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Search for Trilepton Nucleon Decay via p → eþ νν and p → μþ νν in the
Super-Kamiokande Experiment
V. Takhistov,7 K. Abe,1,29 Y. Haga,1 Y. Hayato,1,29 M. Ikeda,1 K. Iyogi,1 J. Kameda,1,29 Y. Kishimoto,1,29 M. Miura,1,29
S. Moriyama,1,29 M. Nakahata,1,29 Y. Nakano,1 S. Nakayama,1,29 H. Sekiya,1,29 M. Shiozawa,1,29 Y. Suzuki,1,29 A. Takeda,1,29
H. Tanaka,1 T. Tomura,1,29 K. Ueno,1 R. A. Wendell,1,29 T. Yokozawa,1 T. Irvine,2 T. Kajita,2,29 I. Kametani,2K. Kaneyuki,2,29,* K. P. Lee,2 T. McLachlan,2 Y. Nishimura,2 E. Richard,2 K. Okumura,2,29 L. Labarga,3 P. Fernandez,3S. Berkman,5 H. A. Tanaka,5 S. Tobayama,5 J. Gustafson,4 E. Kearns,4,29 J. L. Raaf,4 J. L. Stone,4,29 L. R. Sulak,4
M. Goldhaber,6,* G. Carminati,7 W. R. Kropp,7 S. Mine,7 P. Weatherly,7 A. Renshaw,7 M. B. Smy,7,29 H. W. Sobel,7,29
K. S. Ganezer,8 B. L. Hartfiel,8 J. Hill,8 W. E. Keig,8 N. Hong,9 J. Y. Kim,9 I. T. Lim,9 T. Akiri,10 A. Himmel,10
K. Scholberg,10,29 C. W. Walter,10,29 T. Wongjirad,10 T. Ishizuka,11 S. Tasaka,12 J. S. Jang,13 J. G. Learned,14 S. Matsuno,14
S. N. Smith,14 T. Hasegawa,15 T. Ishida,15 T. Ishii,15 T. Kobayashi,15 T. Nakadaira,15 K. Nakamura,15,29 Y. Oyama,15
K. Sakashita,15 T. Sekiguchi,15 T. Tsukamoto,15 A. T. Suzuki,16 Y. Takeuchi,16 C. Bronner,17 S. Hirota,17 K. Huang,17
K. Ieki,17 T. Kikawa,17 A. Minamino,17 A. Murakami,17 T. Nakaya,17,29 K. Suzuki,17 S. Takahashi,17 K. Tateishi,17
Y. Fukuda,18 K. Choi,19 Y. Itow,19 G. Mitsuka,19 P. Mijakowski,34 J. Hignight,20 J. Imber,20 C. K. Jung,20 C. Yanagisawa,20
H. Ishino,21 A. Kibayashi,21 Y. Koshio,21 T. Mori,21 M. Sakuda,21 R. Yamaguchi,21 T. Yano,21 Y. Kuno,22 R. Tacik,23,31
S. B. Kim,24 H. Okazawa,25 Y. Choi,26 K. Nishijima,27 M. Koshiba,28 Y. Suda,28 Y. Totsuka,28,* M. Yokoyama,28,29
K. Martens,29 Ll. Marti,29 M. R. Vagins,29,7 J. F. Martin,30 P. de Perio,30 A. Konaka,31 M. J. Wilking,31 S. Chen,32 Y. Zhang,32
K. Connolly,33 and R. J. Wilkes33(Super-Kamiokande Collaboration)
1
Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan3
Department of 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, Japan20
Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794-3800, USA
21
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
22
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
23
Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan, S4SOA2, Canada
24
Department of Physics, Seoul National University, Seoul 151-742, Korea
25
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan
26
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
27
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
28
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
29
Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo,
Kashiwa, Chiba 277-8582, Japan30
Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario, M5S1A7, Canada
31
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T2A3, Canada
32
Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
20031-9007=14=113(10)=101801(6)101801-1© 2014 American Physical Society

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Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
34
National Centre For Nuclear Research, 00-681 Warsaw, Poland(Received 6 June 2014; published 4 September 2014)

The trilepton nucleon decay modes p → eþ νν and p → μþ νν violate jΔðB − LÞj by two units. Using
data from a 273.4 kt yr exposure of Super-Kamiokande a search for these decays yields a fit consistent withno signal. Accordingly, lower limits on the partial lifetimes of τp→eþ νν > 1.7 × 1032 years and τp→μþ νν >2.2 × 1032 years at a 90% confidence level are obtained. These limits can constrain Grand Unified Theories
which allow for such processes.
DOI: 10.1103/PhysRevLett.113.101801

PACS numbers: 13.30.Ce, 11.30.Fs, 12.10.Dm, 14.20.Dh

There is strong theoretical motivation for a grand unified
theory (GUT) [1,2] as an underlying description of nature.
Unification of the running couplings, charge quantization,
as well as other hints point to the standard model (SM)being an incomplete theory. Though the GUT energy scale
is inaccessible to accelerator experiments a signature
prediction of these theories is an unstable proton withlifetimes that can be probed by large underground experiments. Observation of proton decay would constitute strong
evidence for physics beyond the SM, and nonobservation
imposes stringent constraints on GUT models.
One of the simplest unification scenarios, based onminimal SU(5), has been decisively ruled out by limits
on p → eþ π 0 [3–5]. On the other hand, models based onminimal supersymmetric (SUSY) extensions are strongly
constrained by bounds from p → ν̄K þ [6], and with signsof SUSY unobserved at the Large Hadron Collider (LHC)[7,8], there is reinvigorated interest in other approaches andpossible signatures. A popular scenario may be found in a
left-right symmetric partial unification of Pati and Salam(PS) [9] and its embedding into SO(10), providing a naturalright-handed neutrino candidate and unifying quarks andleptons. In the scheme of Refs. [10,11], trilepton modes
such as p → eþ νν and p → μþ νν could become significant. This work describes searches for these modes. Theirobservation, coupled with nonobservation of p → eþ π 0 ,may allow for differentiation between PS and its SO(10)embedding [11]. Violating baryon and lepton number by
two units jΔðB − LÞj ¼ 2, unusual for standard decay
channels, may lead to favorable implications for baryogenesis [12]. Interestingly, these trilepton proton decay
modes were offered as an explanation [13,14] of theatmospheric neutrino flavor “anomaly” [15,16] before
neutrino oscillations were established [17].
In this analysis, the data collected at Super-Kamiokande(SK) during the data taking periods of SK-I (May 1996–
July 2001, 1489.2 live days), SK-II (January 2003–October
2005, 798.6 live days), SK-III (September 2006–August
2008, 518.1 live days) and the ongoing SK-IV experiment(September 2008–October 2013, 1632.3 live days), corresponding to a combined exposure of 273.4 kt yr, areanalyzed. The 50 kiloton SK water Cherenkov detector(22.5 kton fiducial volume) is located beneath a one-km

rock overburden (2700 m water equivalent) in the Kamioka
mine in Japan. Details of the detector design and performance in each SK period, as well as calibration, data
reduction, and simulation information can be found elsewhere [18,19]. This analysis considers only events in which
all observed Cherenkov light was fully contained within the
inner detector.
The trilepton decay modes p → eþ νν and p → μþ νν are
the first three-body nucleon decay searches undertaken by
SK. Since the neutrinos cannot be observed, the only
signature is the appearance of a charged lepton, eþ or μþ.
Accordingly, the invariant mass of the decay nucleon
cannot be reconstructed. Unlike two-body decays, where
each final-state particle carries away about half of thenucleon rest mass energy, in these three-body decays the
charged lepton has a broad energy distribution, whosemean is 313 MeV for the decay of a free proton. Thus,
atmospheric neutrino interactions dominate the lepton
energy spectra and require a search for the proton decay
signal superimposed on a substantial background. Limits
on these modes from the IMB-3 [3] and Fréjus [20]experiments, 1.7 × 1031 and 2.1 × 1031 years, wereobtained via simple counting techniques. In contrast, we
employ energy spectrum fits. This technique is particularly
well suited to three-body searches with large backgrounds
as it takes full advantage of the signal and background
spectral information.
The detection efficiency for nucleon decays in water isestimated from Monte Carlo (MC) simulations in which all
protons within the H2 O molecule are assumed to decay
with equal probability. Signal events are obtained bygenerating final state particles from the proton’s decay
with energy and momentum uniformly distributed within
the phase space. Conservation of kinematic variables
constrain the processes to produce viable particle spectra.
Specifics of the decay dynamics, which are model dependent but are not taken into account here, can play a role indetermining the energy distributions of the resulting particles in three-body decays. The assumption of a flat phasespace, as employed within this analysis, was validated bycomparing the final state charged lepton spectrum generated with a flat phase space to the spectrum originatingfrom the three-body phase space of muon decay (reaction),

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as recently proposed [21] to account for decays encompassing a broad range of models. We have confirmed that
adopting a nonflat phase space does not significantly alter
the results of the analysis, because the charged lepton
spectra do not have sufficiently different shapes (even forthe decay of a free proton, which is minimally smeared).
Thus, we conclude, that employing flat phase space in thesignal simulation, which has been previously assumed inother similar searches [3,20] without much justification, iswarranted.
In the signal simulation, the effects of Fermi momentum
and the nuclear binding energy as well as nucleon-nucleon
correlated decays are taken into account [22,23]. Fermi
momentum distributions are simulated using a spectral
function fit to 12 C electron scattering data [24]. Considering
only events generated within the fiducial volume (FV) of
the detector, the signal MC simulation consists of roughly
4000 events for each of the SK data periods.
Atmospheric neutrino background interactions are generated using the flux of Honda et al. [25] and the NEUT
simulation package [26], which uses a relativistic Fermi gas
model. The SK detector simulation [19] is based on the
GEANT-3 [27] package. A background MC simulation
corresponding to a 500 year exposure of the detector isgenerated for each SK period.
The following event selection criteria are applied to thefully contained data: (1) a single Cherenkov ring is present,(2) the ring is showering (electronlike) for p → eþ νν andnonshowering (muonlike) for p → μþ νν, (3) there are zero
decay electrons for p → eþ νν and one decay electron forp → μþ νν, (4) the reconstructed momentum lies in therange 100 MeV=c ≤ pe ≤ 1000 MeV=c for p → eþ νν
and in the range 200 MeV=c ≤ pμ ≤ 1000 MeV=c forp → μþ νν. Reconstruction details may be found in
Ref. [28]. The signal detection efficiency is defined as
the fraction of events passing these selection criteria
compared to the total number of events generated within
the true fiducial volume (see Table I). The increase inefficiency seen in SK-IV for the p → μþ νν mode is caused
by a 20% improvement in the detection of muon decay
electrons after an upgrade of the detector electronics for thisperiod [19].
In the case of p → eþ νν, the dominant (78%) background after selection criteria are applied is due to νequasielastic charged current (CCQE) interactions. The
majority of the remaining background is due to νe andνμ charged current (CC) pion production as well as the all
flavor’s neutral current (NC) single pion production (12%and 5%, respectively). There are minor contributions fromother processes such as coherent pion production (order of1%). Similarly for the p → μþ νν mode, νμ CCQE interactions dominate (80%), with the largest remaining contribution coming from CC single pion production (15%).
Additionally there are slight contributions from NC pion
production, CC coherent and multiple-pion production(around 1% each). Processes not mentioned here are
negligible.
A spectrum fit is performed on the reconstructed charged
lepton momentum distributions of selected candidates. The
foundation of the fit is a χ 2 minimization with systematic
errors accounted for by quadratic penalties (“pull terms") as
described in Ref. [29]. The χ 2 function is defined as
 NX
N bins 
syserr 
X
ϵj 2
N obs
i
obs
obs
χ ¼2
zi − N i þ N i ln
þ
;
zi
σj
i¼1
j¼1
2

zi ¼ αN backi
N syserr
N syserr
X j ϵj 
X j ϵj sig1þ
þ βN i 1 þ
;
fi
fi
σj
σj
j¼1
j¼1
ð1Þ

sig
back
where i labels the analysis bins. The terms N obs
i , Ni , Ni
are the number of observed data, signal MC and background MC events in bin i. The MC expectation in a bin istaken to be N exp¼ αN backþ βN sigiii , with α and β denoting
the background (atmospheric neutrino) and signal (nucleon
decay) normalizations. The jth systematic error isaccounted for by the “pull term,” where ϵj is the fit error
parameter and f ji is the fractional change in the MC
expectation bin due to a 1 sigma uncertainty σ j of theerror. A two-parameter fit is performed to the parameters α
and β, with the point ðα; βÞ ¼ ð1; 0Þ set to correspond to no
signal hypothesis. With the signal spectrum normalized byarea to the background prior to the fit, β ¼ 1 corresponds tothe amount of nucleon decay events equal to the quantity ofthe background MC simulation after detector live timenormalization. The parameter space of ðα; βÞ is allowed tovary in the intervals of (α ∈ ½0.8; 1.2, β ∈ ½0.0; 0.2). Theχ 2 of Eq. (1) is minimized with respect to ϵj according to∂χ 2 =∂ϵj ¼ 0, yielding a set of equations which are solved
iteratively, and the global minimum is defined as the best

TABLE I. Best fit parameter values, signal detection efficiency for each SK running period, 90% C.L. value of β parameter, allowed
number of nucleon decay events in the full 273.4 kt yr exposure (SK-I: 91.7, SK-II: 49.2, SK-III: 31.9, SK-IV: 100.5) and a partial
lifetime limit for each decay mode at 90% C.L.
Decay
mode

Best fit valuesðα; βÞ

Signal efficiency for SK-I, -II, -III, -IV (%)(efficiency uncertainty)

β90 C:L:

Signal events at 90% C.L.
(N 90 C:L: )τ=B(×1032 yrs)

p → eþ νν
p → μþ νν

(1.05, 0.03)(0.99, 0.02)

88.8, 88.0, 89.2, 87.8 (0.5, 0.5, 0.5, 0.5)
64.4, 65.0, 67.0, 78.4 (0.7, 0.7, 0.7, 0.6)

0.06
0.05

459
286

1.7
2.2

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fit. The confidence level intervals are later derived from theχ 2 minimization at each point in the ðα; βÞ plane after
subtracting off this global minimum. Namely, the C.L. limit
is based on the constant Δχ 2 critical value corresponding
to the 90% C.L. for a fit with 1 degree of freedom,
after profiling out β’s dependence on α from the twoparameter fit.
Combining signal and background into each analysis
MC expectation bin, as employed in a typical fit of this sort(see Ref. [29]), is an approximate approach where systematic errors for signal as well as background are applied toevery analysis bin which contains both. In this analysis we
employ a more accurate error treatment, splitting signal andbackground (doubling the number of analysis bins) for theapplication of systematic errors and then recombining themduring the χ 2 minimization. A total of 72 momentum bins
(18, 50-MeV=c wide bins for each SK period) are considered for p → eþ νν, corresponding to 144 MC bins when
the background and signal are separated. In the case ofp → μþ νν a total of 64 momentum bins (16, 50-MeV=cwide bins for each SK period) are used in the analysis,corresponding to 128 MC bins with background and signal
separated.
Systematic errors may be divided into several categories:
background systematics, detector and reconstruction
systematics, and signal systematics. Detector andreconstruction systematics are common to both signal
and background.
This study starts by considering all 154 systematic
uncertainties which are taken into account in the standard
SK neutrino oscillation analysis [30], along with two
signal-specific systematic effects related to correlated
decays and Fermi momentum. In order to select which
systematic uncertainties to include in the limit calculation,
only error terms with at least one jf ji j > 0.05 are used in theanalysis. Loosening the selection to jf ji j > 0.01 does not
significantly affect the analyses results but greatly increases
the number of errors to be treated. After selection, there are
11 systematic error terms for both p → eþ νν andp → μþ νν. The main systematic contributions originate
from energy calibration uncertainties (common error toboth signal and background), uncertainties related to theatmospheric neutrino flux, and uncertainties in the signal
simulation. The complete list of errors, their uncertainties,
and fitted pull terms can be found in Table II. Errors
specific to signal and background are denoted by S and B,
respectively, while those that are common to both aredenoted by SB.
Performing the fit allows us to obtain the overall background and signal normalizations α and β. For the modep → eþ νν the data’s best fit point is found to be ðα; βÞ ¼
ð1.05; 0.03Þ with χ 2 ¼ 65.6=70 dof, while for p → μþ ννthe result is ðα; βÞ ¼ ð0.99; 0.02Þ with χ 2 ¼ 66.1=62 dof.
The Δχ 2 ð¼ χ 2 − χ 2min Þ values corresponding to no proton
decay signal being present, are 1.5 and 0.5 for p → eþ ννand p → μþ νν modes, respectively. These outcomes are
consistent with no signal present at 1σ level. Extracting the
90% confidence level allowed value of β (β90 C:L: .) from thefit, which is found to be 0.06 for p → eþ νν and 0.05 forp → μþ νν, respectively, a lower lifetime limit on these
decays can be set. From β90 C:L: . the amount of signal
allowed at the 90% confidence level can be computed as
N 90 C:L: ¼ β90 C:L: N signal . The partial lifetime limit for eachdecay mode is then calculated according toτ90 C:L: =B ¼

Psk4

sk¼sk1 λsk ϵsk N

nucleons

N 90 C:L:;ð2Þ

where B represents the branching ratio of a process,N nucleons is the number of nucleons per kiloton of water(3.3 × 1032 protons), ϵsk is the signal efficiency in each SK
phase, λsk is the corresponding exposure in kiloton · years,
and N 90 C:L: . is the amount of signal allowed at the 90%
confidence level. The signal efficiency, number of decay
sources, as well as the signal normalization values used forthe lifetime calculation can be found in Table I. The fitted
momentum spectra as well as residuals for both modes

TABLE II. Systematic errors of the nucleon decay spectrum fits, with 1σ uncertainties and resulting fit pull terms. Errors specific tosignal and background are denoted by S and B, while those that are common to both by SB.
Decay mode
Systematic error

1-σ uncertainty (%)

p → eþ νν
Fit pull (σ)

p → μþ νν
Fit pull (σ)

Final state interactions (FSIs)
Flux normalization (Eν < 1 GeV)
Flux normalization (Eν > 1 GeV)M A in ν interactions
Single meson cross section in ν interactions
Energy calibration of SK-I, -II, -III, -IV
Fermi model comparison
Nucleon-nucleon correlated decay

10
25a
15b
10
10
1.1, 1.7, 2.7, 2.3
10c
100

0.08
−0.36
−0.86
0.32
−0.36
0.51, −1.01, 0.44, 0.39
−0.25
−0.05

−0.55
−0.42
−0.90
0.48
−0.16
−0.50, 0.06, −0.16, 0.25
0.02
0.01

Uncertainty linearly decreases with log Eν from 25% (0.1 GeV) to 7% (1 GeV).
Uncertainty is 7% up to 10 GeV, linearly increases with log Eν from 7% (10 GeV) to 12% (100 GeV) and then 20% (1 TeV).
Comparison of spectral function and Fermi gas model.

abc101801-4

B
B
B
B
B
SB
S
S

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PRL 113, 101801 (2014)

900
1200
700
600

800

EventsEvents1000

SK I-IV µ-like
DATA
Signal 90CL
ATM + Signal (best fit)

800

SK I-IV e-like
DATA
Signal 90CL
ATM + Signal (best fit)

600

500
400
300

400

200
100

0

0

100
50
0
-50
-100
100

100
50
0
-50
-100
200

EventsEvents

200

200

300

400

500

600

700

800

900

1000

Momentum (MeV/c)

300

400

500

600

700

800

900

1000

Momentum (MeV/c)

FIG. 1. Reconstructed momentum distribution for 273.4 kt yr of combined SK data (black dots), the best fit result for the atmospheric
neutrino background and signal Monte Carlo simulation (solid line) as well as the 90% confidence level allowed amount of nucleon
decay (hatched histogram) for p → eþ νν (left) and p → μþ νν (right). Residuals from data after background subtraction (bottom
histograms).

appear in Fig. 1. Momentum spectra for the 273.4 kt yr of
combined SK data (black dots), the best-fit result for theatmospheric neutrino background, and signal Monte Carlosimulation (solid line) as well as the amount of nucleon
decay allowed at the 90% confidence level (hatchedhistogram) for p → eþ νν (left) and p → μþ νν (right) are
shown. Residuals from data after the background MC
simulation is subtracted are also depicted (bottom histograms). From the analysis we set partial lifetime limits of
1.7 × 1032 and 2.2 × 1032 years for p → eþ νν andp → μþ νν, respectively. The sensitivity to these modes
is calculated to be 2.7 × 1032 and 2.5 × 1032 years. The
lifetime limits found in this study are an order of magnitudeimprovement over the previous results [3,20]. These results
provide strong constraints to both the permitted parameter
space of Refs. [11,12], which predict lifetimes of around1030 –1033 years, and on other GUT models which allow for
similar processes. We note, that the analyses presented inthis work are only weakly model dependent, due to theassumption of a flat phase space in the signal generation.
However, this assumption agrees well with alternative
phase space considerations [21] in the context of vectoror scalar-mediated proton decays, which are typical of GUT
models [1,2,9].
We gratefully acknowledge cooperation of the Kamioka
Mining and Smelting Company. The Super-Kamiokande
experiment was built and has been operated with funding
from the Japanese Ministry of Education, Culture, Sports,
Science and Technology, the United States Department ofEnergy, and the U.S. National Science Foundation.
Some of us have been supported by funds from the
Korean Research Foundation (BK21), the National
Research Foundation of Korea (NRF-20110024009), theState Committee for Scientific Research in Poland(Grant No. 1757/B/H03/2008/35), the Japan Society for
Promotion of Science, and the National Natural Science
Foundation of China under Grant No. 10575056.

*

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