Dinucleon and Nucleon Decay to Two-Body Final States with no Hadrons inSuper-Kamiokande

S. Sussman,4, ∗ K. Abe,1, 42 C. Bronner,1 Y. Hayato,1, 42 M. Ikeda,1 K. Iyogi,1 J. Kameda,1, 42 Y. Kato,1

Y. Kishimoto,1, 42 Ll. Marti,1 M. Miura,1, 42 S. Moriyama,1, 42 T. Mochizuki,1 M. Nakahata,1, 42 Y. Nakajima,1, 42

Y. Nakano,1 S. Nakayama,1, 42 T. Okada,1 K. Okamoto,1 A. Orii,1 G. Pronost,1 H. Sekiya,1, 42 M. Shiozawa,1, 42

Y. Sonoda,1 A. Takeda,1, 42 A. Takenaka,1 H. Tanaka,1 T. Yano,1 R. Akutsu,2 T. Kajita,2, 42 Y. Nishimura,2

K. Okumura,2, 42 R. Wang,2 J. Xia,2 L. Labarga,3 P. Fernandez,3 F. d. M. Blaszczyk,4 C. Kachulis,4 E. Kearns,4, 42

J. L. Raaf,4 J. L. Stone,4, 42 S. Berkman,5 J. Bian,6 N. J. Griskevich,6 W. R. Kropp,6 S. Locke,6 S. Mine,6

P. Weatherly,6 M. B. Smy,6, 42 H. W. Sobel,6, 42 V. Takhistov,6, † K. S. Ganezer,7, ‡ J. Hill,7 J. Y. Kim,8

I. T. Lim,8 R. G. Park,8 B. Bodur,9 K. Scholberg,9, 42 C. W. Walter,9, 42 O. Drapier,10 M. Gonin,10 J. Imber,10

Th. A. Mueller,10 P. Paganini,10 T. Ishizuka,11 T. Nakamura,12 J. S. Jang,13 K. Choi,14 J. G. Learned,14

S. Matsuno,14 R. P. Litchfield,15 A. A. Sztuc,15 Y. Uchida,15 M. O. Wascko,15 N. F. Calabria,16 M. G. Catanesi,16

R. A. Intonti,16 E. Radicioni,16 G. De Rosa,17 A. Ali,18 G. Collazuol,18 F. Iacob,18 L. Ludovici,19 S. Cao,20

M. Friend,20 T. Hasegawa,20 T. Ishida,20 T. Kobayashi,20 T. Nakadaira,20 K. Nakamura,20, 42 Y. Oyama,20

K. Sakashita,20 T. Sekiguchi,20 T. Tsukamoto,20 KE. Abe,21 M. Hasegawa,21 Y. Isobe,21 H. Miyabe,21

T. Sugimoto,21 A. T. Suzuki,21 Y. Takeuchi,21, 42 Y. Ashida,22 T. Hayashino,22 S. Hirota,22 M. Jiang,22

T. Kikawa,22 M. Mori,22 KE. Nakamura,22 T. Nakaya,22, 42 R. A. Wendell,22, 42 L. H. V. Anthony,23 N. McCauley,23

A. Pritchard,23 K. M. Tsui,23 Y. Fukuda,24 Y. Itow,25, 26 M. Murrase,25 P. Mijakowski,27 K. Frankiewicz,27

C. K. Jung,28 X. Li,28 J. L. Palomino,28 G. Santucci,28 C. Vilela,28 M. J. Wilking,28 C. Yanagisawa,28, §

D. Fukuda,29 K. Hagiwara,29 H. Ishino,29 S. Ito,29 Y. Koshio,29, 42 M. Sakuda,29 Y. Takahira,29 C. Xu,29

Y. Kuno,30 C. Simpson,31, 42 D. Wark,31, 37 F. Di Lodovico,32 B. Richards,32 S. Molina Sedgwick,32 R. Tacik,33, 46

S. B. Kim,34 M. Thiesse,35 L. Thompson,35 H. Okazawa,36 Y. Choi,38 K. Nishijima,39 M. Koshiba,40

M. Yokoyama,41, 42 A. Goldsack,42, 31 K. Martens,42 M. Murdoch,42 B. Quilain,42 Y. Suzuki,42 M. R. Vagins,42, 6

M. Kuze,43 Y. Okajima,43 T. Yoshida,43 M. Ishitsuka,44 J. F. Martin,45 C. M. Nantais,45 H. A. Tanaka,45

T. Towstego,45 M. Hartz,46 A. Konaka,46 P. de Perio,46 S. Chen,47 L. Wan,47 and A. Minamino48

(The Super-Kamiokande Collaboration)1Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan

2Research Center for Cosmic Neutrinos, Institute for Cosmic RayResearch, University of Tokyo, Kashiwa, Chiba 277-8582, Japan

3Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain4Department of Physics, Boston University, Boston, MA 02215, USA

5Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T1Z4, Canada6Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA

7Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USA8Department of Physics, Chonnam National University, Kwangju 500-757, Korea

9Department of Physics, Duke University, Durham NC 27708, USA10Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, F-91120 Palaiseau, France

11Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan12Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan

13GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea14Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA15Department of Physics, Imperial College London , London, SW7 2AZ, United Kingdom

16Dipartimento Interuniversitario di Fisica, INFN Sezione di Bari and Universita e Politecnico di Bari, I-70125, Bari, Italy17Dipartimento di Fisica, INFN Sezione di Napoli and Universita di Napoli, I-80126, Napoli, Italy

18Dipartimento di Fisica, INFN Sezione di Padova and Universita di Padova, I-35131, Padova, Italy19INFN Sezione di Roma and Universita di Roma “La Sapienza”, I-00185, Roma, Italy

20High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan21Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan

22Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan23Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom

24Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan25Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan

26Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya, Aichi 464-8602, Japan27National Centre For Nuclear Research, 00-681 Warsaw, Poland

28Department of Physics and Astronomy, State University of New York at Stony Brook, NY 11794-3800, USA29Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan

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30Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan31Department of Physics, Oxford University, Oxford, OX1 3PU, United Kingdom

32School of Physics and Astronomy, Queen Mary University of London, London, E1 4NS, United Kingdom33Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, SK, S4SOA2, Canada

34Department of Physics, Seoul National University, Seoul 151-742, Korea35Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, United Kingdom

36Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan37STFC, Rutherford Appleton Laboratory, Harwell Oxford, and

Daresbury Laboratory, Warrington, OX11 0QX, United Kingdom38Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea

39Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan40The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan

41Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan42Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University ofTokyo Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8583, Japan

43Department of Physics,Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan44Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan

45Department of Physics, University of Toronto, ON, M5S 1A7, Canada46TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T2A3, Canada

47Department of Engineering Physics, Tsinghua University, Beijing, 100084, China48Faculty of Engineering, Yokohama National University, Yokohama, 240-8501, Japan

(Dated: December 3, 2018)

Using 0.37 megaton·years of exposure from the Super-Kamiokande detector, we search for 10dinucleon and nucleon decay modes that have a two-body final state with no hadrons. Thesebaryon and lepton number violating modes have the potential to probe theories of unification andbaryogenesis. For five of these modes the searches are novel, and for the other five modes we improvethe limits by more than one order of magnitude. No significant evidence for dinucleon or nucleondecay is observed and we set lower limits on the partial lifetime of oxygen nuclei and on the nucleonpartial lifetime that are above 4 × 1033 years for oxygen via the dinucleon decay modes and up toabout 4× 1034 years for nucleons via the single nucleon decay modes.

One of the biggest unanswered questions about ouruniverse is the origin of the matter/antimatter asymme-try that we observe. Non-conservation of baryon num-ber, B, is one of the three necessary conditions to createa baryon asymmetry where none previously existed [1].Since B is an accidental symmetry in the Standard Model(SM) of particle physics, observation of B violation wouldimply new physics beyond the Standard Model. Manytheoretical extensions of the SM allow violation of Band/or lepton number, L, and predict experimentallyobservable processes (see reviews in [2] and [3]). Thesearches for ten such B-violating processes via nucleon ordinucleon decay in Super-Kamiokande are detailed in thisLetter. Four of the eight dinucleon decay modes studiedhere have ∆(B − L) = −2, with two nucleons decaying toa lepton and an antilepton. A scenario in which baryonasymmetry would remain after ∆(B − L) = −2 decays inthe early universe is discussed in Ref. [4]. Three of theeight dinucleon decay modes, with two nucleons decayingto two antileptons, violate each of B and L by two units,but conserve the quantity (B − L). These modes are in-teresting in the context of models such as [5–8], and areshown in Ref. [9] to be competitive with LHC measure-ments in probing the mass scale of new physics. The finaldinucleon decay mode and the two single-nucleon decaymodes studied here are radiative; these decay modes canarise in various models of grand unification, but are often

predicted to have suppressed decay rates [10, 11]. The ra-diative modes have similar experimental signatures as theother modes studied; they also have similar signatures tothe previously searched p→ e+π0 and p→ µ+π0 modes,but have the benefit of higher detection efficiency due tothe lack of hadronic interactions.

The ten decay modes we search for in Super-Kamiokande data are characterized by two back-to-backCherenkov rings and no hadrons. The dinucleon decaymodes in these three categories are: (i) pp → e+e+,nn → e+e−, nn → γγ, (ii) pp → e+µ+, nn → e+µ−,nn → e−µ+, and (iii) pp → µ+µ+, nn → µ+µ−. Weclassify the modes as follows: (i) both rings are shower-ing (NN → ee), (ii) one ring is showering and the otheris non-showering (NN → eµ), and (iii) both rings arenon-showering (NN → µµ). Figure 1 illustrates howdistinct these final states are seen in Super-Kamiokande,due to their well-separated, bright rings. The nucleondecay modes with identical experimental signatures, butlower invariant mass, are (i) p→ e+γ and (ii) p→ µ+γ.We do not include the search for dinucleon decays intotau leptons because there would be missing momentumand some subsequent tau decay modes are hadronic.

The Super-Kamiokande (SK) water Cherenkov detec-tor, with a fiducial volume of 22.5 kilotons, contains1.2 × 1034 nucleons. SK lies one kilometer under Mt.Ikenoyama in Japan’s Kamioka Observatory. The detec-

3

FIG. 1. (color online) An SK event display of a typical pp→e+µ+ event shown in θ-φ view. The non-showering ring (fromthe µ+) is on the left and the showering ring (from the e+)is on the right. The energy of each ring is approximately900 MeV.

tor is cylindrical with a diameter of 39.3 meters and aheight of 41.4 meters, optically separated into an innerand an outer region. Eight-inch photomultiplier tubes(PMTs) line the outer detector facing outwards and serveprimarily as a veto for cosmic ray muons, and 20-inchPMTs face inwards to measure Cherenkov light in theinner detector [12].

SK has collected data for four different detector peri-ods, accumulating 91.5, 49.1, 31.8 and 199.3 kiloton·yearsof exposure during SK-I, SK-II, SK-III, and SK-IV, re-spectively. During SK-I, the inner detector photocathodecoverage was 40%, but the SK-II period had a reducedphoto-coverage of 19% after recovery from an accident.For SK-II, the remaining PMTs were evenly distributedto maintain isotropic detector uniformity. SK-II effi-ciency is only ∼2% lower than the other detector periodsfor these dinucleon and nucleon decay searches becausethe rings still have many hits. In the subsequent peri-ods, SK-III and SK-IV, we restored the original photo-coverage of 40%. The SK-IV period benefited from anelectronics upgrade described in Ref. [13]: a “deadtimefree” data acquisition system enables SK-IV to detect the2.2 MeV gamma ray emission from neutron capture onhydrogen, which occurs about 200 µsec after the primaryevent.

For each dinucleon or nucleon decay mode studied, wesimulated 100,000 signal Monte Carlo (MC) events withvertices uniformly distributed throughout the detectorand final state particle momenta uniformly distributed inphase space. Fermi motion, nuclear binding energy, andcorrelated decay are simulated in the dinucleon and nu-cleon decay signal MC [14, 15]. Unlike the atmospheric νMC, where the Fermi momentum distribution of the nu-cleons follows the Fermi gas model, the signal MC Fermimomentum distribution follows a spectral function fit toelectron-12C scattering data [16]. We address this dif-ference between signal and atmospheric ν event samplesby computing the systematic uncertainty in signal effi-ciency based on our choice of nuclear model. Correlateddecay is a hypothesized effect where the total mass and

momentum distributions are smeared out in a “tail” dueto the correlated motion of a nearby nucleon. For bothnucleons and pairs of nucleons, we assume that 10% ofsuch decays are affected by the correlated motion of anadditional nucleon [17]. Lepton rescattering within thenucleus is negligible.

The atmospheric ν MC sample corresponds to an ex-posure of 500 years for each of the four SK periods, 2000years in total. Events in this sample are weighted assum-ing two-flavor mixing as is done in recent dinucleon andnucleon analyses [14, 15, 18]. Details of the cross-sectionsand flux modeling used in this sample are discussed inrecent SK nucleon decay analyses [14, 18]. Event ratesobtained from this sample are normalized to the relevantSK detector livetime.

Details of the neutron simulation and neutron taggingalgorithm used for both the signal and atmospheric νMC samples can be found in Ref. [18]. Neutron taggingcan only be done for the SK-IV period; it reduces theexpected number of background events by about 50% forour searches, and impacts signal efficiency by only a fewpercent.

Although the selection criteria for all ten modes aresimilar, the two single-nucleon decay modes have morebackground due to their lower total mass. We adapt ourstrategy, as is done in Ref. [18], to perform a two-boxanalysis which allows us to study free and bound protonsseparately.

The following selection criteria are applied to signalMC, atmospheric ν MC, and data:

(A1) Events must be fully contained in the inner detectorwith the event vertex within the fiducial volume(two meters inward from the detector walls),

(A2) There must be two Cherenkov rings,

(A3) Both rings must be showering for the pp → e+e+,nn → e+e−, nn → γγ and p → e+γ modes; onering must be showering and one ring must be non-showering for the pp → e+µ+, nn → e+µ−, nn →e−µ+ and p → µ+γ modes; both rings must benon-showering for the pp → µ+µ+, nn → µ+µ−

modes (see note in [19]),

(A4) There must be zero Michel electrons for the pp →e+e+, nn → e+e−, nn → γγ and p → e+γ modes;there must be less than or equal to one Michel elec-tron for the pp→ e+µ+, nn→ e+µ−, nn→ e−µ+

and p → µ+γ modes; there is no Michel electroncut for the pp → µ+µ+, nn → µ+µ− modes (seenote in [20]),

(A5) The reconstructed total mass, Mtot, should be1600 ≤ Mtot ≤ 2050 MeV/c2 for the dinucleondecay modes; the reconstructed total mass shouldbe 800 ≤ Mtot ≤ 1050 MeV/c2 for the nucleon de-cay modes,

4

FIG. 2. (color online) Invariant mass vs. total momentum for several dinucleon and nucleon decay modes after cut (A4). Theleft panels show signal MC, where green corresponds to SK-IV nucleon decay MC and blue corresponds to SK-IV dinucleondecay MC for the labeled modes. The signal MC distributions for all SK periods look similar; only 10,000 signal MC eventsare plotted for each mode in order to more clearly show the shape of the distribution. The middle panels show atmosphericν MC corresponding to 2000 years of SK exposure, and the right panels show SK-I through SK-IV data. The marker size isenlarged for data in the signal boxes.

(A6) The reconstructed total momentum, Ptot, shouldbe 0 ≤ Ptot ≤ 550 MeV/c for the dinucleon decaymodes; for the nucleon decay modes, it should be100 ≤ Ptot ≤ 250 MeV/c for the event to be in the“High Ptot” signal box and 0 ≤ Ptot ≤ 100 MeV/cfor the event to be in the “Low Ptot” signal box,

(A7) [SK-IV nucleon decay searches only] There must bezero tagged neutrons.

Figure 2 shows the distributions of signal MC events(left panels), atmospheric neutrino background (middle),and data (right) as a function of Ptot versus Mtot after cut(A4). The signal selection efficiencies and backgroundrates are summarized in Table I for each of the decaymodes and each of the SK running periods. The sig-nal efficiency for the two nucleon decay modes is ∼ 50%for the “High Ptot”signal box and ∼ 28% for the “LowPtot” signal box for each SK period. It is worth notingthat these signal efficiencies are significantly higher thanthose of the similar event signature in the p → `+π0

decay mode searches. These differences are due to thefact that the π0 undergoes nuclear effects before exitingthe nucleus while the γ does not. For the eight dinu-cleon decay modes, the signal efficiency is ∼80% for each

SK period. Due to the high total mass required in (A5),the modes are virtually background-free (as shown in themiddle panels of Fig. 2).

Background estimates are done in one of the two fol-lowing ways, depending on the number of backgroundevents that fall in the signal box: (1) for signal regionsthat contain more than 10 events from 2000 years of at-mospheric ν MC, the background is estimated by thetraditional method of counting the number of events thatfall inside the signal region; or, (2) for signal regions thatare nearly background-free, an extrapolation method isused to estimate the expected background using the dis-tribution of events nearby (but outside) the signal region.The background extrapolation is done by measuring thedistance from the center of the signal box to the loca-tion of each nearby event in mass-momentum parameterspace, and then fitting an exponential to the distribu-tion of distances. Integration of the exponential functionup to the radius which approximates the signal box (250units in mass-momentum parameter space) gives the es-timated background inside the signal region. A similarestimation method was done in Ref. [21]. Backgroundrate for p → e+γ “Low Ptot” is estimated by extrapo-

5

FIG. 3. (color online) Total mass (Mtot) and total momentum(Ptot) projections for p → µ+γ after cut (A4). The red his-togram shows atmospheric ν MC corresponding to 2000 yearsof SK exposure normalized to SK-I through SK-IV data. Theselection criteria are indicated by the vertical blue lines.

lation to be 0.089 events/Mton·yr; we take double thisvalue (0.18 ± 0.18 events/Mton·yr) as a conservative es-timate of the background rate for this decay mode. Simi-larly, we extrapolate for all of the dinucleon decay modes,finding background rates of 0.008 (NN → ee), 0.033(NN → eµ), and 0.006 (NN → µµ) events/Mton·yr.We conservatively take the largest of these and doubleit as our estimate of expected background for all of thedinucleon decay modes: 0.07± 0.07 events/Mton·yr.

We find zero candidate events for the eight dinucleondecay modes. For the nucleon decay mode p → e+γ,we also find zero candidate events. We observe twocandidate events during the SK-IV period for the p →µ+γ decay mode in the “High Ptot” signal box when0.23± 0.14stat± 0.07sys events were expected. The Pois-son probability to see two or more events in the SK-IV livetime given an expected rate of 0.23 events is2.3%. One of the two candidates was previously found inRef. [18]. The other candidate is more ambiguous sinceit lacks a Michel electron. This may be an indicationthat the event is due to a νen → e−p charged-currentquasielastic interaction, where the non-showering ring isdue to a proton rather than a muon. Requiring a Michelelectron would have eliminated this event, however sucha requirement was not applied for the p → µ+γ mode

in order to be consistent with cut (A4) for the dinucleondecay mode. Fig. 3 shows the agreement of data andatmospheric ν MC for p→ µ+γ.

Table II summarizes the systematic uncertainties in thesignal efficiency and in the background rate for each ofthe nucleon and dinucleon decay modes. The dominantcontributions to uncertainty in the signal efficiency arisefrom uncertainties in the areas of reconstruction, corre-lated decay, and nuclear model. To assess the impact ofdifferences in the reconstruction of data and MC, for ev-ery variable used in the selection, we compute the percentshift of the atmospheric ν MC distribution necessary tominimize its chi-square against the corresponding datadistribution. The cut value in the event selection is thenshifted by that percentage and applied to the signal MCto recalculate the efficiency. The total systematic uncer-tainty due to reconstruction is calculated by summingin quadrature the independent percent changes in signalefficiency due to each percent-shifted cut. For nucleondecay in the SK-IV period only, we also add in quadra-ture with the other reconstruction uncertainties an ad-ditional 10% uncertainty due to neutron tagging, as wasdone in Ref. [18]. This is the reason that the reconstruc-tion uncertainties for nucleon decay are ∼6% larger thanthe corresponding uncertainties for dinucleon decay. Toestimate the uncertainty in the signal efficiency arisingfrom uncertainties in correlated decay, we assume 100%uncertainty on the correlated decay effect, reweight thecorrelated decay events accordingly, and recalculate thesignal efficiency, taking the overall change in signal effi-ciency as the systematic uncertainty. The nuclear modeluncertainty is estimated as the percent change in signalefficiency when the Fermi gas model is used to computethe true momentum of the protons within the signal MCevents instead of the spectral function fit to data de-scribed earlier.

The systematic uncertainty on the rate of backgroundevents is conservatively taken to be 100% for decay modeswhere the background events are scarce (all dinucleon de-cay modes, and the p→ e+γ “Low Ptot” nucleon decay).For the other nucleon decay signal regions, we use anevent-by-event database with uncertainty weights from73 sources of background systematic uncertainty includ-ing uncertainties in flux, cross section and energy calibra-tion, as described in the 2018 SK oscillation analysis [22].

Lifetime limits are computed using a Bayesian method,assuming that the SK-I through SK-IV datasets have cor-related systematic uncertainties [23]. For the nucleondecay modes, the systematic uncertainties of the “HighPtot” and “Low Ptot” search boxes are treated as inde-pendent datasets with fully correlated systematic uncer-tainties. The conditional probability distribution for thedecay rate is given by Eq. 1, where Γ is the decay rate andfor dataset i, λi is the exposure (given in proton-years fornucleon decay and in oxygen-years for dinucleon decay),εi is the efficiency, bi is the number of background events,

6

Decay mode Efficiency (%) Background (Events/livetime)SK-I SK-II SK-III SK-IV SK-I SK-II SK-III SK-IV

p→ e+γHigh Ptot 51.0± 0.2 49.5± 0.2 50.8± 0.2 50.6± 0.2 0.01± 0.01 0.02± 0.02 < 0.01 0.07± 0.07Low Ptot 27.6± 0.1 26.1± 0.1 27.6± 0.1 27.5± 0.1 0.02± 0.02 0.01± 0.01 0.01± 0.01 0.04± 0.04

p→ µ+γHigh Ptot 50.2± 0.2 49.7± 0.2 51.0± 0.2 48.1± 0.2 0.22± 0.14 0.14± 0.11 0.07± 0.07 0.23± 0.14Low Ptot 29.1± 0.1 28.3± 0.1 29.0± 0.1 29.4± 0.1 0.02± 0.02 0.01± 0.01 < 0.01 0.02± 0.02

NN → ee 80.9± 0.1 77.2± 0.1 79.5± 0.1 78.6± 0.1 0.01± 0.01 < 0.01 < 0.01 0.01± 0.01

NN → eµ 84.1± 0.1 83.7± 0.1 83.4± 0.1 81.7± 0.1 0.01± 0.01 < 0.01 < 0.01 0.01± 0.01

NN → µµ 86.3± 0.1 85.9± 0.1 86.0± 0.1 82.8± 0.1 0.01± 0.01 < 0.01 < 0.01 0.01± 0.01

TABLE I. Summary of the number of expected background events (with statistical uncertainty only) for the livetimes of SK-I(91.5 kiloton·years), SK-II (49.1 kiloton·years), SK-III (31.8 kiloton·years), and SK-IV (199.3 kiloton·years). The dinucleondecay efficiency/background rate for a group of modes is the average of the efficiencies/background rates for the individualmodes (the efficiencies are similar in the same group of modes.)

Decay mode Signal efficiency uncertainty (%) Background rate uncertainty(%)

ReconstructionCorrelated Nuclear

Decay Model

p→ e+γHigh Ptot 10.5 3.5 2.4 40.4Low Ptot 8.1 2.9 5.3 100

p→ µ+γHigh Ptot 10.3 3.5 3.7 31.0Low Ptot 8.0 3.1 5.8 44.0

NN → ee 5.7 8.0 — 100

NN → eµ 2.6 8.4 — 100

NN → µµ 4.4 8.7 — 100

TABLE II. Summary of the systematic uncertainties (percentage contribution) on signal efficiency and background rate forthe nucleon and dinucleon decay searches. The uncertainties from SK-I to SK-IV are averaged by the live time.

P (Γ|ni)=

∫ λ∫ ε∫ b e−(Γλi(λ)εi(ε)+bi(b))(Γλi(λ)εi(ε) + bi(b))ni

ni!P (Γ)P (λi(λ)|λi,0, σλi,0)P (εi(ε)|εi,0, σεi,0)P (bi(b)|bi,0, σbi,0)dλ dε db

(1)

and ni is the number of candidate events. Since the sys-tematic errors are correlated for all datasets, integratingthe prior probability distribution up to b in some datasetimplies that we integrate the prior distribution in dataseti up to bi(b).

We assume a Gaussian prior distributionP (λi(λ)|λi,0, σλi,0

) for λi with a mean value of λi,0and σλi,0 given by the 1% percent systematic uncer-tainty in exposure. We also assume Gaussian priorsP (εi(ε)|εi,0, σεi,0) and P (bi(b)|bi,0, σbi,0) for εi and bi withstandard deviations set to the total percent systematicuncertainties in efficiency and background, respectively.To require a positive lifetime, P (Γ) is 1 for Γ ≥ 0 andotherwise 0. We calculate the upper bound of the decayrate Γlimit as in Eq. 2, with a 90% confidence level (CL):

Therefore we obtain the lower bound on the partiallifetime limit of a decay mode: τ/B = 1/Γlimit. Table IIIsummarizes the partial lifetime limits obtained for theten decay modes studied, and these are also shown in

CL =

∫ Γlimit

Γ=0

∏Ni=1 P (Γ|ni)dΓ∫∞

Γ=0

∏Ni=1 P (Γ|ni)dΓ

. (2)

relation to previous measurements in Fig. 4.

We searched for the 10 dinucleon and nucleon decaymodes characterized by a two-body final state with nohadrons in the Super-Kamiokande data with an accumu-lated exposure of 0.37 megaton·years. No significant ev-idence for dinucleon or nucleon decay was observed, andwe set lower limits on the partial lifetimes that are above4× 1033 years for the dinucleon decay modes, 4.1× 1034

years for p → e+γ, and 2.1 × 1034 years for p → µ+γ.For five of the modes, the limits are novel, and the limitsfor all 10 modes are the most stringent by over one orderof magnitude.

We gratefully acknowledge the cooperation of the

7

Decay modeLifetime limit

per oxygen nucleus per nucleon(×1033 years) (×1034 years)

pp→ e+e+ 4.2 —nn→ e+e− 4.2 —nn→ γγ 4.1 —pp→ e+µ+ 4.4 —nn→ e+µ− 4.4 —nn→ e−µ+ 4.4 —pp→ µ+µ+ 4.4 —nn→ µ+µ− 4.4 —p→ e+γ — 4.1p→ µ+γ — 2.1

TABLE III. Summary of the partial lifetime limits for eachof the ten dinucleon and nucleon decay modes, including sys-tematic uncertainties, at 90% CL.

FIG. 4. (color online) The partial lifetime limits set by Super-Kamiokande for these ten modes, compared with previouslimits set by the Frejus and IMB detectors [24, 25]. Notethat Frejus set dinucleon decay lifetime limits per iron nucleusrather than per oxygen nucleus.

Kamioka Mining and Smelting Company. The Super-Kamiokande experiment has been built and operatedfrom funding by the Japanese Ministry of Education,Culture, Sports, Science and Technology, the U.S. De-partment of Energy, and the U.S. National Science Foun-dation.

∗ Corresponding author: sarafs@bu.edu

† also at Department of Physics and Astronomy, UCLA,CA 90095-1547, USA.

‡ Deceased.§ also at BMCC/CUNY, Science Department, New York,

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