PRL 113, 121802 (2014)

PHYSICAL REVIEW LETTERS

week ending
19 SEPTEMBER 2014

Search for Nucleon Decay via n → ν̄π0 and p → ν̄πþ in Super-Kamiokande
K. Abe,1,27 Y. Hayato,1,27 T. Iida,1 K. Iyogi,1 J. Kameda,1,27 Y. Koshio,1,27 Y. Kozuma,1 Ll. Marti,1 M. Miura,1,27
S. Moriyama,1,27 M. Nakahata,1,27 S. Nakayama,1,27 Y. Obayashi,1,27 H. Sekiya,1,27 M. Shiozawa,1,27 Y. Suzuki,1,27
A. Takeda,1,27 Y. Takenaga,1 K. Ueno,1 K. Ueshima,1 S. Yamada,1 T. Yokozawa,1 C. Ishihara,2 H. Kaji,2 T. Kajita,2,27
K. Kaneyuki,2,27,* K. P. Lee,2 T. McLachlan,2 K. Okumura,2 Y. Shimizu,2 N. Tanimoto,2 L. Labarga,3 E. Kearns,4,27
M. Litos,4 J. L. Raaf,4,† J. L. Stone,4,27 L. R. Sulak,4 M. Goldhaber,5,* K. Bays,6 W. R. Kropp,6 S. Mine,6 C. Regis,6A. Renshaw,6 M. B. Smy,6,27 H. W. Sobel,6,27 K. S. Ganezer,7 J. Hill,7 W. E. Keig,7 J. S. Jang,8,‡ J. Y. Kim,8 I. T. Lim,8J. B. Albert,9 K. Scholberg,9,27 C. W. Walter,9,27 R. Wendell,9 T. M. Wongjirad,9 T. Ishizuka,10 S. Tasaka,11 J. G. Learned,12
S. Matsuno,12 S. N. Smith,12 T. Hasegawa,13 T. Ishida,13 T. Ishii,13 T. Kobayashi,13 T. Nakadaira,13 K. Nakamura,13,27
K. Nishikawa,13 Y. Oyama,13 K. Sakashita,13 T. Sekiguchi,13 T. Tsukamoto,13 A. T. Suzuki,14 Y. Takeuchi,14,27 M. Ikeda,15
A. Minamino,15 T. Nakaya,15,27 Y. Fukuda,16 Y. Itow,17,18 G. Mitsuka,17 T. Tanaka,17 C. K. Jung,19 G. D. Lopez,19 I. Taylor,19
C. Yanagisawa,19 H. Ishino,20 A. Kibayashi,20 S. Mino,20 T. Mori,20 M. Sakuda,20 H. Toyota,20 Y. Kuno,21 M. Yoshida,21S. B. Kim,22 B. S. Yang,22 H. Okazawa,23 Y. Choi,24 K. Nishijima,25 M. Koshiba,26 M. Yokoyama,26,27 Y. Totsuka,26,*
K. Martens,27 J. Schuemann,27 M. R. Vagins,27,6 S. Chen,28 Y. Heng,28 Z. Yang,28 H. Zhang,28 D. Kielczewska,29
P. Mijakowski,29 K. Connolly,30 M. Dziomba,30 E. Thrane,30,§ and R. J. Wilkes30(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
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
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
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
9
Department of Physics, Duke University, Durham, North Carolina 27708, USA
10
Junior College, Fukuoka Institute of Technology, Fukuoka 811-0214, Japan
11
Information and Multimedia Center, Gifu University, Gifu, Gifu 501-1193, Japan
12
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
13High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
14
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
15
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
16
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
17
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan
18
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya, Aichi 464-8602, Japan
19
Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794-3800, USA
20
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
21
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
22
Department of Physics, Seoul National University, Seoul 151-742, Korea
23
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan
24
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
25
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
26
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
27
Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba 277-8583, Japan
28
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
29
Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland
30
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 21 May 2013; revised manuscript received 26 August 2014; published 19 September 2014)2

We present the results of searches for nucleon decay via n → ν̄π 0 and p → ν̄π þ using data from a combined
172.8 kt · yr exposure of Super-Kamiokande-I,-II, and-III. We set lower limits on the partial lifetime for each ofthese modes: τn→ν̄π 0 > 1.1 × 1033 years and τp→ν̄π þ > 3.9 × 1032 years at a 90% confidence level.
DOI: 10.1103/PhysRevLett.113.121802

0031-9007=14=113(12)=121802(6)PACS numbers: 13.30.-a, 11.30.Fs, 14.20.Dh, 29.40.Ka

121802-1© 2014 American Physical Society

PRL 113, 121802 (2014)

PHYSICAL REVIEW LETTERS

Although there is strong theoretical support that nature
can be described by a grand unified theory (GUT) [1,2],
there is currently no direct experimental evidence. Oneof the most powerful ways to test grand unification is tolook for proton (or bound neutron) decay. Most GUTs havean unstable proton; in the absence of an observation, setting
experimental limits on the proton lifetime can provide
useful constraints on the nature of GUTs. Observation, on
the other hand, would be tantalizing evidence of new
physics beyond the Standard Model.
One of the more simple but interesting candidates for
grand unification is SO(10), where the Standard Model’s
SU(3), SU(2), and U(1) are contained within the larger
gauge group. The class of models based on SO(10)unification generally make predictions for neutrino masses
and mixing that are broadly in accord with all known
neutrino mixing data [3,4]. The minimal supersymmetricSO(10) model with a 126 Higgs field described in Ref. [3]is the particular motivation for the analysis presented here.
In addition to predicting neutrino mass and mixing inagreement with observations, it leaves R parity unbroken,
which guarantees the existence of stable dark matter. For
some region of its allowed parameter space, this model
predicts that the dominant nucleon decay modes will be
p → ν̄π þ and n → ν̄π 0 .
In this Letter, the fully contained (FC) atmospheric
neutrino data (i.e., having activity only within the innerdetector region and no activity in the outer detector)
collected during the first three running periods of SuperKamiokande (Super-K, SK) are analyzed in a search forboth p → ν̄π þ and n → ν̄π 0 : SK-I (May 1996–July 2001,
1489.2 live days), SK-II (January 2003–October 2005,
798.6 live days), and SK-III (September 2006–August
2008, 518.1 live days). The combined data set corresponds
to an exposure of 172.8 kt · yr.
The 50-kiloton (22.59-kt fiducial) Super-K water
Cherenkov detector is located beneath 1 km of rock overburden (2700-meters water equivalent) in the Kamioka
mine in Japan. Details of the detector design, calibration,and simulations in SK-I may be found in Ref. [5], and a
discussion of the reduced photosensor coverage in SK-II
may be found in Ref. [6]. In SK-III, the photosensor
coverage is recovered to the original 40% level of SK-I.
The efficiency of detecting nucleon decay occurring in
the water is estimated by Monte Carlo (MC) simulation. As
discussed in detail in Ref. [6], all nucleons in the H2 O
molecule are assumed to decay with equal probability, andFermi motion, nuclear binding energy, and meson-nuclear
interactions in oxygen are taken into account.
The n → ν̄π 0 (p → ν̄π þ ) decay mode results in a π 0 (π þ )with mean momentum 460 MeV=c (458.8 MeV=c),smeared by the Fermi motion of nucleons bound in oxygen,but uniquely determined for decays of the two free protons
in the water’s hydrogen nuclei. The pion’s momentum isalso affected by nuclear interactions as it travels through theweek ending
19 SEPTEMBER 2014

nucleus; it may undergo scattering, charge exchange, orabsorption. Pion-nucleon interactions are carefully simulated to reflect our understanding of the processes, which
may affect the ability to detect pions in water.
Since the final state neutrino is undetected, these twomodes of nucleon decay are particularly challenging. It is
not possible to develop a set of selection cuts that will
eliminate most of the background of atmospheric neutrino
interactions with a single pion and no other detectedparticles in the final state. Instead, we select events thatappear to have only a single π 0 or π þ and perform aspectrum fit to their reconstructed momentum distributions,
respectively. In this method, the nearly monoenergetic
pions from nucleon decay would appear as a bump on
top of the broad distribution of pions from atmospheric
neutrino interactions. Atmospheric neutrino background
events are simulated using the NEUT neutrino interaction
MC simulation [7] with an atmospheric neutrino flux
calculated by Honda et al. [8], then passed through a
GEANT-3-based [9] custom detector simulation that is
described in detail in Ref. [10].
The event selection cuts applied to the FC atmospheric
neutrino data are (i) the number of Cherenkov rings is twofor n → ν̄π 0 (one for p → ν̄π þ ), (ii) all rings are showering(electronlike) for n → ν̄π 0 [nonshowering (muonlike) forp → ν̄π þ ], (iii) the number of electrons from muon decay iszero for n → ν̄π 0 (zero or one for p → ν̄π þ ), and (iv) thereconstructed momentum is less than 1000 MeV=c. For then → ν̄π 0 sample only, there is one additional requirement(v): that the reconstructed invariant mass of the π 0 is
between 85 and 185 MeV=c2 . A discussion of the momentum reconstruction and performance can be found in
Refs. [6,11], and the method of decay electron finding is
discussed in Ref. [10]. The selected fraction of single pions
in the atmospheric neutrino MC simulation with thesecuts is shown as a function of reconstructed momentum for
SK-I in the top panel of Fig. 1 for π 0 and the bottom for π þ.
The efficiency curves for the SK-II and SK-III periods,
not shown here but treated individually in the fit, are very
similar to the SK-I curves shown in the figure. For theπ 0 mode, the majority of atmospheric neutrino-induced
background events that pass the selection cuts arise fromneutral current (NC) single pion production (76%). The
other backgrounds are due to charged current (CC) single
pion production with the outgoing charged lepton below
Cherenkov threshold (7%), NC multiple pion production(7%), and small fractions of other processes (less than a few
percent each). As this background is overwhelmingly madeup of pions and their selection efficiency as a function of
momentum is not flat, the uncertainty in selection efficiency is treated as a systematic error binned in momentum.
Efficiency is defined as the fraction of all FC events in thefiducial volume (FCFV) with at least one π 0 and no decay
electrons, which pass the selection cuts for n → ν̄π 0. For
the π þ sample, a large fraction of the background events is121802-2

PRL 113, 121802 (2014)
1

TABLE I. Sources of atmospheric neutrino-and antineutrinoinduced background for the p → ν̄π þ decay mode.

Event selection efficiency

0.9
0.8

Interaction mode

0.7

Fraction of background

CCQE (νn → μp)
Single π (νN → lN 0 π ðþ=−=0Þ )Multi π (νN → lN 0 ðnπÞ)
Other

0.6
0.5

0.75
0.20
0.03
0.02

0.4
0.3

The SK particle identification (PID) algorithm onlyclassifies Cherenkov rings as showering (e ; γ) or nonshowering (μ ; π  ), as described in Ref. [10]. Another
PID algorithm that uses additional information about theCherenkov ring opening angle to attempt further classification between μ and π  rings also exists [6], but was
shown to add no improvement to this analysis; thus, noattempt is made to separate muon-induced rings from pioninduced rings.
The fit to the reconstructed momentum spectrum is a χ 2minimization based on a Poisson probability with systematic errors taken into account by quadratic penalties (pullterms). This technique is the same as that described by
Fogli et al., in Ref. [12]. The χ 2 is defined as

0.2
0.1
0

0

100 200 300 400 500 600 700 800 900 1000

Reconstructed π0 momentum (MeV/c)
1
0.9
0.8

Event selection efficiency

week ending
19 SEPTEMBER 2014

PHYSICAL REVIEW LETTERS

0.7
0.6
Muon-origin, 0 decay e
Muon-origin, 1 decay e
Pion-origin, 0 decay e
Pion-origin, 1 decay e

0.5
0.4

χ2 ¼ 2

0.3

i¼1

0.2

0

N exp
i

þ N obs
i ln

0.1
0

nX
bins 

100 200 300 400 500 600 700 800 900 1000


N syserr
X j 1þ
f i ϵj − N obs
i
j¼1

 NX

syserr 
ϵj 2
N obs
i
þ
;
PN syserr j
σj
N exp
j¼1
i ð1 þ
j¼1 f i ϵj Þ
ð1ÞReconstructed μ -like momentum (MeV/c)

FIG. 1 (color online). Event selection efficiencies for atmospheric neutrino MC as a function of reconstructed momentum
for n → ν̄π 0 selection cuts (top) and p → ν̄π þ selection cuts(bottom). For the π þ sample, all momenta are calculated assuming a muon hypothesis. The atmospheric neutrino events thatmake up the background for the p → ν̄π þ mode are treatedseparately in the spectrum fit according to their origin.

of nonpionic origin, as shown in the first row of Table I.
Since the shape and level of the selection efficiency differ
for backgrounds of pionic and muonic origin, these twocases are treated as separate systematic errors in the
spectrum fit. The pion detection efficiency is lower thanthat of the muons; this is due to the fact that pions, unlike
muons, may undergo hadronic interactions in the water.
Efficiency curves in this case are calculated using the MC
truth neutrino interaction mode in the denominator todetermine what fraction of events pass the p → ν̄π þselection cuts for (1) FCFV events that originate fromCC quasielastic (CCQE) interactions (muonic origin) and(2) FCFV events that originate from interactions that truly
have a π þ (pionic origin).

where i indexes the data bins, N exp
is the MC expectation,iand N obs
is the number of observed events in the ith bin.
i
The Monte Carlo simulation expectation is given by
N exp¼ αN bkg
þ βN sigiii , where α and β are the normalization
parameters for background (atmospheric neutrinos) andsignal (nucleon decay), respectively. In the two-dimensional
fit space, the allowed ranges of the parameters are definedsuch that a value of 1.0 for α (atmospheric neutrino
background normalization) and a value of 0.0 for β (nucleon
decay signal event normalization) would indicate that the
SK data are perfectly described by the atmospheric neutrino
simulation alone, with no contribution from nucleon
decay. The effect of the jth systematic error is included
via a “pull term,” which includes the error parameter ϵjand f ji , which is the fractional change in the MC expectation
for bin i that would occur for a one-sigma change insystematic error σ j. In total, 30 bins are used to computethe value of χ 2 for the n → ν̄π 0 analysis (10 for SK-I, 10
for SK-II, and 10 for SK-III), and 60 bins are used forthe p → ν̄π þ analysis. The number of bins in the π þanalysis is double that of the π 0 analysis due to the presenceof two independent subsamples (events with zero and121802-31Chgx

π+/- → π0
π0 → π+/- Particle Production

Fraction of π events

0.8

Scattering
0.6

Absorption
0.4

0.2

No interaction
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

True π momentum (GeV/c)

FIG. 2 (color online). Cumulative fractions of nuclear effects
for π 0 as a function of true π 0 momentum for atmospheric
neutrino interactions. The fractions of events that undergo charge
exchange, multiple particle production, scattering, and absorption
are shown by various shades as labeled. Pions that exit thenucleus without experiencing any nuclear effect are indicated by
the portion labeled “No interaction.”

one decay electron, respectively) in the selected data forthat decay mode.
Equation 1 is minimized with respect to the ϵj accordingto ∂χ 2 =∂ϵj ¼ 0, which yields a set of iteratively solved
equations in the epsilons. The χ 2 is calculated by thisprocedure for 10 000 points in the fit parameter space(α∶½0.8; 1.2; β∶½0.0; 0.2Þ. Each SK run period uses an
independent sample of 500 years of atmospheric neutrino
MC simulation and an independent sample of 5000 eventsof the pertinent nucleon decay MC simulation to calculate

TABLE II.
after fit.

Decay moden → ν̄π 0

p → ν̄π þweek ending
19 SEPTEMBER 2014

PHYSICAL REVIEW LETTERS

PRL 113, 121802 (2014)

2N exp
i . The global minimum χ for each decay mode isdefined as that decay mode’s best fit point.
Six sources of systematic uncertainty are considered in
the n → ν̄π 0 analysis, and 15 sources are considered in the
p → ν̄π þ analysis. These can be divided into two classes:
those that are common to all SK run periods and those that
depend on the detector geometry of an individual run
period. Uncertainties in the nuclear effect cross sections(charge exchange and particle production, absorption, andinelastic scattering) are dominant and are treated ascommon to all SK run periods. We neglect other common
uncertainties such as atmospheric neutrino flux andneutrino interaction cross sections because they are overwhelmed by the nuclear effect uncertainties. Uncertainties
in detection efficiency are treated independently for eachsubsample and run period. The detection efficiencies forn → ν̄π 0 nucleon decay signal, for π 0 background, and formuon-induced background in the p → ν̄π þ analysis, aretaken to have an overall 5% uncertainty due to contributions from detector performance uncertainties, as describedin Ref. [6]. The signal and background detection efficiency
uncertainties in each decay mode are treated as fully
correlated. For p → ν̄π þ signal and π þ -induced backgrounds, the detection efficiency uncertainty is estimatedto be larger (15%) due to the possibility that charged pions
may interact hadronically as they travel through the water.
The systematic errors that contribute the most to the fits
are those from nuclear effects. The cumulative fractions ofeach category of nuclear effect are shown in Fig. 2 as afunction of true π 0 momentum for atmospheric neutrino
events (and the corresponding plot for π þ momentum issimilar). We assume an uncertainty of 30% on the crosssection for each nuclear effect, based on the measurements
made in Ref. [13] and estimates made for SK in Ref. [6].

Systematic error terms in the n → ν̄π 0 and p → ν̄π þ spectrum fits, with 1σ uncertainties and resulting size of pull terms

Systematic error

1σ uncertainty (%)

Size of pull after fit(units of σ)Charge exchange þ particle production cross section
Pion absorption cross section
Inelastic scattering cross section
SK-I single π 0 background detection efficiency
SK-II single π 0 background detection efficiency
SK-III single π 0 background detection efficiency
Charge exchange þ particle production cross section
Pion absorption cross section
Inelastic scattering cross section
SK-I muonic background detection efficiency 0 decay-e (1 decay-e)
SK-II muonic background detection efficiency 0 decay-e (1 decay-e)
SK-III muonic background detection efficiency 0 decay-e (1 decay-e)
SK-I pionic background detection efficiency 0 decay-e (1 decay-e)
SK-II pionic background detection efficiency 0 decay-e (1 decay-e)
SK-III pionic background detection efficiency 0 decay-e (1 decay-e)

30
30
30
5
5
5
30
30
30
5(5)
5(5)
5(5)
15(15)
15(15)
15(15)

−1.26
0.83
−0.42
0.08
−0.19
−0.01
−0.61
0.30
−0.12
0.01(0.16)
0.00(0.25)−0.01ð0.18Þ
0.01ð−0.29Þ
0.00ð−0.08Þ
0.00(0.01)

121802-4

week ending
19 SEPTEMBER 2014

PHYSICAL REVIEW LETTERS

PRL 113, 121802 (2014)

TABLE III. Best fit parameter values, signal-detection efficiency for each SK running period, 90% C.L. value of β parameter, andallowed number of nucleon decay events in the full 172.8 kt · yr exposure (SK-I: 91.7, SK-II: 49.2, SK-III: 31.9), and lower partial
lifetime limit for each decay mode at 90% C.L.

Decay mode

Best fitvalues (α, β)Unphysicalbest fit (α, β)Signal efficiency(SK-I,-II,-III)%n → ν̄π 0
p → ν̄π þ(0.940,0.000)(0.976,0.000)(0.976,−0.020)(0.996,−0.010)(48.5, 44.0, 48.5)
0-decay-e: (20.4, 23.0, 22.0)
1-decay-e: (14.8, 12.4, 14.2)

As is seen in the figure, charge exchange and absorption
effects occur with greater frequency in the momentum
range of these decay modes (∼460 MeV=c). The discontinuity at 500 MeV=c is the result of the transition from thecustom simulation used to track pions in the nucleus thatare below 500 MeV=c and the GCALOR simulation of pion
propagation for pions with momentum equal to or above
500 MeV=c. To study the impact of the relative contribution of the different nuclear effects, we varied the systematic uncertainty from 5% of the nominal value to 100% of
the nominal value; this had a negligible impact on the final
number of fitted events. Nevertheless, we are actively
improving the model of pion interactions, and this improvement will be included in future SK analyses.
The systematic errors used in this analysis and theiruncertainties and relative pulls after performing the fitting
procedure are shown in Table II. As can be seen in the table,
all of the systematic error pulls stay near or below 1σ oftheir nominal values after the fit, indicating no strong
tension between data and MC simulation.
In an unconstrained fit, the best fit value for the βparameter (nucleon decay normalization) falls in theunphysical region for both the n → ν̄π 0 and the p →ν̄π þ analyses, preferring a negative amount of nucleon
decay. To avoid this, we constrain the β values to be in thephysical region and determine the 90% C.L. value of βaccording to the Feldman-Cousins prescription [14]. The
partial lifetime lower limit for each decay mode is thencalculated according toτ=B ¼

ΔtεN nucleons;
N 90CL

Number signal events
at 90% C.L. (N 90CL )τ=B (×1032 yrs)

0.020
0.010

19.1
52.8

11.0
3.9

350
SK dataAtm. ν + n → ν π0 MC (best fit)
90% CL allowed n → ν π0
90% CL allowed n → ν π0 (× 5)

Events per 100 MeV/c

300
250
200
150
100
50
0

0

100 200 300 400 500 600 700 800 900 1000

Reconstructed momentum (MeV/c)
SK dataAtm. ν + p → ν π+ MC (best fit)
90% CL allowed p → ν π+
90% CL allowed p → ν π+ (× 5)

Events per 100 MeV/c

1400
1200
1000
800
600
400
200

ð2Þ

0

where B is the decay mode branching ratio, Δt is the
exposure in kt · yr, ε is the overall signal detection
efficiency of the nucleon decay mode, N nucleons is thenumber of nucleons per kiloton of water (2.7 × 1032
neutrons or 3.3 × 1032 protons), and N 90CL is the numberof nucleon decay events allowed at 90% C.L. as determinedfrom the β value.
The physical and unphysical best fit parameter values,
signal detection efficiencies for each running period of SK,
and number of nucleon decay events allowed in the data
sample at 90% C.L. are shown in Table III. Using theconstrained physical best fit parameters and pull terms, the

β90CL

0

100 200 300 400 500 600 700 800 900 1000

Reconstructed momentum (MeV/c)

FIG. 3. Reconstructed momentum for 172.8 kt · yr of SK-I þ
II þ III data (black dots), best fit result of atmospheric neutrino
plus nucleon decay MC simulation (solid line), and the 90% C.L.
allowed amount of nucleon decay (hatched histogram) forn → ν̄π 0 (top) and p → ν̄π þ (bottom). The dashed line shows
how a positive signal of nucleon decay would look, corresponding to five times the limit we set on the decay partial lifetimes.
The p → ν̄π þ nucleon decay contribution in the bottom figure
is reconstructed at lower momentum than the expected value(458.8 MeV=c) because a muon hypothesis is assumed in thereconstruction.

121802-5

PRL 113, 121802 (2014)

PHYSICAL REVIEW LETTERS

resulting fitted momentum spectra are shown combined
for all running periods as the solid black lines in Fig. 3,
with the nonobservation 90% C.L. allowed amount ofsignal nucleon decay shown by the hatched histogram andoverlaid SK data by black dots. The 90% C.L. partial
lifetime lower limits we set for these two decay modes arethen τn→ν̄π0 > 1.1 × 1033 and τp→ν̄πþ > 3.9 × 1032 years. In
comparison, the predicted range of partial lifetimes allowed
for the SO(10) model presented in Ref. [3] is τn→ν̄π0 ¼
2τp→ν̄πþ ≤ 5.7 − 13 × 1032 years; the model’s allowed
ranges are nearly ruled out by the limits presented here.
These limits represent an order of magnitude improvement
over previously published limits for these two decay modes[15–17] and can be used to more tightly constrain other
GUT models that allow these modes.
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, Science, Sports
and Culture, and the U.S. Department of Energy.

*

Deceased.
Corresponding author.
‡
Present address: GIST College, Gwangju Institute of
Science and Technology, Gwangju 500-712, Korea.
†§

week ending
19 SEPTEMBER 2014

Present address: Department of Physics and Astronomy,
University of Minnesota, Minneapolis, Minnesota 55455,
USA.
[1] H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438(1974).
[2] J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974).
[3] H. Goh, R. Mohapatra, S. Nasri, and S. Ng, Phys. Lett. B
587, 105 (2004).
[4] K. Babu, J. Pati, and Z. Tavartkiladze, J. High Energy Phys.
06 (2010) 084.
[5] S. Fukuda et al., Nucl. Instrum. Methods A 501, 418 (2003).
[6] H. Nishino et al., Phys. Rev. D 85, 112001 (2012).
[7] Y. Hayato, Nucl. Phys. B, Proc. Suppl. 112, 171(2002).
[8] M. Honda, T. Kajita, K. Kasahara, S. Midorikawa, and
T. Sanuki, Phys. Rev. D 75, 043006 (2007).
[9] CERN Program Library Long Writeup W5013 (1993).
[10] Y. Ashie et al., Phys. Rev. D 71, 112005 (2005).
[11] C. Regis et al., Phys. Rev. D 86, 012006 (2012).
[12] G. L. Fogli, E. Lisi, A. Marrone, D. Montanino, and
A. Palazzo, Phys. Rev. D 66, 053010 (2002).
[13] D. Ashery, I. Navon, G. Azuelos, H. K. Walter,
H. J. Pfeiffer, and F. W. Schlepütz, Phys. Rev. C 23, 2173
(1981).
[14] G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873
(1998).
[15] C. McGrew et al., Phys. Rev. D 59, 052004 (1999).
[16] K. S. Hirata et al., Phys. Lett. B 220, 308 (1989).
[17] D. Wall et al., Phys. Rev. D 62, 092003 (2000).

121802-6