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Search for Dinucleon Decay into Kaons in Super-Kamiokande
M. Litos,1,† K. Abe,2 Y. Hayato,2,3 T. Iida,2 M. Ikeda,2 K. Iyogi,2 J. Kameda,2 K. Kobayashi,2 Y. Koshio,2 Y. Kozuma,2M. Miura,2 S. Moriyama,2,3 M. Nakahata,2,3 S. Nakayama,2 Y. Obayashi,2 H. Ogawa,2 H. Sekiya,2 M. Shiozawa,2,3
Y. Suzuki,2,3 A. Takeda,2 Y. Takenaga,2 Y. Takeuchi,2,3 K. Ueno,2 K. Ueshima,2 H. Watanabe,2 S. Yamada,2
T. Yokozawa,2 S. Hazama,4 C. Ishihara,4 H. Kaji,4 T. Kajita,4,3 K. Kaneyuki,4,3,* T. McLachlan,4 K. Okumura,4 Y. Shimizu,4N. Tanimoto,4 M. R. Vagins,3,5 E. Kearns,1,3 J. L. Stone,1,3 L. R. Sulak,1 F. Dufour,1 J. L. Raaf,1 B. Henning,1
M. Goldhaber,6 K. Bays,5 D. Casper,5 J. P. Cravens,5 W. R. Kropp,5 S. Mine,5 C. Regis,5 M. B. Smy,5,3 H. W. Sobel,5,3
K. S. Ganezer,7 J. Hill,7 W. E. Keig,7 J. S. Jang,8 J. Y. Kim,8 I. T. Lim,8 J. B. Albert,9 T. Wongjirad,9 R. Wendell,9K. Scholberg,9,3 C. W. Walter,9,3 S. Tasaka,10 J. G. Learned,11 S. Matsuno,11 Y. Watanabe,12 T. Hasegawa,13 T. Ishida,13
T. Ishii,13 T. Kobayashi,13 T. Nakadaira,13 K. Nakamura,13,3 K. Nishikawa,13 H. Nishino,13 Y. Oyama,13 K. Sakashita,13
T. Sekiguchi,13 T. Tsukamoto,13 A. T. Suzuki,14 A. Minamino,15 T. Nakaya,15,3 Y. Fukuda,16 Y. Itow,17 G. Mitsuka,17T. Tanaka,17 C. K. Jung,18 G. Lopez,18 C. McGrew,18 R. Terri,18 C. Yanagisawa,18 N. Tamura,19 H. Ishino,20
A. Kibayashi,20 S. Mino,20 T. Mori,20 M. Sakuda,20 H. Toyota,20 Y. Kuno,21 M. Yoshida,21 S. B. Kim,22 B. S. Yang,22
T. Ishizuka,23 H. Okazawa,24 Y. Choi,25 K. Nishijima,26 Y. Yokosawa,26 M. Koshiba,27 M. Yokoyama,27 Y. Totsuka,27,*
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(The Super-Kamiokande Collaboration)
1

Department of Physics, Boston University, Boston, Massachusetts 02215, USA
Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan
3
Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan
4
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan
5
Department of Physics and Astronomy, University of California, Irvine, Irvine, California 92697-4575, USA
6
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, 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
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
11
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
12
Physics Division, Department of Engineering, Kanagawa University, Kanagawa, Yokohama 221-8686, Japan
13
High 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, Japan18
Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794-3800, USA
19
Department of Physics, Niigata University, Niigata, Niigata 950-2181, Japan20
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 Systems Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8561, Japan
24
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka 425-8611, Japan
25
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
26
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
27
The University of Tokyo, Bunkyo, Tokyo 113-0033, 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 10 October 2013; published 4 April 2014)2

A search for the dinucleon decay pp → K þ K þ has been performed using 91.6 kton · yr data fromSuper-Kamiokande-I. This decay provides a sensitive probe of the R-parity-violating parameter λ112 00.
A boosted decision tree analysis found no signal candidates in the data. The expected background
was 0.28  0.19 atmospheric neutrino induced events and the estimated signal detection efficiency

0031-9007=14=112(13)=131803(6)131803-1© 2014 American Physical Society

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was 12.6%  3.2%. A lower limit of 1.7 × 1032 years has been placed on the partial lifetime of the
decay 16 O → 14 CK þ K þ at 90% C.L. A corresponding upper limit of 7.8 × 10−9 has been placed on theparameter λ112 00.
DOI: 10.1103/PhysRevLett.112.131803

PACS numbers: 13.30.Eg, 12.60.Jv

Dinucleon decay is the name given to the process where
the quarks of two bound nucleons interact to produce a
decay. This process could be mediated by the exchange
of a non–standard model particle. An exclusively mesonic
final state would conserve charge, momentum, and angularmomentum, and violate only baryon number by two units.
In this regard, dinucleon decay is sensitive to different
processes than single nucleon decay, which must violate
both baryon and lepton number.
In this Letter, we describe our search for dinucleon
decay via the reaction pp → K þ K þ in 16 O → 14 C K þ K þ .
Dinucleon decay modes with final-state kaons are particularly interesting in the context of supersymmetry, in which
the diagram for the reaction includes R-parity-violatinginteraction vertices, characterized by the ΔB ¼ 1 coupling
constant λ112 00 (see Fig. 1). It is expected that dinucleon
decay into kaons is the most sensitive experimental probeof the magnitude of λ112 00 [1–3]. Several comprehensive
reviews of current phenomenological limits on the λijk 00
parameters exist in the literature [4–6]. Dinucleon decay tokaons also constrains generic [nonsupersymmetric (SUSY)]
models of baryon number violation [7].
The Fréjus tracking iron calorimeter experiment [8] isthe only other experiment to have performed a direct searchfor ΔB ¼ 2 dinucleon decay modes with visible final-stateparticles. The Fréjus Collaboration searched for final statescomposed of either leptons or pions through such channels
as pp → eþ eþ and pp → π þ π þ using the iron in thedetector as the progenitor nucleus [9]. No evidence wasseen for pionic or leptonic decay modes. The Fréjus
dinucleon decay study was based on a 2:0 kton · yr
exposure, corresponding to about 2.1 × 1031 iron · yrs.
Partial lifetime limits were placed on the pionic andleptonic decay modes that were on the order of 1030 years[9,10]. The Fréjus study did not include any searches for
dinucleon decay into final states with kaons.

In this Letter, the data collected during the SK-I
data-taking period (May 1996–July 2001; 1489.2 daysof live time) are analyzed, corresponding to 91.6 kton · yrs
or 3.1 × 1033 oxygen · yrs of exposure. The SuperKamiokande (SK) water Cherenkov detector is locatedbeneath a 2700-m water equivalent overburden of rock,under the peak of Mt. Ikenoyama in Kamioka, Gifu
prefecture in Japan. For details on the detector design,
calibration, data reduction, and simulations, see Ref. [11].
This study concentrates only on events in which all of theCherenkov light was fully contained in the inner detector.
The data used in this study is the same set used for otherproton decay and atmospheric neutrino studies performed
at Super-Kamiokande.
There are three dinucleon decay modes with a final
state composed exclusively of kaons: pp → K þ K þ ,pn → K þ K 0 , and nn → K 0 K 0 . The decay mode into
two charged kaons features the most distinct experimental
signature. The charged kaons are ejected from the parent
nucleus with a momentum of roughly 800 MeV=c , above
their Cherenkov threshold in water of 563 MeV=c , and are
therefore directly detectable. The muons produced in the
kaon decay chain are also above the Cherenkov threshold
and are detectable, as are the electromagnetic showers due
to gamma-rays from π 0 decay. Decays involving neutralkaons are less efficiently identified, due to the K 0 L escaping
the detector and the high branching fraction of K 0 S toπ þ π − , which proves to be a difficult signature to discern ina water Cherenkov detector.
The branching ratios of the three most probable final
states of pp → K þ K þ are shown in Table I. The thirdcolumn in the table shows the final-state combinatorics, andthe fourth column shows the detectable relative rates as
obtained from the Monte Carlo simulation. The detectable
relative rates include detection inefficiencies due to hadronic interactions that consume one or both of the K þ
before they are able to decay. The leading hadronic effects
TABLE I. Final-state branching ratios (B.R.) and detectable
relative rate (D.R.R.) from the pp → K þ K þ Monte Carlo simulation. Only kaon decay branches to μþ νμ and π þ π 0 wereconsidered.

FIG. 1. Feynman diagram for pp → K þ K þ in a supersymmetric framework. λ112 00 appears in two interaction vertices.

Decay mode

Final state

B.R

D.R.R.

pp → K þ K þμþ νμ μþ νμμ þ νμ π þ π 0
πþ π0 πþ π0

40%
26%
4%
70%

30%
19%
3%
52%

Total

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which occur while the K þ travels through the water. Charge
exchange occurs at a rate of 9.5% per K þ.
The only source of background in this analysis is frommulti-ring events produced by multi-GeV atmospheric
neutrino interactions. The Monte Carlo program used tomodel these events is described in Ref. [12]. The rate ofthese types of events in the Super-Kamiokande detector isabout 2.5 per day. Multiring events are produced whenmesons from the hadronic recoil produces visible rings.
Rings produced by recoiling protons, while generally rare,
are also present in the final background sample [13]. Other
mechanisms, such as multiple scattering and hadronic interactions of pions, can also contribute to multiple background
events.
The experimental signature of this dinucleon decay has
features not seen in Super-Kamiokande searches for typical
proton decay modes, such as p → eþ π 0 and p → νK þ
[14,15]. The distinguishing features of the signal events
are the visible Cherenkov rings produced by charged
kaons above the Cherenkov threshold and the large spatial
separation between the vertices of the kaon decay products.
A cartoon illustration of the event geometry is shown in
Fig. 2. Because of the relatively long lifetime of the charged
kaons (12 ns), they are expected to travel a distance ofabout 1.3 m until slowing to a stop and ultimately decaying.
About 27% of the kaons in our simulation decayed in flight.
The operating principle of this analysis is to reconstruct
all events in the data according to the hypothesis that they
were created by dinucleon decay into kaons with a final
state corresponding to one of those listed in Table I. The
resulting reconstructed variables describing the event under
the dinucleon decay hypothesis are then fed into a boosted
decision tree trained on Monte Carlo signal and background events which yields an ultimate discriminatory
variable representing how signal-like or background-likeeach event appears to be. The final cut on the boosted
decision tree output is optimized based upon the significance for finding a single signal event.
The event reconstruction is performed in a two-stepprocess. In the first step, each ring is reconstructed on an

FIG. 2. Cartoon illustration of an expected event geometry forthe final state pp → K þ K þ → μþ νμ π þ π 0 . The Fermi momentumof the parent nucleons will actually distort the back-to-backsymmetry of the kaon vectors. Dashed lines indicate particles
undetectable in a water Cherenkov detector.

week ending
4 APRIL 2014individual basis using three particle-type hypotheses: K þ ,μþ , and γ. Each ring is assigned a direction of travel,
Cherenkov opening angle, and momentum corresponding
to all three particle-type hypotheses. Unlike previous SK
analyses, where a single event vertex is defined, a newly
developed algorithm assigns an independent vertex foreach ring. A showering likelihood independent of particle
type is also assigned to each ring. The showering likelihood
quantifies how likely a ring was to have originated from anelectromagnetic showering particle (i.e., e or γ), or a more
massive, nonshowering particle (i.e., p, K  , π  , or μ ) basedon the light pattern of the ring [12]. A special light-masking
algorithm is utilized in the ring reconstruction that allows
a single ring to be considered independently of all other lightin the detector [16]. This masking is crucial for resolving themultiple particle vertices in the pp → K þ K þ signal events.
In the second step, all of the rings in the event areconsidered together, after which the final particle-type
assignment for each ring is made. The reconstructed ring
variables and the event topology are used in conjunction toclassify each ring as either a K þ candidate, μþ candidate, or γ
candidate—the three detectable particle types in the signal
events—using the pp → K þ K þ hypothesis. We note thatthe π þ from K þ → π þ π 0 , though just above the Cherenkov
threshold, would not generate enough light to be detectable
amidst the many other, brighter rings, and thus no attempt
is made to identify them in this study.
After having classified all rings as either K þ, μþ , or γ
candidates, we categorize the event based on the breakdown of its constituent rings. Monte Carlo studies showthat only certain event categories are likely to arise from adinucleon decay event by this method of ring accounting.
Eight event categories are selected to continue past theevent reconstruction and precuts (described below) phaseof the analysis, and are listed in the left column of Table II.
Just prior to the selection on event category, the following precuts are applied to the data and Monte Carlo samples
to reduce a significant portion of the background while
retaining the majority of the signal: 3 ≤ number of foundrings ≤ 5; 1000 ≤ total number of photoelectrons in the
inner detector ≤ 11 000; 0 ≤ number of found muon-decay
electrons ≤ 2; distance from event vertex to nearest wall
> 200 cm, where the event vertex is determined by the event’s
best kaon candidates resulting from the ring reconstruction
method described previously. A total of 27 events in thedata pass both the precuts and event category selection, withan expected background of 33.9 events and a signal efficiencyof 21.9% predicted by the Monte Carlo calculation.
Following precuts and selection on event category, theremaining events are processed by a boosted decision tree
(BDT) [17]. One of the primary advantages of a BDT overother multivariate techniques is that the inclusion of weak
discriminatory variables does not lessen its performance[18]. In total, 37 BDT input variables are used in thisanalysis [16].

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TABLE II. Efficiency of all simulated pp → K þ K þ events, expected neutrino background events, and actual data
events passing the precuts and the final BDT cut for the pp → K þ K þ Monte Carlo, the atmospheric neutrinoMonte Carlo, and the SK-I data, respectively. Poisson probabilities to observe at least the number of events in thedata given the expected background in each category are shown in parentheses, where it is assumed all events in thedata were induced by atmospheric neutrinos.

Category

pp → K þ K þ
MC efficiency (%)
Precuts
BDT

Atm. ν MC
events/SK-I exposure
Precuts
BDT

K þ K þ μþK þ μþ μþ
K þ μþ γγ
K þ K þ μþ μþKþKþγK þ K þ μþ γ
K þ K þ γγ
K þ K þ μþ γγ
Total

6.1
5.6
4.6
2.7
1.1
1.1
0.6
0.2
21.9

0.6
6.1
26.1
0.0
0.4
0.3
0.3
0.1
33.9

0 (53%)
5 (42%)
22 (25%)0 (98%)
0 (67%)
0 (73%)
0 (75%)
0 (93%)
27 (13%)

0
0
0
0
0
0
0
0
0

the BDT all corresponded to the K þ K þ → μþ νμ μþ νμ final
state, shown in Table II. The purities of the ring classifications for the final signal sample are 93%, 82%, and 67%
for the K þ , μþ , and γ candidates, respectively. In about

ν→×The most powerfully discriminating BDT input variables
are the distance between the reconstructed vertices of
the kaon-decay product candidates (e.g., two μþ candidate
vertices produced in the same event), and the reconstructed
momentum of the K þ candidates, which assumes thecandidate particles have a mass of 493.7 MeV=c2 . In thecase of the former, the vertex separation distance is large
for the signal events, in which the kaon-decay points are
spatially separated, and short for the background events, inwhich all particles originate from a single neutrino interaction
vertex. In the case of the latter, the distribution of the K þcandidate momenta for the signal should be strongly peakedaround 800 MeV=c. After precuts and selection on event
category, remaining atmospheric neutrino background
events have a broader distribution of reconstructed kaoncandidate momentum. The BDT input distributions for thesevariables are shown in Fig. 3 for the Monte Carlo and theSK-I data.
The ROOT-based TMVA [18] package is used to executethe boosted decision tree. The adaptive boosting method
is used with 500 trees, and the Gini index is used for thenode separation criteria. The cost complexity method isused to prune the BDT after training.
The placement of the final cut on the BDT output isdeterminedby the ﬃpoint which maximizes the significancepﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ(Sig:= Sig: þ Bkg.) for identifying one simulated signal
event among the number of simulated background events
predicted to pass precuts and selection on event category.
The background was modeled using the Super-Kamiokande
atmospheric neutrino Monte Carlo calculation normalized
to the SK-I livetime. By this criteria, the final cut point
is determined to be at 0.12, yielding a signal efficiency of
12.6%  3.2% and an expected background of 0.28  0.19
events.
The event categories with the highest detection efficiencies in the final signal Monte Carlo sample which passed

0.07
0.08
0.08
0.00
0.02
0.03
0.00
0.00
0.28

ν
→

×

5.0
1.8
1.0
2.5
0.8
1.0
0.3
0.2
12.6

SK-I Data
eventsPrecuts (PPoisson )Final BDT Cut

FIG. 3. Two highly discriminating variables used as inputs for
the BDT. Top: Reconstructed vertex separation of kaon-decay
product candidates (e.g., two μþ candidates). Plots are generated
after precuts. Bottom: Reconstructed momentum of K þ candidates, which assumes the candidate particles have a mass of
493.7 MeV=c2 . Plots are generated after precuts and selection on
event category. The number of entries per event in a histogram
depend on the BDT event category. The integral of the pp →K þ K þ Monte Carlo is normalized to the atmospheric neutrinoMonte Carlo.

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two-thirds of the final signal sample every ring in the event
is correctly classified.
The background Monte Carlo sample remaining after the
final BDT cut is dominated by charged-current νμ interactions in which one or more pions are produced. Abouthalf of the K þ candidate rings in the simulated background
events are generated by muons. The remaining half aremostly generated by charged pions and protons. None of
the rings in the final background sample are generated bykaons. About half of the μþ candidates are generated bycharged pions; the other half are generated by muons,
protons, electrons, and gammas in roughly equal amounts.
Two-thirds of the γ candidates are generated by gammas;
the remaining third is generated by electrons. The strengthof the showering or nonshowering likelihood in determining the particle type is clearly demonstrated here.
The primary source of systematic error for the signal
detection efficiency arises from the uncertainty in the Fermi
momentum of the parent nucleons, which is estimated to be24% of the Fermi momentum values used in simulationsof the signal. The Fermi motion in our simulation is based on
the model used by Nakamura et al. [19], and the estimatederror is based on the difference between their experimental
data and the prediction of the model. The Fermi momentum
determines the opening angle between the two kaons, which
has a strong influence on ring classification and signal-tobackground discrimination. The total systematic error on thesignal efficiency is estimated to be 25% [16].
The largest source of systematic error for the backgroundestimation (50%) arose from uncertainties related to thesimulation of pion propagation through water. The second
largest source of systematic uncertainty (30%) is fromtraining bias of the BDT method. This was estimated bycomparing a Monte Carlo set that was independent of the
training set used to construct the BDT. The third largest
source (20%) is related to hadronic effects of pions
propagating through the nucleus in the atmospheric neutrino background. The total systematic error on the background rate is estimated to be 68% [16].
The final boosted decision tree output for the data isoverlaid on the signal and background Monte Carlo in
Fig. 4. A breakdown of the signal efficiency, expectedbackground, and events in the data after the precuts stage(including selection on event category) and after the BDT
stage is shown in Table II. No signal candidate events arefound in the data. A partial lifetime limit for the dinucleon
decay channel pp → K þ K þ is calculated per oxygen
nucleus at a 90% confidence level, giving
τ=BRpp→Kþ Kþ > 1.7 × 1032 years.
This limit is about 2 orders of magnitude larger than thepreviously published limits for dinucleon decay modes
established by Fréjus [10].

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FIG. 4. Final output of the decision tree. Events to the right ofthe cut at 0.12 are considered signal candidates. All data points
are consistent with background; no signal candidates are found in
the data. Final signal efficiency: 12.6%  3.2%. Final expectedbackground contamination: 0.28  0.19 events.

Using our partial lifetime limit for pp → K þ K þ, we
calculate a corresponding upper limit on the magnitude of
the ΔB ¼ 1 R-parity-violating parameter λ112 00 following
the relation given by Ref. [3], where we have assumed theratio between the SUSYand hadronic scales to be 1.1 × 10−3
and a common superpartner mass of 300 GeV= c2 . Our
upper-limit calculation is
0.64years 1=4
jλ112 00 j <¼ 7.8 × 10−9 .
τpp→Kþ Kþ
Our new constraint on λ112 00 is over two orders ofmagnitude more restrictive than ∼10−6 , the estimate basedon rough nuclear lifetime limits of 1030 years [3–6].
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,
Science, Sports and Culture, and the United States
Department of Energy.

*

Deceased.
Present address: SLAC National Accelerator Laboratory,
Menlo Park, CA 94025, USA.
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