PHYSICAL REVIEW D 95, 012004 (2017)

Search for proton decay via p → eþ π0 and p → μþ π0
in 0.31 megaton · years exposure of theSuper-Kamiokande water Cherenkov detector
K. Abe,1,31 Y. Haga,1 Y. Hayato,1,31 M. Ikeda,1 K. Iyogi,1 J. Kameda,1,31 Y. Kishimoto,1,31 M. Miura,1,31 S. Moriyama,1,31
M. Nakahata,1,31 T. Nakajima,1 Y. Nakano,1 S. Nakayama,1,31 A. Orii,1 H. Sekiya,1,31 M. Shiozawa,1,31 A. Takeda,1,31
H. Tanaka,1 T. Tomura,1,31 R. A. Wendell,1,31 R. Akutsu,2 T. Irvine,2 T. Kajita,2,31 K. Kaneyuki,2,31,* Y. Nishimura,2E. Richard,2 K. Okumura,2,31 L. Labarga,3 P. Fernandez,3 J. Gustafson,4 C. Kachulis,4 E. Kearns,4,31 J. L. Raaf,4
J. L. Stone,4,31 L. R. Sulak,4 S. Berkman,5 C. M. Nantais,5 H. A. Tanaka,5 S. Tobayama,5 M. Goldhaber,6,*
W. R. Kropp,7 S. Mine,7 P. Weatherly,7 M. B. Smy,7,31 H. W. Sobel,7,31 V. Takhistov,7 K. S. Ganezer,8 B. L. Hartfiel,8J. Hill,8 N. Hong,9 J. Y. Kim,9 I. T. Lim,9 R. G. Park,9 A. Himmel,10 Z. Li,10 E. O’Sullivan,10 K. Scholberg,10,31
C. W. Walter,10,31 T. Wongjirad,10 T. Ishizuka,11 S. Tasaka,12 J. S. Jang,13 J. G. Learned,14 S. Matsuno,14 S. N. Smith,14
M. Friend,15 T. Hasegawa,15 T. Ishida,15 T. Ishii,15 T. Kobayashi,15 T. Nakadaira,15 K. Nakamura,15,31 Y. Oyama,15
K. Sakashita,15 T. Sekiguchi,15 T. Tsukamoto,15 A. T. Suzuki,16 Y. Takeuchi,16,31 T. Yano,16 S. V. Cao,17 T. Hiraki,17
S. Hirota,17 K. Huang,17 T. Kikawa,17 A. Minamino,17 T. Nakaya,17,31 K. Suzuki,17 Y. Fukuda,18 K. Choi,19
Y. Itow,19 T. Suzuki,19 P. Mijakowski,20 K. Frankiewicz,20 J. Hignight,21 J. Imber,21 C. K. Jung,21 X. Li,21
J. L. Palomino,21 M. J. Wilking,21 C. Yanagisawa,21,† D. Fukuda,22 H. Ishino,22 T. Kayano,22 A. Kibayashi,22
Y. Koshio,22 T. Mori,22 M. Sakuda,22 C. Xu,22 Y. Kuno,23 R. Tacik,24,33 S. B. Kim,25 H. Okazawa,26 Y. Choi,27
K. Nishijima,28 M. Koshiba,29 Y. Totsuka,29,* Y. Suda,30 M. Yokoyama,30,31 C. Bronner,31 M. Hartz,31 K. Martens,31
Ll. Marti,31 Y. Suzuki,31 M. R. Vagins,31,7 J. F. Martin,32 A. Konaka,33 S. Chen,34 Y. Zhang,34 and R. J. Wilkes35(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 British Columbia,
Vancouver, British Columbia V6T1Z4, Canada
6
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
7
Department of Physics and Astronomy, University of California,
Irvine, Irvine, California 92697-4575, USA
8
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
9
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
10
Department of Physics, Duke University, Durham North Carolina 27708, USA
11
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
12
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
13
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
14
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
15High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
16
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan17
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan18
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
19
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan
20
National Centre For Nuclear Research, 00-681 Warsaw, Poland
21
Department of Physics and Astronomy, State University of New York at Stony Brook,
New York 11794-3800, USA
22
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
23
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
24
Department of Physics, University of Regina, 3737 Wascana Parkway, Regina SK S4SOA2, Canada
25
Department of Physics, Seoul National University, Seoul 151-742, Korea
26
Department of Informatics in Social Welfare, Shizuoka University of Welfare,
Yaizu, Shizuoka 425-8611, Japan
27
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea

2470-0010=2017=95(1)=012004(10)012004-1© 2017 American Physical Society

K. ABE et al.

PHYSICAL REVIEW D 95, 012004 (2017)28

Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
29
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan30
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
31
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
32
Department of Physics, University of Toronto, 60 St., Toronto, Ontario M5S1A7, Canada
33
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T2A3, Canada
34
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
35
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 13 October 2016; published 6 January 2017)
We have searched for proton decay via p → eþ π 0 and p → μþ π 0 using Super-Kamiokande data from
April 1996 to March 2015, 0.306 megaton · years exposure in total. The atmospheric neutrino backgroundrate in Super-Kamiokande IV is reduced to almost half that of phase I-III by tagging neutrons associatedwith neutrino interactions. The reach of the proton lifetime is further enhanced by introducing new signal
criteria that select the decay of a proton in a hydrogen atom. No candidates were seen in the p → eþ π 0
search. Two candidates that passed all of the selection criteria for p → μþ π 0 have been observed, but these
are consistent with the expected number of background events of 0.87. Lower limits on the proton lifetime
are set at τ=Bðp → eþ π 0 Þ > 1.6 × 1034 years and τ=Bðp → μþ π 0 Þ > 7.7 × 1033 years at 90% confidence
level.
DOI: 10.1103/PhysRevD.95.012004

I. INTRODUCTION
Grand unified theories (GUTs) [1] are motivated by theapparent convergence of the running couplings of thestrong, weak, and electromagnetic forces at high energy(1015 –1016 GeV). Such a high energy scale is out of thereach of accelerators; however, a general feature of GUTs istheir prediction of the instability of protons by baryon
number violating decays. The grand unification idea issuccessful in many aspects; these include an understandingof electric charge quantization, the coexistence of quarks
and leptons and their quantum numbers, and as an
explanation of the scale of the neutrino masses. Proton
decay now remains as a key missing piece of evidence for
grand unification [2].
In GUTs, nucleon decay can proceed via exchange of a
massive gauge boson between two quarks. The favoredgauge-mediated decay mode in many GUTs is p → eþ π 0 .
On the other hand, the flipped SUð5Þ GUT model [3]predicts that the p → μþ π 0 mode can have a branchingratio comparable to that of the p → eþ π 0 mode. Water
Cherenkov detectors are suitable for these decay modes
because all final state particles after the proton decay aredetectable since they are above the Cherenkov threshold,enabling reconstruction of the proton mass and momentum
to distinguish these events from atmospheric neutrino
backgrounds. The dominant inefficiency comes from
Fermi momentum of protons and pion interactions inside
the nucleus, which distorts the reconstructed proton mass*

Deceased.
Also at BMCC/CUNY, Science Department, New York,New York, USA.
†and momentum distributions. However, the two hydrogenatoms in a water molecule are outside of the oxygen
nucleus; these act as free protons which are not subject
to the nuclear effects. As a result, water Cherenkov
detectors can achieve high efficiency for p → eþ π 0 and
p → μþ π 0 searches.
In the minimal SU(5) GUT [4], the predicted proton
lifetime to eþ π 0 is 10311 years, which has been ruled out
by experimental results from IMB [5], Kamiokande [6],and Super-Kamiokande [7–9]. However, longer lifetimes
for this decay mode (∼1035 years) are predicted by otherclasses of GUTs e.g., minimal SUSY SU(5) [10], flipped
SU(5) [3], SO(10) [11], etc., which are subject to experimental tests. The experimental searches for the gaugemediated proton decays are further motivated by thediscovery of a Higgs-like boson with a mass around
125 GeV=c2 [12,13]. This paper describes the search for
p → eþ π 0 and p → μþ π 0 by improved analysis techniqueswith 0.306 megaton · years of Super-Kamiokande data.
II. SUPER-KAMIOKANDE DETECTOR
Super-Kamiokande (SK) is a large upright cylindricalwater Cherenkov detector, 39 m in diameter and 41 m inheight, containing 50 ktons of pure water. Details of thedetector have been described in Ref. [14]. The previous
publication of p → eþ π 0 and p → μþ π 0 limits [9] reported
results using 220 kiloton · years exposure with 90% confidence level lower limits on the proton lifetime set at 1.3 ×1034 and 1.1 × 1034 years, respectively. In the SK-I period,
the photocathode coverage inside the inner detector was
40%; this was reduced to 19% during SK-II. After

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production and installation of replacement 50-cm photomultiplier tubes (PMTs), the photocathode coverage insidethe detector was recovered to the original 40% in 2006.
The period between July 2006 and September 2008 is
defined as SK-III. In the summer of 2008, the detector
readout electronics were upgraded with improved performance, including a “deadtime free” data acquisition
system that records all successive PMT hit information[15]. This has been the configuration of the detector since
September 2008; it is called SK-IV. The new configurationof the detector contributes to improved tagging efficiencyof Michel decay electrons in SK-IV. The tagging efficiency of Michel electrons is estimated to be 99% for SKIV and 82% for the period before SK-IV by using p →μþ π 0 MC samples. It also enables tagging of neutrons in
SK-IV. The signature of the neutron, 2.2 MeV gamma ray
emission from the neutron capture on hydrogen with a meancapture time of 200 μ sec is too faint to be triggered by thedata acquisition system used in SK-I through SK-III. The
upgraded electronics in SK-IV adopt a triggerless readout
scheme to record every hit, including all hits by 2.2 MeV
gamma rays. A software trigger is then issued after every
fully contained event to save all hits within a 500 μ sec
timing window for physics analyses. In this paper, we use
data from April 1996 up to March 2015, corresponding to4973 live days or 306.3 kton · years in total by summing up
91.7, 49.2, 31.9, 133.5 kton · years of SK-I, II, III, andIV data.
III. NEUTRON TAGGING
Neutron tagging can benefit proton decay analyses,
providing an additional handle for rejecting the atmospheric neutrino interactions that are the main background to
proton decays. Atmospheric neutrino interactions are often
accompanied by neutrons, while the probability of aneutron being emitted by deexcitation of a nucleus after
proton decay is rather small, and no neutron is produced in
the decay of a free proton. Furthermore, these proton decay
modes do not produce neutrons in secondary interactions inwater because the final state particles in these decay modes
are lepton and gammas. The neutron tagging algorithm wasoriginally developed to identify antineutrino interactions,in which a neutron is often emitted; the supernova relicneutrino search [16], the cosmic-ray-muon spallation
background measurement [17], and the neutrino oscillation analysis [18] have been improved by this technique.
To find 2.2 MeV γ candidates, we search for hit clusters
with ≥ 7 hits within a 10 ns sliding time window, aftertime-of-flight (TOF) subtraction using the vertex of theprompt neutrino interaction. Sixteen variables describedin Ref. [18] are input to a neural network to distinguishthe 2.2 MeV γ signal from background. The efficiencyof neutron tagging by this method is estimated to be
20.5  2.1% with a mistagging probability of 1.8%. The
performance of the neutron tagging was confirmed byintroducing a neutron source (americium-beryllium) into
the SK tank [16].
IV. SIMULATION
Our simulation of the atmospheric neutrino cross sections and flux is modeled by NEUT [19] and HKKM [20].
In the case of atmospheric neutrino interactions, neutrons
are generated in primary interactions (10%), hadron andmeson interactions in the nucleus (17%), and interactionsof hadrons in water (73%). For hadron-water interactions atenergies below 3.5 GeV, our simulation uses the NucleonMeson-Transport-Code (NMTC), which is based on the
Bertini intranuclear hadronic cascade model [21]. For low
energy (< 20 MeV) neutron propagation, the Monte Carlo
Ionization Chamber Analysis Package (MICAP) code [22]is employed. Thermalized neutrons are then simulated until
capture on hydrogen and emission of 2.2 MeV γ-rays.
Neutrons can also be generated via the deexcitation process
and muon capture in water. These are not taken into accountin our atmospheric neutrino simulation, but are instead
included in our uncertainty by comparison of data andatmospheric ν Monte Carlo. In order to include all possible
low energy backgrounds, real data taken by a random
trigger are added into the simulated neutron data.
The proton decay simulation has been updated since theprevious paper [23] by implementation of proton andneutron emission at deexcitation from s-state [24], and7.5% of p → eþ π 0 events in oxygen are accompanied by aneutron.
A π 0 produced by bound proton decay interacts via
the strong interaction and there is a significant probabilityof reinteraction within the nucleus prior to escape.
NEUT also simulates the pion final state interactions(π-FSI). The NEUT π-FSI model is a microscopic cascade
where the pion is propagated classically through thenuclear medium in finite steps; it is capable of simulating
various nuclei. The π-FSI model has been tuned tovarious π  -nucleus experimental data including C, O,
Al, Fe, and has been updated [25] since the previous
paper [9]. The left panel in Fig. 1 shows the π þ crosssections of the external data and MC on 12 C [26], which
has the largest number of data points. After tuning, theestimated rates of neutral pion absorption and charge
exchange have increased around 500 MeV=c, which
affects the distribution of the number of rings and causes
a 5% reduction of estimated signal efficiency. Large angle
scattering in the nucleus has also increased, which
modifies the reconstructed proton mass and momentum
distributions, resulting in a 7% reduction in estimatedselection efficiency for p → eþ π 0 and p → μþ π 0 . The
right panel of Fig. 1 shows the fraction of π 0 interactions
as a function of the pion momentum after the tune. The
same plot for the previous simulation can be foundin [27].

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1
Reactive (TunedFSI)
Reactive (OldFSI)
Quasi-elastic
Absorption
Single CX
π Production

450
400
350

Charge exchange

Scattering

Fraction300

σ (mb)

π production

0.8

250
200

0.6

Absorption

0.4

150
100

0.2

No interaction

50
0
0

200

400

600

800

1000

1200

1400

0
300

1600

π+ Initial Momentum (MeV/c)

350

400

450

500

550

600

FIG. 1. The left panel shows π þ cross sections on 12 C as a function of momentum. Open circles indicate existing data [26], solid anddashed lines show after and before the tune, respectively. The colors correspond to the total cross section and exclusive channels: total(black), elastic scattering (green), absorption (red), charge exchange (blue), and π production (light blue). The right panel shows
cumulative fractions of neutral pion final state interactions as a function of momentum generated by p → eþ π 0 MC. The fractions ofevents that undergo charge exchange, multiple π production, scattering, and absorption are shown by the various shades as labeled.
Neutral pions that exit the nucleus without experiencing any final state interactions are indicated by the portion labeled “No interaction.”

The following cuts are applied to signal MC, atmospheric ν MC, and data:(Cut-1) events must be fully contained in the inner detector
with the vertex position within the fiducial volume,
which is defined as 2 meters inward from thedetector walls (FCFV),(Cut-2) there must be 2 or 3 Cherenkov rings,(Cut-3) all rings must be electronlike for p → eþ π 0 and one
ring must be μ-like for p → μþ π 0,
(Cut-4) there must be no Michel electrons for p → eþ π 0
and one electron for p → μþ π 0,
(Cut-5) reconstructed π 0 mass should be 85 < Mπ0 <185 MeV=c2 for 3 ring events,(Cut-6) reconstructed total mass should be 800 < M tot <1050 MeV=c2 and reconstructed total momentum
Ptot should be less than 250 MeV=c,
and for SK-IV only,(Cut-7) there must be no tagged neutrons.
After (Cut-1), 41k FCFVevents remain in data for the entire
period. The events which contain two rings are allowed in(Cut-2) because one gamma ray from π 0 may fail toreconstruct if the opening angle of the two gammas is small,or the energy of the gamma is small. The fraction of 2- and3-ring events in p → eþ π 0 MC before (Cut-5) are 45% and55%, respectively. The requirement (Cut-7) rejects about
50% of the background but reduces selection efficiency by
3%, in which both true and fake neutrons contribute.
Figure 2 shows the number of tagged neutrons for p →eþ π 0 (upper) and p → μþ π 0 (lower) after applying (Cut-1)
through (Cut-5), excluding the signal region defined by(Cut-6). These figures show that the neutron multiplicity inthe atmospheric neutrino MC (solid histogram) agrees wellwith data (dots). The dashed histograms show the true
number of captured neutrons in the MC, indicating that
additional background rejection can be achieved if theneutron tagging efficiency is improved in the future whengadolinium is dissolved in the SK water [28].
A new analysis technique [29] is applied in thispaper. The signal region defined by (Cut-6) is divided
into two regions: Ptot < 100 MeV=c and 100 ≤ Ptot <250 MeV=c. The region below 100 MeV=c is dominated
1200
1000
800
600

Number of events

V. SELECTION CRITERIA

400
200
0
450
400
350
300
250
200
150
100
50
0

0

2

4

6

8

10

Neutron multiplicity

FIG. 2. Distribution of the number of tagged neutrons for
p → eþ π 0 (top) and p → μþ π 0 (bottom) after applying (Cut-1)
through (Cut-5), excluding the signal region defined by (Cut-6).
Dots show SK-IV data with 133.5 kton · years exposure, the solid
histogram shows the multiplicity of tagged neutrons per event in
the atmospheric ν MC, and the dashed histogram shows the true
multiplicity of neutrons per event.

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1000
800

p→e+π0 MC

Atmospheric ν MC

Data

+ 0

Atmospheric ν MC

Data

Total momentum (MeV/c)

600
400
200
0
1000
p→μ π MC

800
600
400
200
0

0

500

1000

0

500

1000

0

500

1000

Total mass (MeV/c2)

FIG. 3. Reconstructed proton mass vs total momentum for p → eþ π 0 (top) and p → μþ π 0 (bottom) after all cuts except (Cut-6). The
left panels show signal MC, where light blue corresponds to free protons and dark blue is bound protons. The middle panels show
atmospheric ν MC corresponding to 500 years live time of SK, and the right panels show SK-I to SK-IV data which contain 3408 and
1180 events for p → eþ π 0 and p → μþ π 0 , respectively. The dot size is enlarged in the signal box.

Number of events

10 3

π

10 2
10
1

π

-1

10

-2

10

-3

10

-4

10

μπ

Number of events

10
1

μπ

-1

10

-2

10

-3

10

-4

10

0

500

1000

0

Total mass (MeV/c 2)

500

1000

Total momentum (MeV/c)

FIG. 4. Distributions of reconstructed invariant mass (left) and total momentum (right) for p → eþ π 0 in the top panels and forp → μþ π 0 in the bottom panels, after all selection cuts except cuts on the plotted variable. The dark blue histograms correspond to90% confidence level allowed signal and the histograms filled by light blue show the portion contributed by free proton decay. The redhistograms show atmospheric ν MC, and the dots are data with 0.306 Mton · years exposure. Vertical dashed lines indicate the signal
regions. The peak around 150 MeV=c2 in the total mass distribution of atmospheric ν and data in the left top panel arises from π 0
decays.

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PHYSICAL REVIEW D 95, 012004 (2017)

by free protons, and the region 100 ≤ Ptot < 250 MeV=c isdominated by bound protons. A reduced systematic error
for < 100 MeV=c can be achieved because the initial
protons and the products of the proton decay do not sufferfrom any of the various nuclear interactions. In addition,
background contamination from atmospheric neutrinos
is concentrated in the 100 ≤ Ptot < 250 MeV=c, while
the region below 100 MeV=c is nearly background free.
Figure 3 shows the reconstructed proton mass vs total
momentum distribution for signal and atmospheric ν MC,
combining all data from SK-I through SK-IV. In the signal
MC plots, the light blue dots show the free proton case andthe dark blue dots show bound protons. Figure 4 shows
one-dimensional distributions of reconstructed proton massand momentum of p → eþ π 0 and p → μþ π 0 for the signal,
atmospheric ν MC, and data after all cuts except the cut on
the plotted variable. The data and the atmospheric ν MC
agree in both cases.
The new two-box analysis achieves better discovery
reach. For example, the 3σ discovery reach in the proton
lifetime for p → eþ π 0 is 13.3% higher than the conventional single-box analysis for the current exposure, and20.9% higher for an exposure of 1 megaton · year, which
may be achieved by the next generation of detectors [30].

VI. RESULTS
Table I shows efficiency, expected number of background
events, and number of observed events for each region of
total momentum for p → eþ π 0 and p → μþ π 0 . The signal
efficiencies in SK-I and -II are decreased in comparison to
the previous paper due to the updated π-FSI model.
Efficiencies for p → μþ π 0 in SK-IV are significantly higher
than the other data-taking periods because of Michelelectron tagging efficiency that was achieved with the
new electronics. The background rate in SK-I/II/III isconsistent with the measurement in the 1 kton water
Cherenkov detector using the K2K accelerator neutrino
beam [31]. Background rates in SK-IV for both decay modes
are almost half that of SK-I/II/III, which is a result of thecontribution from neutron tagging. In the entire signal
region, with 306.3 kiloton · years exposure, the expectedbackground for p → eþ π 0 is 0.61 events (0.07 and 0.54
events in lower and higher momentum box, respectively)
and no candidates were observed, while for p → μþ π 0 theestimated background is 0.87 events (0.05 and 0.82 events inlower and higher momentum box, respectively) and two
candidates have been observed in the higher momentum
box. Assuming a Poisson distribution with mean 0.87, theTABLE I. Summary of the p → eþ π 0 and p → μþ π 0 proton decay modes. The selection efficiencies and expectedbackgrounds with quadratic sum of statistical and systematic errors, and number of observed events are shown foreach detector period. Low Ptot and high Ptot are defined as Ptot <100 MeV=c and 100 ≤ Ptot <250 MeV=c,
respectively.

Exp.

SK-I

SK-II

SK-III

SK-IV

kt · yrs

91.7

49.2

31.9

133.5

Eff.(%)

18.8  1.9

18.3  1.9

19.6  2.0

18.7  1.9

BKG

0.03þ0.03−0.02
0.36þ0.30
−0.20

<0.01

<0.01

0.26þ0.27−0.17

0.09þ0.21−0.08

0.02þ0.03
−0.02

OBS

0

0

0

0

Eff.(%)

20.4  3.6

20.2  3.6

20.5  3.6

19.4  3.4

BKG

0.22  0.08

0.12  0.04

0.06  0.02

0.15  0.06(=Mt · yr)

2.4  0.8

2.5  0.9

1.8  0.7

1.1  0.3

OBS

0

0

0

0

Eff.(%)

16.4  1.5

16.0  1.5

16.4  1.5

20.1  1.9

BKG

0.03þ0.02
−0.02

<0.01

<0.01

0.31þ0.26−0.17

0.10þ0.13−0.07

0.22þ0.22−0.14

0.01þ0.02
−0.01

0

0

0

p → eþ π 0
Low Ptot(=Mt · yr)
High Ptot

0.18þ0.25−0.13

p → μþ π 0
Low Ptot(=Mt · yr)
OBSHigh Ptot

0.09þ0.21−0.08
0Eff.(%)

15.3  2.8

15.3  2.8

16.5  3.0

18.2  3.3

BKG

0.33  0.10

0.14  0.05

0.12  0.04

0.23  0.08(=Mt · yr)

3.6  1.1

2.9  0.9

3.7  1.2

1.7  0.6

0

0

0

2

OBS

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TABLE II. Summary of systematic errors for efficiencies, backgrounds, and exposures in percent (%). Low Ptot
and high Ptot are defined as Ptot < 100 MeV=c and 100 ≤ Ptot < 250 MeV=c, respectively. For SK-IV only, aneutron tagging uncertainty is included, and the total systematic error for SK-IV is also shown including thisuncertainty, both in parentheses.
p → eþ π 0
Efficiency

p → μþ π 0

low Ptothigh Ptot

low Ptothigh Ptot

π-FSI
Correlated decay
Fermi momentum
Reconstruction

2.8
1.9
8.5
4.6

10.6
9.1
9.3
5.6

2.9
1.7
8.0
3.7

12.1
9.0
9.6
3.3

Total

10.2

17.7

9.4

18.2

Flux
Cross section
π-FSI
Reconstruction(neutron tag)

7.0
14.5
15.4
21.7
10

6.9
10.4
15.4
21.7
10

7.0
8.4
14.2
21.7
10

7.0
7.8
14.4
21.7
10

Total (I/II/III)

31.2

29.4

28.1

28.1

(IV)

32.7
1.0

31.1
1.0

29.9
1.0

29.8
1.0

Background

Exposure

probability to see ≥2 events is 22% and is still consistent
with background. The first candidate was observed at
257 kton · years exposure and the second candidate wasobserved at 277 kton · years exposure. A KolmogorovSmirnov test is carried out to examine the assumption ofa constant event rate. The obtained p-value is 5.2%, which isconsistent with the assumption.
Table II shows a summary of the systematic errors. The
dominant systematic uncertainty in the efficiency of both
decay modes in the Ptot < 100 MeV=c region comes fromuncertainty in the Fermi momentum. In the proton decay
MC, the momentum distribution of the bound nucleon issimulated based on experimental data [32], which is compared with the Fermi gas model to estimate the uncertainty.
Uncertainties in energy scale, uniformity of the detector,
particle identification, vertex shift, opening angle, and ringcounting are all taken into account as reconstruction error.
Uncertainties in the 100 ≤ Ptot < 250 MeV=c region are
generally larger because they are mostly bound protons that
suffer from uncertainties associated with π-FSI, correlated
decays with other nucleons [33], and Fermi motion. The
leading uncertainties in the background estimate come fromcross section, π-FSI, and reconstruction. An additional
systematic error for neutron tagging is assigned only for
SK-IV. As shown in Fig. 2 and Ref. [18], neutron multiplicity in atmospheric neutrino data and MC agree well.
Also, as described in Sec. III, the data with neutron source iscompared with MC in several detector positions. The
systematic error on neutron tagging is assigned to be
10% estimated by the maximum deviation between data
and MC. The run time of SK is well defined and systematic
uncertainty in the exposure is negligibly small (1%).

Both of the observed candidates for p → μþ π 0 are
located near the boundary of the signal region. The firstcandidate has a reconstructed proton mass of 903 
19 MeV=c2 and 248  5 MeV=c total momentum. The
first candidate is categorized as a 2-ring event; the e-likering has momentum 375 MeV=c, the μ-like ring has
551 MeV=c momentum, and there is a 158° opening angle
between the two rings. For the second candidate, the ringcounting algorithm originally found one μ-like ring and two
e-like rings. However, one of the e-like rings (orange ringin Fig. 5) is judged as a fake ring at the final stage of ringcounting. This final stage discards rings caused by multiple
Coulomb scattering of charged particles, which is done byexamination of a ring’s angle relative to other rings and by
visible energy; it is applied to both data and MC. As aresult, the second candidate is judged as a 2-ring event. In
the final result of the reconstruction, the second candidate
has a reconstructed proton mass of 832  17 MeV=c2 anda total momentum of 238  5 MeV=c calculated from theremaining e-like ring with 461 MeV=c, the μ-like ring with
391 MeV=c, and the 149° angle between the two rings. If
the third ring had not been rejected, the reconstructedinvariant mass from the two e-like rings would have been
104 MeV=c2 , which could be gammas from π 0 decay. The
total momentum and proton mass would increase to289 MeV=c and 880 MeV=c2 , respectively, which would
move the event outside of the defined signal region.1
1This event is judged as a 3-ring event, but leaves the signal
box if we use updated PMT gain correction, introduced in 2016,
which depends on PMT production year.

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PHYSICAL REVIEW D 95, 012004 (2017)

in Table II [23]. The lower limit of the nucleon decay rate,Γlimit , isR Γlimit QN¼8i¼1 PðΓjni ÞdΓ
QN¼8
C:L: ¼ RΓ¼0;
ð2Þ∞i¼1 PðΓjni ÞdΓΓ¼0
where C.L. is the confidence level, taken to be 90%. The
lower lifetime limit of p → lþ π 0 (lþ denotes eþ or μþ ) is
given by
τ=Bp→lþ π0 ¼1Γlimit:ð3Þ

The results of the limit calculation combining the tworegions are
τ=Bp→eþ π0 > 1.6 × 1034 yr; τ=Bp→μþ π 0 > 7.7 × 1033 yr;
at the 90% confidence level. τ=Bp→μþ π0 is lower than
τ=Bp→eþ π0 , and this is also lower than our previous
publication [9] because of the two observed events, which
are consistent with atmospheric neutrino background.
FIG. 5. Event display of the second candidate event, zoomed to
the region of the rings. The blue solid line and the tan dashed line
show the reconstructed e-like and μ-like rings, respectively. The
dark orange solid line shows an additional e-like ring that was
identified in the initial ring counting process, but it is rejectedby the ring correction because it is too close in angle to theother e-like ring (blue line). As a result, this event is judged as a
two-ring event.

VII. LIFETIME LIMITThe observed events are consistent with expected backgrounds and a proton lifetime limit is calculated using a
Bayesian method [34,35]. In Ref. [23], the proton lifetime
was calculated combining different search methods as well
as different run periods. The same method is used here for
combining Ptot < 100 MeV=c and 100 ≤ Ptot < 250 MeV=c.
For measurements i ¼ 1–4 (Ptot < 100 MeV=c, SK-I–SKIV) and 5–8 (100 ≤ Ptot < 250 MeV=c, SK-I–SK-IV), theconditional probability distribution for the decay rate isexpressed as
ZZZ −ðΓλi ϵi þbi ÞeðΓλi ϵi þ bi ÞniPðΓjni Þ ¼
ni !
× PðΓÞPðλi ÞPðϵi ÞPðbi Þdλi dϵi dbi

ð1Þ

where ni is the number of candidate events in the ith proton
decay search, λi is the true detector exposure, ϵi is the true
detection efficiency, and bi is the true number of background events. The decay rate prior probability distributionPðΓÞ is 1 for Γ ≥ 0 and otherwise 0. Pðλi Þ, Pðϵi Þ, andPðbi Þ are the prior probability distributions for detector
exposure, efficiency, and background, respectively, which
are assumed to be Gaussian distributions with σ described

VIII. CONCLUSION
We analyzed 0.306 megaton · years of SuperKamiokande data to search for proton decay via
p → eþ π 0 and p → μþ π 0 . Neutron tagging was introducedin SK-IV and it succeeds in rejecting half of the backgrounds. The signal region from SK-I to SK-IV was
divided into two regions of Ptot to obtain better sensitivity.
We observed zero events (0.07 and 0.54 expected background in lower and higher momentum box, respectively)
for p → eþ π 0 and two events in the higher momentum box(0.05, and 0.82 expected background in lower and higher
momentum box, respectively) for p → μþ π 0. The obtained
proton lifetime limits at 90% confidence level are > 1.6 ×1034 yr for p → eþ π 0 and > 7.7 × 1033 yr for p → μþ π 0.
ACKNOWLEDGMENTS
We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande experiment has been built and operated fromfunding by the Japanese Ministry of Education, Culture,
Sports, Science and Technology, the U.S. Department ofEnergy, and the U.S. National Science Foundation. Someof us have been supported by funds from the National
Research Foundation of Korea NRF-2009-0083526(KNRC) funded by the Ministry of Science, ICT, andFuture Planning, the European Union H2020 RISEGA641540-SKPLUS), the Japan Society for the
Promotion of Science, the National Natural Science
Foundation of China under Grant No. 11235006, theNational Science and Engineering Research Council(NSERC) of Canada, and the Scinet and Westgrid consortia
of Compute Canada.

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