PRL 115, 121803 (2015)

PHYSICAL REVIEW LETTERS

week ending
18 SEPTEMBER 2015

Search for Nucleon and Dinucleon Decays with an Invisible Particle and a Charged
Lepton in the Final State at the Super-Kamiokande Experiment
V. Takhistov,7 K. Abe,1,30 Y. Haga,1 Y. Hayato,1,30 M. Ikeda,1 K. Iyogi,1 J. Kameda,1,30 Y. Kishimoto,1,30 M. Miura,1,30
S. Moriyama,1,30 M. Nakahata,1,30 T. Nakajima,1 Y. Nakano,1 S. Nakayama,1,30 A. Orii,1 H. Sekiya,1,30 M. Shiozawa,1,30
A. Takeda,1,30 H. Tanaka,1 T. Tomura,1,30 R. A. Wendell,1,30 T. Irvine,2 T. Kajita,2,30 I. Kametani,2 K. Kaneyuki,2,30,*
Y. Nishimura,2 E. Richard,2 K. Okumura,2,30 L. Labarga,3 P. Fernandez,3 J. Gustafson,4 C. Kachulis,4 E. Kearns,4,30
J. L. Raaf,4 J. L. Stone,4,30 L. R. Sulak,4 S. Berkman,5 C. M. Nantais,5 H. A. Tanaka,5 S. Tobayama,5 M. Goldhaber,6,*
G. Carminati,7 W. R. Kropp,7 S. Mine,7 P. Weatherly,7 A. Renshaw,7 M. B. Smy,7,30 H. W. Sobel,7,30 K. S. Ganezer,8B. L. Hartfiel,8 J. Hill,8 N. Hong,9 J. Y. Kim,9 I. T. Lim,9 A. Himmel,10 Z. Li,10 K. Scholberg,10,30 C. W. Walter,10,30
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,15,30 Y. Oyama,15 K. Sakashita,15
T. Sekiguchi,15 T. Tsukamoto,15 A. T. Suzuki,16 Y. Takeuchi,16,30 T. Yano,16 S. Hirota,17 K. Huang,17 K. Ieki,17 T. Kikawa,17
A. Minamino,17 T. Nakaya,17,30 K. Suzuki,17 S. Takahashi,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,† H. Ishino,22 T. Kayano,22 A. Kibayashi,22 Y. Koshio,22 T. Mori,22 M. Sakuda,22 Y. Kuno,23 R. Tacik,24,32
S. B. Kim,25 H. Okazawa,26 Y. Choi,27 K. Nishijima,28 M. Koshiba,29 Y. Suda,29 Y. Totsuka,29 M. Yokoyama,29,30,†
C. Bronner,30 M. Hartz,30 K. Martens,30 Ll. Marti,30 Y. Suzuki,30 M. R. Vagins,30,7 J. F. Martin,31 P. de Perio,31 A. Konaka,32
S. Chen,33 Y. Zhang,33 and R. J. Wilkes34(The 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, 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, Saskatchewan 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
28
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
29
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
30
Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba 277-8582, Japan
31
Department of Physics, University of Toronto, 60 St., Toronto, Ontario M5S1A7, Canada
32
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T2A3, Canada

20031-9007=15=115(12)=121803(6)121803-1© 2015 American Physical Society

PRL 115, 121803 (2015)

PHYSICAL REVIEW LETTERS

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Department of Engineering Physics, Tsinghua University, Beijing 100084, China
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 5 August 2015; published 18 September 2015)34

Search results for nucleon decays p → eþ X, p → μþ X, n → νγ (where X is an invisible, masslessparticle) as well as dinucleon decays np → eþ ν, np → μþ ν, and np → τþ ν in the Super-Kamiokande
experiment are presented. Using single-ring data from an exposure of 273.4 kton · yr, a search for these
decays yields a result consistent with no signal. Accordingly, lower limits on the partial lifetimesof τp→eþ X > 7.9 × 1032 yr, τp→μþ X > 4.1 × 1032 yr, τn→νγ > 5.5 × 1032 yr, τnp→eþ ν > 2.6 × 1032 yr,
τnp→μþ ν > 2.2 × 1032 yr, and τnp→τþ ν > 2.9 × 1031 yr at a 90% confidence level are obtained. Some ofthese searches are novel.
DOI: 10.1103/PhysRevLett.115.121803

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

Many signs indicate that the standard model of particle
physics is an incomplete description of nature. Gauge
coupling unification, charge quantization, and other features suggest a more unified account, such as a grandunified theory (GUT) [1–4], as an underlying fundamental
theory. While the unification scale (∼1015 –1016 GeV) is
unreachable by accelerators, rare processes predicted bythese theories, such as proton decay, can be probed by large
underground detectors. Being a signature prediction of
GUTs, observation of an unstable proton would constituterobust evidence for physics beyond the standard model,
while nonobservation will stringently constrain theoreticalmodels.
The simplest unification scenarios based on minimal
SU(5) and supersymmetric (SUSY) SU(5) have been
decisively ruled out by bounds on p → eþ π 0 [5–7] andp → ν̄K þ [8]. Many alternative scenarios as well as
potential signatures are possible (see [9] for review).
In this Letter, we analyze a broad class of nucleon anddinucleon decay channels with a showering or nonshowering single Cherenkov ring signature within the SuperKamiokande (SK) experiment, using the technique ofspectral fit [10,11]. First, we have considered two general
two-body decays p → eþ X and p → μþ X, where X is asingle unknown invisible particle which is assumed to bemassless. These searches are distinct from the modeldependent inclusive analyses of [12,13] listed in theParticle Data Group [14]. Similarly, we also considern → νγ. Though this radiative process is suppressed, it
has a clean signature and has been considered in the context
of SU(5) [15], with some models [9] predicting a lifetimeof 10381 yr.
While single nucleon ΔB ¼ 1 processes have been ingeneral well studied, dinucleon ΔB ¼ 2 channels also pose
great interest. These higher-dimensional processes canbecome significant in models which suppress proton decay
and could be connected to baryogenesis [16], accounting forthe observed baryon asymmetry of the Universe [17]. Such aconnection may already be hinted at from the requirementof baryon number violation as a necessary condition for
explaining the asymmetry [18]. The disappearance ΔB ¼ 2

reactions, with invisible final state particles, have beenstudied and no signal excess was observed [19–21]. The
channels np → eþ ν, np → μþ ν, and np → τþ ν violate thebaryon number by two units and violate the lepton number
by either two or zero units. They can become significant inmodels with an extended Higgs sector [16,22], which could
be considered in the context of GUTs [23]. While the τ
cannot occur in single nucleon decay, in dinucleon decay theτ channel is allowed [24]. The process np → τþ ν has notbeen experimentally studied before and in addition to theelectron and muon channel searches we present the firstsearch in the τ channel.
In this work, SK data are analyzed from an exposure of
the 22.5 kton fiducial mass for 273.4 kton yr, covering four
running periods (SK-I through SK-IV). Details of thedetector design and performance in each SK period, canbe found in [25,26]. This analysis considers only events inwhich all observed Cherenkov light was fully contained
within the inner detector.
Since final-state neutrinos or X (by definition) are notobserved, the only signature of p → eþ X, p → μþ X,
n → νγ, np → eþ ν, and np → μþ ν is a single charged
eþ or μþ lepton, or single γ. Thus, the invariant mass of theinitial state cannot be reconstructed and the signal will besuperimposed on a substantial atmospheric neutrino background in the e-like and μ-like momentum spectra. For the
np → τþ ν decay, only the τ → eþ νν and τ → μþ νν channels are considered, with the respective branching ratios of
17.8% and 17.4%. This allows us to perform all the analyses
within a unified framework. The previous searches forn → νγ, np → eþ ν, and np → μþ ν, which were performed
with a smaller detector using a counting method, resulted in
the lifetime limits of 2.8 × 1031 yr [5], 2.8 × 1030 yr [19],and 1.6 × 1030 yr [19], respectively. In contrast, the spectral
fit employed within this work allows utilization of the extra
information from the energy dependence of signal, background, and the systematic errors. This methodology has
been recently employed in the SK nucleon decay [11,27] anddark matter analyses [28].
The nucleon decay signal events are obtained fromMonte Carlo (MC) simulations, in which all the nucleons

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PRL 115, 121803 (2015)

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PHYSICAL REVIEW LETTERSof the water H2 O molecule are assumed to decay with equal
probability. The final state particles are generated withenergy and momentum uniformly distributed in phasespace. The effects of Fermi motion, nuclear binding energy,
as well as nucleon-nucleon correlated decays [29] are taken
into account for both nucleon [30–32] and dinucleon
searches [33]. The signal Fermi momentum distributions
are simulated using a spectral function fit to electron-12 C
scattering data [34]. The SK detector simulation [26] isbased on the GEANT-3[35] package, with the TAUOLA [36]package employed for decaying the τ leptons. For the
np → τþ ν mode we generated three MC samples, with theτ decaying to eþ νν, μþ νν, and all decay channels. The latterallows us to study sample contamination in the two selected
leptonic τ channels from the hadronic τ channels and thus
identify sample purity after the event selection. We haveconfirmed that the resulting MC charged lepton spectrafrom τ → eþ νν and τ → μþ νν decays agree with thetheoretical formula [37]. For p → eþ X and p → μþ X
modes, the invisible X particle cannot be a fermion by
spin conservation, but in our spin-insensitive MC it was
simulated as a neutrino. In total, around 4200 signal eventswere generated within the fiducial volume for each SK
period for single nucleon decays and around 8400 for
dinucleon decays.
Atmospheric neutrino background interactions weregenerated using the flux of Honda et al. [38] and theNEUT simulation package [39], which uses a relativistic
Fermi gas model. Background MC corresponding to a
500-year exposure of the detector was simulated for eachdetector phase. We used the same atmospheric neutrino MC
simulation as the standard SK oscillation analysis [40].
The event selection applied to the fully contained datais the following: (i) a single Cherenkov ring is present,(ii) the ring is showering (electronlike) for p → eþ X,
n → νγ, np → eþ ν, and np → τþ νðτ → eþ ννÞ andnonshowering (muonlike) for p → μþ X, np → μþ ν, and
np → τþ νðτ → μþ ννÞ, (iii) there are zero decay electrons
for modes with an e-like ring and one decay electron for
those with a μ-like ring, (iv) the reconstructed momentum
lies in the range 100 MeV=c≤ pe ≤ 1000 MeV=c for
p → eþ X, n → νγ and in the range 200 MeV=c ≤ pμ ≤1000 MeV=c for p → μþ X, with the range extended to100–1500 MeV=c for dinucleon decays with an e-like ringand 200–1500 MeV=c for those with a μ-like ring. In total,
approximately 37 000 fully contained events were obtainedin the SK-I to SK-IV data-taking periods. After the criteria(i)–(iv) have been applied, the final data samples for single
nucleon decay searches with an e-like ring contain 8500
events and 6000 events for the case of μ-like ring, with
momenta up to one GeV=c. To search for dinucleon decays
we consider lepton momenta up to 1500 MeV=c. The final
samples for the dinucleon modes contain 9500 events forthe e-like channels and 6500 events for the μ-like ones. See
Ref. [41] for details regarding reconstruction.

The signal detection efficiency is defined as the fractionof events passing selection criteria compared to the total
number of events generated within the true fiducial volume.
The average detection efficiency for e-like channels isð94.0  0.4Þ% for all SK data-taking periods. For the μ-likechannels, the average detection efficiency is 76.4  0.6%
for SK-I to SK-III and 91.7  0.4% for SK-IV. The increasein efficiency observed in SK-IV for channels with a μ-like
ring, comes from a 20% improvement in the detection ofmuon decay electrons after an upgrade of the detector
electronics [26].
For the e-like momentum spectrum up to 1500 MeV=c,
the dominant background contribution, composing 75.8%of the events, comes from the νe charged-current (CC)quasielastic (QE) neutrino channel. The νe CC single-pion
production constitutes 13.0% of the background, while theνe CC coherent-pion, CC multipion, and neutral-current(NC) single-pion productions contribute around 1.1%,
1.1%, and 1.6%, respectively. About 3.5% and 1.1% ofevents come from νμ NC single-pion and coherent-pion
production. For the μ-like momentum spectrum up to1500 MeV=c, the dominant contribution of around 78.6%
comes from νμ CCQE. Similarly, νμ CC single-pion, CC
coherent-pion, and CC multipion as well as NC single-pion
production contribute around 16.2%, 1.4%, 1.6% and 0.8%,
respectively.
After event selection, a spectral fit is performed on thereconstructed charged lepton momentum distribution of theevents. The χ 2 minimization fit is based on the Poisson
distribution, with the systematic uncertainties accounted forby quadratic penalties (“pull terms”) [10]. The χ 2 functionused in the analysis isχ2 ¼ 2

nX
bins
i¼1



 NX
syserr 
ϵj 2
N obs
i
obs
N exp
ln
þ
N
−
1
þ
;
i
i
σj
N exp
i
j¼1

N syserr
X j ϵj 
;
1þ
fi
σj
j¼1

N exp
¼ ½αN back
þ βN sig
i
i
i 

ð1Þ

sig
back
where i labels the analysis bin. The terms N obs,
i , Ni , Niexp
N i are the numbers of observed data, signal MC, background MC, and the total (signal and background) MC
events in each bin i. The index j labels the systematic
errors, while ϵj and f ji correspond to the fit error parameterand the fractional change in the N exp
bin due to 1-sigmaierror uncertainty σ j, respectively. The fit is performed fortwo parameters α and β, which denote the background andsignal normalizations, respectively. After the event selection, the signal MC distribution is normalized to thebackground by the integral, which in turn is normalized
to the SK live time. This allows us to identify the fit point
ðα; βÞ ¼ ð1; 0Þ with the no-signal hypothesis. Similarly,ðα; βÞ ¼ ð0; 1Þ signifies that the data are described bysignal only, with the signal amount equal to background121803-3

PRL 115, 121803 (2015)

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PHYSICAL REVIEW LETTERSTABLE I. Systematic errors of spectrum fits, with 1σ uncertainties and resulting fit pull terms. Errors specific to signal and backgroundare denoted by S and B, while those that are common to both by SB.
Decay mode
Systematic error
Final state interactions
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

1-σ uncertainty (%)
10
25a
15b
10
10
1.1, 1.7, 2.7, 2.3
10c100

p → eþ X

p → μþ X

Fit pull (σ)
0.10
−0.23
−1.44
0.69
−0.55
0.58, −0.91, 0.48, 0.38
−0.08
0.00

Fit pull (σ)
−0.60
−0.08
−0.50
0.23
−0.14
−0.54, 0.07, −0.14, 0.26
0.70
0.06

B
B
B
B
B
SB
S
S

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).
Estimated from comparison of spectral function and Fermi gas model.

abc

MC normalized (prefit) to live time. The χ 2 minimization iscarried out over each α and β in the grid according to∂χ 2 =∂ϵj ¼ 0. The resulting global minimum is defined as
the best fit. Further details on the fit and specifics ofsystematic error treatment can be found in [11,28,42]. For
the np → τþ νν mode, after the appropriate event selection
is applied to both MC samples of τ → eþ νν and τ → μþ νν,
the samples are combined for the fit, allowing us to obtain asingle value for the permitted number of nucleon decays
at 90% C.L.
The systematic errors can be divided into signal-specific(S), background-specific (B) as well as detector andreconstruction errors, which are common to both signal
and background (SB). The two signal specific systematics
are from Fermi motion and nucleon-nucleon correlated
decay. For background, in order to methodically selectthe dominant systematics, we started from more than 150
errors employed in the SK oscillation analysis [42]and chose those which affect the analyses bins by morethan 5% (jf ji j ≥ 0.05). Relaxing this criteria to 1% does
not significantly alter the results, but complicates theanalysis [11]. As in [11], we have found that the dominant
contributions originate from uncertainties related toneutrino flux and energy calibration (common to bothsignal and background). Including the signal systematics,
the total number of considered errors is 11 and they are
the same for all modes. In Table I we display the complete list of systematics, their uncertainties and fitted
pull terms for two representative examples p → eþ X andp → μþ X.
The spectral fit determines the overall backgroundand signal normalizations α and β, with the fit results
displayed in Table II. The outcome shows that no significant signal excess has been observed, with the dataΔχ 2 ¼ χ 2 − χ 2min being within 1σ of the background only
hypothesis for all search modes except for p → μþ X, which
is within 2σ.
The lower lifetime limit on the processes can then becomputed from the 90% confidence level value of β(β90 C:L: ), which translates into the allowed amount ofsignal at 90% confidence level according to
N 90 C:L: ¼ β90 C:L: · N signal , where N signal is the total numberof signal events. The partial lifetime limit is then calculatedfromτ90 C:L: =B ¼

PSK4

sk¼SK1 λsk ϵsk N

nucleons

N 90 C:L:;ð2Þ

TABLE II. Best fit (α; β) parameter values, best fit χ 2 =d:o:f:, no signal Δχ 2 , 90% C.L. value of β parameter, allowed number ofnucleon decay events in the full 273.4 kton yr exposure and a partial lifetime limit for each decay mode at 90% C.L. The sensitivity andlifetime limit for dinucleon decay modes are per 16 O nucleus.
Decay mode

Best fit

Best fit

No signal

Data

Data

Sensitivity

τ=Bp → eþ X
n → νγp → μþ X
np → eþ ν
np → μþ ν
np → τþ ν(α; β)(1.050, 0.002)(1.045, 0.004)(0.960, 0.016)(0.955, 0.000)(0.910, 0.000)(0.910, 0.000)

χ 2 =d:o:f:
70.9=70
70.5=70
63.2=62122.5=110
97.0=102224.6=214

Δχ 2
0.19
0.43
3.43
0.00
0.00
0.00

β90 C:L:
0.013
0.015
0.032
0.004
0.005
0.006

N 90 C:L:
108
125
187
33
36
96

(×1031 yr)
79
58
77
10
11
1

(×1031 yr)
79
55
41
26
20
3

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1200

1200

1000

Events

600

600

400

400

200

200
0

100

Residual
Events

0

100
50
0
-50

50
0
-50

-100

-100

100
90
80
70
60
50
40
30
20
10
0

100
90
80
70
60
50
40
30
20
10
0

e-like Signal (SK I-IV)
p → eXn → νγnp → eνnp → τ(eνν) ν

0

200

400

600

800

1000

1200

μ-like (SK I-IV)
Data
Atm. Nu. (fit)800

EventsEventsResidual
Events1000

e-like (SK I-IV)
Data
Atm. Nu. (fit)800

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PHYSICAL REVIEW LETTERS

PRL 115, 121803 (2015)

1400

Momentum [MeV/c]

μ-like Signal (SK I-IV)
p → μXnp → μνnp → τ(μνν) ν

0

200

400

600

800

1000

1200

1400

Momentum [MeV/c]

FIG. 1 (color online). (Top) Reconstructed momentum distribution for 273.4 kton yr of combined SK data (black dots) and the best-fit
result for the atmospheric neutrino background Monte Carlo simulations (solid line). The corresponding residuals are shown below, after
fitted background subtraction from data. (Bottom) The 90% confidence level allowed nucleon decay signal (hatched histograms), from thesignal and background MC fit to data. All modes are shown (overlaid), with e-like channels on the left and μ-like channels on the right.

where B is the branching ratio of a process, ϵsk and λsk are
the signal efficiency and the exposure in kton yr for each
SK phase, N 90 C:L: is the amount of signal allowed at
the 90% confidence level, and N nucleons is the number ofnucleons per kiloton of water, corresponding to 3.3 × 1032 ,2.7 × 1032 , and 3.3 × 1031 for proton, neutron, and dinucleon decay searches, respectively.
The resulting fitted spectra for the 273.4 kton · yr of
combined SK data can be found in Fig. 1. The upper figures
display the best-fit result for atmospheric neutrino background (solid line) without the signal fitted to the data
(black dots) and the corresponding residuals after the fitted
MC is subtracted from the data. It is seen that the background MC describes the data well. The bottom figures
display the 90% C.L. allowed signal (hatched histogram),obtained from the fit of background with signal to data,with all the e-like and μ-like spectra overlaid with all themodes. The N 90 C:L: as well as resulting sensitivities andcalculated lifetime limits for the decays are shown in
Table II. The sensitivities were obtained assuming thatdata are described by background. For the np → τν mode
we have combined the τ channels eþ νν and μþ νν, weighted
by their respective branching ratios. This limit is thenmultiplied by 1.15 to account for roughly 85% sample

purity of the tau channels. We set the lower limits on thepartial lifetimes of the decay modes at the 90% C.L., withthe results shown in Table II.
In conclusion, the single Cherenkov ring momentum
spectra in Super-Kamiokande are well described by atmospheric neutrinos, including the effect of neutrino oscillationand systematic uncertainties, up to 1500 MeV=c. We findno evidence for any contribution from the six different
nucleon and dinucleon decay modes that would produce ashowering or nonshowering Cherenkov ring. The results ofthis analysis provide a stringent test of new physics. The
obtained limits represent more than an order of magnitudeimprovement over the previous analyses of n → νγ [5] andtwo orders of magnitude for np → eþ ν and np → μþ ν[19]. The searches for p → eþ X, p → μþ X (where X is aninvisible, massless particle) and np → τþ ν, are novel. The
dinucleon decay limits restrict ΔB ¼ 2 processes with L
violated by either zero or two units.
We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande experiment was built and has been operated
with funding from the Japanese Ministry of Education,
Culture, Sports, Science and Technology, the U.S. Department of Energy, and the U.S. National Science Foundation.

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PHYSICAL REVIEW LETTERS

Deceased.
Also at BMCC/CUNY, Science Department, New York,New York, USA.
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