0
0
0
0

0
0
0
0
0
0

0
0
0
0
0
0

p → μþ π 0

Conventional (Lower) 17.0  1.6 16.2  1.5 17.5  1.6 19.9  1.9 0.03  0.02
<0.01
0.01  0.01
<0.01
(Upper) 16.7  3.1 16.5  2.8 16.8  3.0 18.9  3.7 0.19  0.06 0.10  0.04 0.06  0.02 0.34  0.12
Additional(Lower) 11.1  1.5 8.8  1.2 11.0  1.4 12.7  1.2
<0.01
<0.01
<0.01
<0.01
(Upper) 12.0  2.3 12.6  2.3 12.5  2.2 14.7  2.6 0.02  0.02 0.03  0.01 0.02  0.01 0.12  0.06
Enlarged(Lower) 16.0  1.5 14.9  1.4 16.4  1.5 18.7  1.7 0.03  0.02 0.01  0.01 0.01  0.01
<0.01
(Upper) 16.0  2.9 15.8  2.7 16.1  2.9 18.2  3.4 0.21  0.07 0.14  0.04 0.08  0.03 0.46  0.15

0
0
0
0
0
0

0
0
0
0
0
0

0
0
0
0
0
0

0
1
0
0
0
1

evaluated in each fiducial volume separately. For the signal
selection efficiency, the uncertainties associated withthe reconstruction in the additional fiducial volume are
relatively higher than those in the conventional fiducial
volume. As mentioned above, the reconstruction uncertainty is dominated by uncertainty in the energy scale. Dueto the degraded momentum resolution and the effects ofescaping particles, more signal MC events in the additional
fiducial volume are reconstructed near the total mass andtotal momentum cut boundaries than in the conventional
one (see Figs. 2 and 10). This has the effect of making theselection efficiency in the additional fiducial volume moresensitive to uncertainties in the energy scale.
Concerning the modeling of physics processes, uncertainties in the Fermi momentum, the π FSI, and correlated
decays are considered. The same source uncertainties areused in both fiducial volumes. Because of the worse
momentum resolution in the additional fiducial volume,
more free proton decay events are reconstructed in thehigher Ptot signal region and the fraction of the boundproton decay events is lower than in the conventional
fiducial volume. Since all considered uncertainties have
impacts only on the bound proton decay events, this smaller
bound proton decay event fraction leads smaller uncertainties
in the additional fiducial volume and higher Ptot signal region
for every physics model item. Furthermore, it should be notedthat the uncertainty in the Fermi momentum distribution
manifests as changes in the total reconstructed momentum
and can be aggravated by the reconstruction performance ineach fiducial volume. This uncertainty is estimated basedon the initial 16O proton momentum distribution in models
based on data (see Sec. IV) in comparison with the NEUT’s
Fermi gas model. The degraded momentum reconstruction
performance in the additional fiducial volume smears theeffect from this model change and results in relatively small
uncertainties in the higher Ptot signal region.
Uncertainties affecting the expected number of atmospheric neutrino background events are evaluated combining
the upper and lower Ptot signal regions because there are
only a few events remaining in the latter. The uncertainties
associated with the event reconstruction are evaluated using
the same methods as the signal selection efficiency. The
systematic uncertainty associated with the vertex position,
which is sub-dominant in the reconstruction items andestimated by artificially shifting the vertex position, partially anticorrelates between the conventional and additional fiducial volume, resulting in the smallest uncertainty
after combining the two fiducial volumes. Physics model
uncertainties include those from the neutrino flux, theneutrino interaction (cross section) model, the π FSI model,
and π secondary interactions (SI) in water. Other than thereconstruction uncertainties discussed above, those fromthe neutrino interaction model are dominant. As shown in
TABLE V. Breakdown of interaction modes for background
events remaining in the signal region for the p → eþ π 0 and p →μþ π 0 searches in units of %. Here, CC and NC stand for chargedcurrent and neutral-current, respectively and QE, 1π and DIS
stand for quasielastic scattering, single π production and deep
inelastic scattering, respectively.
p → eþ π 0
RegionConventional
Additional

CCQE
18
21

CC1π
63
62

CCDIS
10
14

NC1π
1
0

NCDIS
8
3

p → μþ π 0
Conventional
Additional

13
7

65
60

18
17

0
0

4
16

112011-11

A. TAKENAKA et al.

PHYS. REV. D 102, 112011 (2020)

FIG. 8. Reconstructed total mass shown against the total momentum distributions for p → eþ π 0 after all cuts except those on thesevariables. The top plots correspond to the conventional and the bottom plots correspond to the additional fiducial volume. The left panels
show the signal MC (SK-I to -IV are combined), where lighter colors show free protons and dark colors show bound protons. The middle
panels show the 2000 year-equivalent atmospheric neutrino MC. The right panels show all the combined data SK-I to -IV. The black box
shows the signal region and for the middle panels the markers in the signal region have been enlarged for visibility.

Table V and Figure 10 the background distributions anduncertainties are similar in the two fiducial volumes.
The systematic uncertainty associated with the charged
current single π production is assigned as the change in the

background after varying the form factors, introduced inSec. IV, by their error size. In the additional (conventional)
fiducial volume this results in a 9.1% (11.8%) change in the
p → eþ π 0 background and a 9.1% (13.9%) change for

FIG. 9. Reconstructed total mass shown against the total momentum distributions for p → μþ π 0 after all cuts except those on thesevariables. The top plots correspond to the conventional and the bottom plots correspond to the additional fiducial volume. The left panels
show the signal MC (SK-I to -IV are combined), where lighter colors show free protons and dark colors show bound protons. The middle
panels show the 2000 year-equivalent atmospheric neutrino MC. The right panels show all the combined data SK-I to -IV. The black box
shows the signal region and for the middle and right panels the markers in the signal region have been enlarged for visibility.

112011-12

SEARCH FOR PROTON DECAY VIA p → eþ π 0 …

PHYS. REV. D 102, 112011 (2020)

p e+ 0103

Conventional Region

102

102

10

10

Conventional Region

1

Number of Events

Number of Events

1
DATA SKI~IV
ATM MCFree Proton
Bound Proton

10-1
10-2

Additional Region

102
10

10-2

10
1
-1

DATA SKI~IV
ATM MCFree Proton
Bound Proton

-2

10

200

600

400

800

1000

0

Total Mass [MeV/c2]

200

400

600

800

Additional Region

102

-1

10

DATA SKI~IV
ATM MCFree Proton
Bound Proton

10-1

1

10-30

+ 0

p

103

DATA SKI~IV
ATM MCFree Proton
Bound Proton

10

-2

10
1000

10-30

Total Momentum [MeV/c]

200

400

600

800

Total Mass [MeV/c2]

1000

0

200

400

600

800

1000

Total Momentum [MeV/c]

FIG. 10. Reconstructed total mass and total momentum distributions for p → eþ π 0 (left) and p → μþ π 0 (right) after all the cuts except
those on the plotted variables. The top panels show the conventional and the bottom panels show the additional fiducial volume. The left
panels show the reconstructed total mass and the right panels show the reconstructed total momentum distributions. The signal MC
histograms are stacked, showing free proton decay events (light color) and bound proton decay events (dark color, hatched). The
combined result from SK-I to -IV is shown normalized by the 90% C.L. upper limit on the signal derived in this work. Atmospheric
neutrino MC (red and green) is normalized by livetime and includes reweighting to the latest SK oscillation fit [28]. Vertical error bars on
the data points denote the statistical uncertainty. Bold lines and arrows show the signal region.

p → μþ π 0 . In the previous analysis this uncertainty was
7.9% and 5.3% for the conventional fiducial volume of
the two modes, respectively. In addition to the above, an
uncertainty on the detector exposure is conservatively
estimated to be 1%.
VII. LIFETIME LIMIT
Since no significant event excess was observed ineither decay mode, lower limits on the partial lifetime ofeach have been calculated using a Bayesian method [37].

In this calculation numbers from the “Enlarged” rows inTables IV, VI and VII have been used for the signal
selection efficiencies, the expected number of background
events, and their systematic uncertainties. Since the search
performance varies depending on the data taking period,
separate exposures from SK-I to -IV are taken into account.
The expected number of background events is also different
between the two Ptot signal regions, and therefore they are
considered separately in the following calculation. The
probability density function used for the proton decayrate (Γ) for the eight signal regions, SK-I to -IV each withTABLE VI. Summary of systematic uncertainties [%] on the signal selection efficiency for each fiducial volume.
The “Enlarged” row shows the result for the combination of the two fiducial volumes. Here “Lower” and “Upper”
show the Ptot < 100 MeV=c and 100 ≤ Ptot < 250 MeV=c signal regions, respectively.
Correlated decay

Fermi momentum

π FSI

Reconstruction

Total(Lower)(Upper)(Lower)(Upper)(Lower)(Upper)

1.7
9.0
2.7
8.4
1.9
8.9

7.2
6.7
7.8
1.0
7.2
5.7

2.8
11.9
3.8
10.6
2.9
11.7

3.5
2.8
10.3
10.0
3.6
3.2

8.6
16.6
13.7
16.8
8.8
16.1

(Lower)(Upper)(Lower)(Upper)(Lower)(Upper)

1.9
9.3
2.0
8.4
1.9
9.2

7.3
8.3
6.8
4.0
7.2
7.7

2.7
13.3
2.9
11.3
2.7
13.0

4.5
4.0
7.1
9.5
4.8
4.5

9.2
18.7
10.4
17.5
9.3
18.2

Regionþ 0p→e πConventional
Additional
Enlargedp → μþ π 0
Conventional
Additional
Enlarged

112011-13

A. TAKENAKA et al.

PHYS. REV. D 102, 112011 (2020)

TABLE VII. Summary of systematic uncertainties [%] on the expected number of atmospheric neutrino
background events for each fiducial volume. They have been evaluated for the combined Ptot < 100 MeV=c
and 100 ≤ Ptot < 250 MeV=c signal regions. Here the “Enlarged” row shows the result for the combination of thetwo fiducial volumes.
Neutrino flux

Neutrino interaction

π FSI and SI

Reconstruction

Total

p → eþ π 0
Conventional
Additional
Enlarged

7.3
7.2
7.3

21.2
17.3
19.8

12.8
13.9
12.7

21.3
25.2
20.5

33.5
34.3
32.0

p → μþ π 0
Conventional
Additional
Enlarged

7.2
7.3
7.3

19.0
16.8
18.3

9.3
11.3
8.0

16.5
21.4
15.6

27.8
30.3
26.3

Region“Lower” and “Upper” total momentum regions, is defined
as follows:
ZZZ −ðΓλi ϵi þbi Þ1eðΓλi ϵi þ bi ÞniPi ðΓjni Þ ¼
Aini !
× PðΓÞPðλi ÞPðϵi ÞPðbi Þdϵi dλi dbi ;ð3Þ

where i is the index of each signal region, Ai is anormalization factor representing the total integral ofPi ðΓjni Þ, ni is the number of observed candidates, λi isthe exposure, ϵi is the signal selection efficiency and bi isthe expected number of background events. The priorprobability on the decay rate PðΓÞ is assumed to beuniform and Pðλi Þ and Pðϵi Þ represent the prior probabilities for the exposure and signal selection efficiency,
respectively. Both are assumed to be Gaussian,8< exp −ðλi −λ2 0i Þ2 ; ðλ > 0Þi
2σ λi
Pðλi Þ ∝ð4Þ:0;ðotherwiseÞ
8
< exp −ðϵi −ϵ0i Þ2 ; ðϵ > 0Þi
2σ 2ϵið5ÞPðϵi Þ ∝:0;ðotherwiseÞ
where λ0i (σ λi ) and ϵ0i (σ ϵi ) are the estimates (systematic
uncertainties) of the exposure and signal selection efficiency,
respectively. For the expected number of background events
the prior probability, Pðbi Þ, is defined as the convolution of a
Gaussian and Poisson distribution:Pðbi Þ ∝8R< ∞ e−B Bnbi exp −ðCi bi2−BÞ2 dB;
:

0

0;

nbi !

2σ b

ðbi > 0ÞiðotherwiseÞ
ð6Þ

where nbi is the expected number of backgrounds in each
500 years atmospheric neutrino MC (before livetime normalization), Ci is a constant factor to normalize MC to thedata livetime and σ bi is the systematic uncertainty on thenumber of background events. The standard deviation ofeach Gaussian is taken as the corresponding systematic
uncertainty described in Sec. VI. With these definitions the
proton decay rate limit at a given confidence level (C.L.) is
calculated as
C:L: ¼

Z Γ¼Γ
Γ¼0

limit

8
Y

Pi ðΓjni ÞdΓ:

ð7Þ

i¼1

As a consequence, lower limits on the partial lifetime are
obtained as:
τlimit1;¼
ΓlimitB

ð8Þ

where B represents the branching ratio of a particular decay
mode. Using the above formulas the resulting limits at
90% C.L. are τ=Bðp → eþ π 0 Þ > 2.4 × 1034 years andτ=Bðp → μþ π 0 Þ > 1.6 × 1034 years. The lifetime limit forthe p → eþ π 0 mode has improved by a factor of 1.5 as is
expected from the increased exposure. On the other hand, forthe p → μþ π 0 mode the limit has improved by a factor of
two because one of the two candidates reported in the last
paper [12] moved out of the present analysis’s signal region
after the updates in the detector calibration described therein.
VIII. CONCLUSION
Improved event selection and reconstruction algorithms
have been introduced to enlarge the fiducial volume of theSuper-Kamiokande detector from 22.5 kton to 27.2 kton.
With the new selection, the non-neutrino backgroundcontamination rate in the additional fiducial volume is
kept within 1%, tolerable level for SK analyses. The
improved search sensitivities for proton decay via p →eþ π 0 and p → μþ π 0 are led by the enlarged fiducial volume
with the improved event reconstruction algorithm.
Using a combined exposure of 450 kton · years representing the full Super-Kamiokande data set from SK-I

112011-14

SEARCH FOR PROTON DECAY VIA p → eþ π 0 …

PHYS. REV. D 102, 112011 (2020)

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 and the Ministry of Education(2018R1D1A3B07050696,
2018R1D1A1B07049158),
the Japan Society for the Promotion of Science, theNational Natural Science Foundation of China underGrants No. 11235006, the Spanish Ministry of Science,
Universities and Innovation (Grant No. PGC2018-099388B-I00), the Natural Sciences and Engineering ResearchCouncil (NSERC) of Canada, the Scinet and Westgrid
consortia of Compute Canada, the National Science Centre,
Poland (2015/18/E/ST2/00758), the Science andTechnology Facilities Council (STFC) and GridPPP, UK,
the European Union’s Horizon 2020 Research andInnovation Programme under the Marie SklodowskaCurie grant agreement no. 754496, H2020-MSCA-RISE2018 JENNIFER2 grant agreement no. 822070, andH2020-MSCA-RISE-2019 SK2HK grant agreement
no. 872549.

[1] H. Georgi and S. L. Glashow, Unity of All ElementaryParticle Forces, Phys. Rev. Lett. 32, 438 (1974); P.
Langacker, Grand unified theories and proton decay, Phys.
Rep. 72, 185 (1981).
[2] H. Georgi, H. R. Quinn, and S. Weinberg, Hierarchy ofInteractions in Unified Gauge Theories, Phys. Rev. Lett. 33,
451 (1974).
[3] H. Fritzsch and P. Minkowski, Unified interactions of
leptons and hadrons, Ann. Phys. (N.Y.) 93, 193 (1975).
[4] F. Gursey, P. Ramond, and P. Sikivie, A universal
gauge theory model based on E6 , Phys. Lett. B 60, 177(1976).
[5] W. de Boer, Grand unified theories and supersymmetry inparticle physics and cosmology, Prog. Part. Nucl. Phys. 33,
201 (1994); G. Bertone, D. Hooper, and J. Silk, Particle dark
matter: Evidence, candidates and constraints, Phys. Rep.
405, 279 (2005); N. Nagata, K. A. Olive, and J. Zheng,
Asymmetric dark matter models in SO(10), J. Cosmol.
Astropart. Phys. 02 (2017) 016; N. Okada, D. Raut, and Q.
Shafi, Inflation, proton decay, and Higgs-portal dark matterin SOð10Þ × Uð1Þϕ , Eur. Phys. J. C 79, 1036 (2019).
[6] R. Barbieri, D. V. Nanopoulos, G. Morchio, and F. Strocchi,
Neutrino masses in grand unified theories, Phys. Lett. 90B,
91 (1980); W. Buchmülle, Neutrinos, grand unificationand leptogenesis, arXiv:hep-ph/0204288v2; P. F. Pérez, A.
Gross, and C. Murgu, Seesaw scale, unification, and proton
decay, Phys. Rev. D 98, 035032 (2018); S. Saad, Origin of a
two-loop neutrino mass from SU(5) grand unification, Phys.
Rev. D 99, 115016 (2019).
[7] G. G. Raffelt, Astrophysical methods to constrain axions
and other novel particle phenomena, Phys. Rep. 198, 1(1990); P. H. Frampton and T. W. Kephart, Natural Strong

CP Conservation in Flipped Physics, Phys. Rev. Lett. 65,
820 (1990); A. Ernst, A. Ringwald, and C. Tamarit, Axion
predictions in SOð10Þ × Uð1ÞPW models, J. High Energy
Phys. 02 (2018) 103; P. F. Pérez, C. Murgui, and A. D.
Plascencia, Axion dark matter, proton decay and unification,
J. High Energy Phys. 01 (2020) 091.
[8] S. M. Barr, A new symmetry breaking pattern forSO(10) and proton decay, Phys. Lett. 112B, 219 (1982);
I. Antoniadis, John Ellis, J. S. Hagelin, and D. V.
Nanopoulos, The flipped SUð5Þ × Uð1Þ string model revamped, Phys. Lett. B 231, 65 (1989).
[9] M. Machacek, The decay modes of the proton, Nucl. Phys.
B159, 37 (1979); N. Maekawa and Y. Muramatsu, Nucleon
decay via dimension-6 operators in anomalous Uð1ÞA
supersymmetric GUT, Phys. Rev. D 88, 095008 (2013);
N. Maekawa and Y. Muramatsu, Flavor changing nucleon
decay, Phys. Lett. B 767, 398 (2017).
[10] J. Ellis, M. A. G. Garcia, N. Nagata, D. V. Nanopoulos,
and K. A. Olive, Proton decay: Flipped vs unflipped SU(5),J. High Energy Phys. 05 (2020) 021.
[11] C. McGrew et al. (IMB Collaboration), Search for nucleon
decay using the IMB-3 detector, Phys. Rev. D 59, 052004(1999); K. S. Hirata et al. (Kamiokande Collaboration),
Experimental limits on nucleon lifetime for lepton þmeson decay modes, Phys. Lett. B 220, 308 (1989); M.
Shiozawa et al. (Super-Kamiokande Collaboration),
Search for Proton Decay via p → eþ π 0 in a Large Water
Cherenkov Detector, Phys. Rev. Lett. 81, 3319 (1998); H.
Nishino et al. (Super-Kamiokande Collaboration), Search
for Proton Decay via p → eþ π 0 and p → μþ π 0 in a Large
Water Cherenkov Detector, Phys. Rev. Lett. 102, 141801(2009).

to -IV and data in the additional fiducial volume, wehave performed searches for proton decay via p → eþ π 0
and p → μþ π 0 . No significant event excess above theatmospheric neutrino backgrounds has been found for
either mode. Lower limits on the partial lifetime of
τ=Bðp → eþ π 0 Þ > 2.4 × 1034 years and τ=Bðp → μþ π 0 Þ >1.6 × 1034 years are set at 90% confidence level. Theselimits indicate a 1.5 times longer lifetime limit for thep → eþ π 0 mode and two times longer for the p → μþ π 0mode than the previous results [12], and are the world’s
most stringent constraints for these decay modes.
ACKNOWLEDGMENTS

112011-15

A. TAKENAKA et al.

PHYS. REV. D 102, 112011 (2020)[12] K. Abe et al. (The Super-Kamiokande Collaboration),
Search for proton decay via p → eþ π 0 and p → μþ π 0 in
0.31 megaton · years exposure of the Super-Kamiokande
water Cherenkov detector, Phys. Rev. D 95, 012004 (2017).
[13] Y. Fukuda et al. (Super-Kamiokande Collaboration), The
Super-Kamiokande detector, Nucl. Instrum. Methods Phys.
Res., Sect. A 501, 418 (2003).
[14] K. Abe et al. (Super-Kamiokande Collaboration), Calibration of the Super-Kamiokande detector, Nucl. Instrum.
Methods Phys. Res., Sect. A 737, 253 (2014).
[15] H. Nishino, K. Awai, Y. Hayato, S. Nakayama, K. Okumura,
M. Shiozawa, A. Takeda, K. Ishikawa, A. Minegishi, and Y.
Arai, High-speed charge-to-time converter ASIC for theSuper-Kamiokande detector, Nucl. Instrum. Methods Phys.
Res., Sect. A 610, 710 (2009).
[16] E. R. Davies, Machine Vision: Theory, Algorithms, Practicalities (Academic Press, San Diego, 1997).
[17] M. Shiozawa, Reconstruction algorithms in the SuperKamiokande large water Cherenkov detector, Nucl. Instrum.
Methods Phys. Res., Sect. A 433, 240 (1999).
[18] T. J. Irvine, Ph.D. thesis, University of Tokyo, 2014.
[19] M. Tanaka et al. (The Super-Kamiokande Collaboration),
Search for proton decay into three charged leptons in 0.37
megaton·years exposure of the Super-Kamiokande, Phys.
Rev. D 101, 052011 (2020)..
[20] Y. Ashie et al. (Super-Kamiokande Collaboration), Measurement of atmospheric neutrino oscillation parameters by
Super-Kamiokande I, Phys. Rev. D 71, 112005 (2005).
[21] K. Nakamura, S. Hiramatsu, T. Kamae, H. Muramatsu, N.
Izutsu, and Y. Watase, The reaction 12Cðe; e0 pÞ at 700 MeV
and DWIA analysis, Nucl. Phys. A268, 381 (1976).
[22] M. G. Mayer and J. H. D. Jensen, Elementary Theory of
Nuclear Shell Structure (Wiley, New York, 1955).
[23] T. Yamazaki and Y. Akaishi, Nuclear medium effects oninvariant mass spectra of hadrons decaying in nuclei, Phys.
Lett. B 453, 1 (1999).
[24] Y. Hayato, NEUT, Nucl. Phys. B, Proc. Suppl. 112, 171(2002); G. Mitsuka, NEUT, AIP Conf. Proc. 967, 208(2007); AIP Conf. Proc. 981, 262 (2008).
[25] L. L. Salcedo, E.Oset, M. J. Vicente-Vacas, and C. GarciaRecio, Computer simulation of inclusive pion nuclear
reactions, Nucl. Phys. A484, 557 (1988).

[26] H. Ejiri, Nuclear deexcitations of nucleon holes associatedwith nucleon decays in nuclei, Phys. Rev. C 48, 1442
(1993).
[27] 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).
[28] K. Abe et al., Atmospheric neutrino oscillation analysis withexternal constraints in Super-Kamiokande I-IV, Phys. Rev.
D 97, 072001 (2018).
[29] D. Rein and L. M. Sehgal, Neutrino excitation of baryon
resonances and single pion production, Ann. Phys. (N.Y.)
133, 79 (1981).
[30] K. M. Graczyk and J. T. Sobczyk, Form factors in the quark
resonance model, Phys. Rev. D 77, 053001; Erratum, Phys.
Rev. D 79, 079903 (2009).
[31] G. M. Radecky et al., Study of single-pion production
by weak charged currents in low-energy νd interactions,Phys. Rev. D 25, 1161 (1982); T. Kitagaki et al., Chargedcurrent exclusive pion production in neutrino-deuterium
interactions, Phys. Rev. D 34, 2554 (1986).
[32] C. Zeitnitz and T. A. Gabriel, The GEANT-CALOR interface and benchmark calculations of ZEUS test calorimeters,
Nucl. Instrum. Methods Phys. Res., Sect. A 349, 106(1994).
[33] HETC: Monte Carlo High-Energy Nucleon-Meson Transport Code, Oak Ridge National Laboratory RSIC Computer
Code Collection CCC-178.
[34] A. Fassó et al., FLUKA92, Proc. 1st Workshop on Simulating Accelerator Radiation Environments, 1993.
[35] J. O. Johnson and T. A. Gabriel, A user’s guide to MICAP:
A Monte Carlo Ionization Chamber Analysis Package,
ORNL/TM-10340 (1988).
[36] S. Mine et al. (K2K Collaboration), Experimental studyof the atmospheric neutrino backgrounds for p → eþ π 0
searches in water Cherenkov detectors, Phys. Rev. D 77,
032003 (2008).
[37] C. Amsler et al. (Particle Data Group Collaboration),
Review of particle physics, Phys. Lett. B 667, 1 (2008);
B. P. Roe and M. B. Woodroofe, Setting confidence belts,
Phys. Rev. D 63, 013009 (2000).

112011-16