Search for Nucleon and Dinucleon Decays with an Invisible Particle and a Charged Lepton in the Final State at the Super-Kamiokande Experiment

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 Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA    K. Abe Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    Y. Haga Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan    Y. Hayato Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    M. Ikeda Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan    K. Iyogi Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan    J. Kameda    Y. Kishimoto    M. Miura    S. Moriyama    M. Nakahata Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    T. Nakajima    Y. Nakano Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan    S. Nakayama Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    A. Orii Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan    H. Sekiya    M. Shiozawa    A. Takeda Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    H. Tanaka Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan    T. Tomura    R. A. Wendell Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    T. Irvine Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    T. Kajita Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    I. Kametani Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    K. Kaneyuki Deceased. Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    Y. Nishimura    E. Richard Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    K. Okumura Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    L. Labarga    P. Fernandez Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain    J. Gustafson Department of Physics, Boston University, Boston, MA 02215, USA    C. Kachulis Department of Physics, Boston University, Boston, MA 02215, USA    E. Kearns Department of Physics, Boston University, Boston, MA 02215, USA Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    J. L. Raaf Department of Physics, Boston University, Boston, MA 02215, USA    J. L. Stone Department of Physics, Boston University, Boston, MA 02215, USA Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    L. R. Sulak Department of Physics, Boston University, Boston, MA 02215, USA    S. Berkman    C. M. Nantais    H. A. Tanaka    S. Tobayama Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T1Z4, Canada    M.  Goldhaber Deceased. Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA    G. Carminati    W. R. Kropp    S. Mine    P. Weatherly    A. Renshaw Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA    M. B. Smy    H. W. Sobel Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    K. S. Ganezer    B. L. Hartfiel    J. Hill Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USA    N. Hong    J. Y. Kim    I. T. Lim Department of Physics, Chonnam National University, Kwangju 500-757, Korea    A. Himmel    Z. Li Department of Physics, Duke University, Durham NC 27708, USA    K. Scholberg    C. W. Walter Department of Physics, Duke University, Durham NC 27708, USA Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    T. Wongjirad Department of Physics, Duke University, Durham NC 27708, USA    T. Ishizuka Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan    S. Tasaka Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan    J. S. Jang GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea    J. G. Learned    S. Matsuno    S. N. Smith Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA    M. Friend    T. Hasegawa    T. Ishida    T. Ishii    T. Kobayashi    T. Nakadaira High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan    K. Nakamura High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    Y. Oyama    K. Sakashita    T. Sekiguchi    T. Tsukamoto High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan    A. T. Suzuki Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan    Y. Takeuchi Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    T. Yano Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan    S. Hirota    K. Huang    K. Ieki    T. Kikawa    A. Minamino Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan    T. Nakaya Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    K. Suzuki    S. Takahashi Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan    Y. Fukuda Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan    K. Choi    Y. Itow    T. Suzuki Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan    P. Mijakowski National Centre For Nuclear Research, 00-681 Warsaw, Poland    K. Frankiewicz National Centre For Nuclear Research, 00-681 Warsaw, Poland    J. Hignight    J. Imber    C. K. Jung    X. Li    J. L. Palomino    M. J. Wilking Department of Physics and Astronomy, State University of New York at Stony Brook, NY 11794-3800, USA    C. Yanagisawa Department of Physics and Astronomy, State University of New York at Stony Brook, NY 11794-3800, USA    H. Ishino    T. Kayano    A. Kibayashi    Y. Koshio    T. Mori    M. Sakuda Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan    Y. Kuno Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan    R. Tacik Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, SK, S4SOA2, Canada TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T2A3, Canada    S. B. Kim Department of Physics, Seoul National University, Seoul 151-742, Korea    H. Okazawa Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan    Y. Choi Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea    K. Nishijima Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan    M. Koshiba    Y. Suda The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan    Y. Totsuka Deceased. The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan    M. Yokoyama The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    C. Bronner    M. Hartz    K. Martens    Ll. Marti    Y. Suzuki Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan    M. R. Vagins Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA    J. F. Martin    P. de Perio Department of Physics, University of Toronto, 60 St., Toronto, Ontario, M5S1A7, Canada    A. Konaka TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T2A3, Canada    S. Chen    Y. Zhang Department of Engineering Physics, Tsinghua University, Beijing, 100084, China    R. J. Wilkes Department of Physics, University of Washington, Seattle, WA 98195-1560, USA
July 13, 2019
Abstract

Search results for nucleon decays , , (where is an invisible, massless particle) as well as dinucleon decays , and in the Super-Kamiokande experiment are presented. Using single-ring data from an exposure of 273.4 kton years, a search for these decays yields a result consistent with no signal. Accordingly, lower limits on the partial lifetimes of years, years, years, years, years and years at a confidence level are obtained. Some of these searches are novel.

pacs:
12.10.Dm,13.30.-a,11.30.Fs,14.20.Dh,29.40.Ka
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The Super-Kamiokande Collaboration

Many signs indicate that the Standard Model (SM) 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 Grand Unified Theory (GUT) Pati and Salam (1973a, b); Georgi and Glashow (1974); Fritzsch and Minkowski (1975), as an underlying fundamental theory. While the unification scale ( GeV) is unreachable by accelerators, rare processes predicted by these theories, such as proton decay, can be probed by large underground detectors. Being a signature prediction of GUTs, observation of an unstable proton would constitute robust evidence for physics beyond the SM, while non-observation will stringently constrain theoretical models.

The simplest unification scenarios based on minimal and supersymmetric (SUSY) have been decisively ruled out by bounds on McGrew et al. (1999); Hirata et al. (1989); Shiozawa et al. (1998) and Kobayashi et al. (2005). Many alternative scenarios as well as potential signatures are possible (see Nath and Fileviez Perez (2007) for review).

In this Letter, we analyze a broad class of nucleon and dinucleon decay channels with a showering or non-showering single Cherenkov ring signature within the Super-Kamiokande (SK) experiment, using the technique of spectral fit Fogli et al. (2002); Takhistov et al. (2014). First, we have considered two general two-body decays and , where is a single unknown invisible particle which is assumed to be massless. These searches are distinct from the model-dependent inclusive analyses of Learned et al. (1979); Cherry et al. (1981) listed in the PDG Olive et al. (2014). Similarly, we also consider . Though this radiative process is suppressed, it has a clean signature and has been considered in the context of Silverman and Soni (1981), with some models Nath and Fileviez Perez (2007) predicting a lifetime of years.

While single nucleon processes have been in general well studied, dinucleon channels also pose great interest. These higher-dimensional processes can become significant in models which suppress proton decay and could be connected to baryogenesis Arnold et al. (2013), accounting for the observed baryon asymmetry of the universe Canetti et al. (2012). Such a connection may already be hinted at from the requirement of baryon number violation as a necessary condition for explaining the asymmetry Sakharov (1967). The disappearance reactions, with invisible final state particles, have been studied and no signal excess was observed Berger et al. (1991); Araki et al. (2006); Litos et al. (2014). The channels , and violate baryon number by two units and violate lepton number by either two or zero units. They can become significant in models with an extended Higgs sector Mohapatra and Senjanovic (1982); Arnold et al. (2013), which could be considered in the context of GUTs Arnellos and Marciano (1982). While the cannot occur in single nucleon decay, in dinucleon decay the channel is allowed Bryman (2014). The process has not been experimentally studied before and in addition to the electron and muon channel searches we present the first search in the channel.

In this work, SK data is analyzed from an exposure of the 22.5 kton fiducial mass for 273.4 ktonyears, covering four running periods (SK-I through SK-IV). Details of the detector design and performance in each SK period, can be found in Fukuda et al. (2003); Abe et al. (2014a). This analysis considers only events in which all observed Cherenkov light was fully contained (FC) within the inner detector.

Since final-state neutrinos or (by definition) are not observed, the only signature of , , , and is a single charged or lepton, or single . Thus, the invariant mass of the initial state cannot be reconstructed and the signal will be superimposed on a substantial atmospheric neutrino background in the -like and -like momentum spectra. For the decay, only the and 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 for , and , which were performed with a smaller detector using a counting method, resulted in the lifetime limits of years McGrew et al. (1999), years Berger et al. (1991) and years Berger et al. (1991), 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 Abe et al. (2013); Takhistov et al. (2014) and dark matter analyses Choi et al. (2015).

The nucleon decay signal events are obtained from Monte Carlo (MC) simulations, in which all the nucleons of the water HO molecule are assumed to decay with equal probability. The final state particles are generated with energy and momentum uniformly distributed in phase space. The effects of Fermi motion, nuclear binding energy as well as nucleon - nucleon correlated decays Yamazaki and Akaishi (2000) are taken into account for both nucleon Nishino et al. (2012); Regis et al. (2012); Abe et al. (2014b) and dinucleon searches Gustafson et al. (2015). The signal Fermi momentum distributions are simulated using a spectral function fit to electron-C scattering data Nakamura et al. (1976). The SK detector simulation Abe et al. (2014a) is based on the GEANT-3 Brun et al. (1994) package, with the TAUOLA Jadach et al. (1993) package employed for decaying the leptons. For the mode we generated three MC samples, with the decaying to , and all decay channels. The latter allows us to study sample contamination in the two selected leptonic channels from the hadronic channels and thus identify sample purity after the event selection. We have confirmed that the resulting MC charged lepton spectra from and decays agree with the theoretical formula Chen and Takhistov (2014). For and modes, the invisible particle cannot be a fermion by spin conservation, but in our spin-insensitive MC it was simulated as a neutrino. In total, around 4,200 signal events were generated within the fiducial volume (FV) for each SK period for single nucleon decays and around 8,400 for dinucleon decays.

Atmospheric neutrino background interactions were generated using the flux of Honda et. al. Honda et al. (2007) and the NEUT simulation package Hayato (2002), which uses a relativistic Fermi gas model. Background MC corresponding to a 500-year exposure of the detector was simulated for each detector phase. We used the same atmospheric neutrino MC as the standard SK oscillation analysis Abe et al. (2015).

The event selection applied to the fully-contained data is the following: (A) a single Cherenkov ring is present, (B) the ring is showering (electron-like) for , , and and non-showering (muon-like) for , and , (C) there are zero decay electrons for modes with an -like ring and one decay electron for those with a -like ring, (D) the reconstructed momentum lies in the range 100 MeV/ 1000 MeV/ for , and in the range 200 MeV/ 1000 MeV/ for , with the range extended to 100-1500 MeV/ for dinucleon decays with an -like ring and 200-1500 MeV/ for those with a -like ring. In total, approximately 37,000 FC events were obtained in the SK-I to SK-IV data-taking periods. After the criteria (A)-(D) have been applied, the final data samples for single nucleon decay searches with an -like ring contain 8,500 events and 6,000 events for the case of -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 9,500 events for the -like channels and 6,500 events for the -like ones. See Ref. Shiozawa (1999) for details regarding reconstruction.

[htb] Decay mode Systematic error 1- uncertainty (%) Fit pull () Fit pull () Final state interactions (FSI) 10  0.10 -0.60  B Flux normalization ( GeV)  25 a -0.23 -0.08  B Flux normalization ( GeV)  15 b -1.44 -0.50  B in interactions 10  0.69  0.23  B Single meson cross-section in interactions 10 -0.55 -0.14  B Energy calibration of SK-I, -II, -III, -IV 1.1, 1.7, 2.7, 2.3 0.58, -0.91, 0.48, 0.38 -0.54, 0.07, -0.14, 0.26  SB Fermi model comparison  10 c -0.08  0.70  S Nucleon-nucleon correlated decay 100  0.00  0.06  S

  • Uncertainty linearly decreases with from 25% (0.1 GeV) to 7% (1 GeV).

  • Uncertainty is 7% up to 10 GeV, linearly increases with from 7% (10 GeV) to 12% (100 GeV) and then 20% (1 TeV).

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

Table 1: Systematic errors of spectrum fits, with uncertainties and resulting fit pull terms. Errors specific to signal and background are denoted by S and B, while those that are common to both by SB.

The signal detection efficiency is defined as the fraction of events passing selection criteria compared to the total number of events generated within the true fiducial volume. The average detection efficiency for -like channels is for all SK data-taking periods. For the -like channels, the average detection efficiency is for SK-I to SK-III and for SK-IV. The increase in efficiency observed in SK-IV for channels with a -like ring, comes from a 20% improvement in the detection of muon decay electrons after an upgrade of the detector electronics Abe et al. (2014a).

For the -like momentum spectrum up to 1500 MeV/c, the dominant background contribution, composing of the events, comes from the charged-current (CC) quasi-elastic (QE) neutrino channel. The CC single-pion production constitutes of the background, while the CC coherent-pion, CC multi-pion and neutral-current (NC) single-pion productions contribute around , and , respectively. About and of events come from NC single-pion and coherent-pion production. For the -like momentum spectrum up to 1500 MeV/c, the dominant contribution of around comes from CCQE. Similarly, CC single-pion, CC coherent-pion and CC multi-pion as well as NC single-pion production contribute around , , and , respectively.

After event selection, a spectral fit is performed on the reconstructed charged lepton momentum distribution of the events. The minimization fit is based on the Poisson distribution, with the systematic uncertainties accounted for by quadratic penalties (“pull terms”) Fogli et al. (2002). The function used in the analysis is

(1)

where labels the analysis bin. The terms , , , are the numbers of observed data, signal MC, background MC

Decay mode Best fit Best fit No signal Data Data Sensitivity
( yr.) ( yr.)
(1.050, 0.002) 70.9/70 0.19 0.013 108 79 79
(1.045, 0.004) 70.5/70 0.43 0.015 125 58 55
(0.960, 0.016) 63.2/62 3.43 0.032 187 77 41
(0.955, 0.000) 122.5/110 0.00 0.004 33 10 26
(0.910, 0.000) 97.0/102 0.00 0.005 36 11 20
(0.910, 0.000) 224.6/214 0.00 0.006 96 1 3
Table 2: Best fit parameter values, best fit d.o.f., no signal , 90% C.L. value of parameter, allowed number of nucleon decay events in the full 273.4 kton years exposure and a partial lifetime limit for each decay mode at 90% C.L. The sensitivity and lifetime limit for dinucleon decay modes are per O nucleus.

and the total (signal and background) MC events in each bin . The index labels the systematic errors, while and correspond to the fit error parameter and the fractional change in the bin due to 1-sigma error uncertainty , respectively. The fit is performed for two parameters and , which denote the background and signal normalizations, respectively. After the event selection, the signal MC distribution is normalized to the background by the integral, which in turn is normalized to the SK livetime. This allows us to identify the fit point with the no-signal hypothesis. Similarly, signifies that the data is described by signal only, with the signal amount equal to background MC normalized (pre-fit) to livetime. The minimization is carried out over each and in the grid according to . The resulting global minimum is defined as the best fit. Further details on the fit and specifics of systematic error treatment can be found in Wendell et al. (2010); Takhistov et al. (2014); Choi et al. (2015). For the mode, after the appropriate event selection is applied to both MC samples of and , the samples are combined for the fit, allowing us to obtain a single value for the permitted number of nucleon decays at 90% CL.

The systematic errors can be divided into signal-specific (S), background-specific (B) as well as detector and reconstruction 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 select the dominant systematics, we started from more than 150 errors employed in the SK oscillation analysis Wendell et al. (2010) and chose those which affect the analyses bins by more than 5% (). Relaxing this criteria to 1% does not significantly alter the results, but complicates the analysis Takhistov et al. (2014). As in Takhistov et al. (2014), we have found that the dominant contributions originate from uncertainties related to neutrino flux and energy calibration (common to both signal and background). Including the signal systematics, the total number of considered errors is 11 and they are the same for all modes. In Table 1 we display the complete list of systematics, their uncertainties and fitted pull terms for two representative examples and .

The spectral fit determines the overall background and signal normalizations and , with the fit results displayed in Table 2. The outcome shows that no significant signal excess has been observed, with the data being within of the background only hypothesis for all search modes except for , which is within .

Figure 1: [Top] Reconstructed momentum distribution for 273.4 kton years of combined SK data (black dots) and the best-fit result for the atmospheric neutrino background Monte Carlo (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 the signal and background MC fit to data. All modes are shown (overlaid), with -like channels on the left and -like channels on the right.

The lower lifetime limit on the processes can then be computed from the 90% confidence level value of (), which translates into the allowed amount of signal at 90% confidence level according to , where is the total number of signal events. The partial lifetime limit is then calculated from

(2)

where is the branching ratio of a process, and are the signal efficiency and the exposure in kton years for each SK phase, is the amount of signal allowed at the 90% confidence level and is the number of nucleons per kiloton of water, corresponding to , and for proton, neutron and dinucleon decay searches, respectively.

The resulting fitted spectra for the 273.4 kton years of combined SK data can be found in Figure 1. The upper figures display best-fit result for atmospheric neutrino background (solid line) without signal fitted to data (black dots) and the corresponding residuals after the fitted MC is subtracted from 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 -like and -like spectra overlaid with all the modes. The as well as resulting sensitivities and calculated lifetime limits for the decays are shown in Table 2. The sensitivities were obtained assuming that data are described by background. For the mode we have combined the channels and , weighted by their respective branching ratios. This limit is then multiplied by 1.15 to account for roughly sample purity of the tau channels. We set the lower limits on the partial lifetimes of the decay modes at the C.L., with the results shown in Table 2.

In conclusion, the single Cherenkov ring momentum spectra in Super-Kamiokande are well described by atmospheric neutrinos, including the effect of neutrino oscillation and systematic uncertainties, up to 1500 MeV/. We find no evidence for any contribution from the six different nucleon and dinucleon decay modes that would produce a showering or non-showering Cherenkov ring. The results of this analysis provide a stringent test of new physics. The obtained limits represent more than an order of magnitude improvement over the previous analyses of McGrew et al. (1999) and two orders of magnitude for and Berger et al. (1991). The searches for , (where is an invisible, massless particle) and are novel. The dinucleon decay limits restrict processes with violated by either zero or two units.

We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. The Super-Kamiokande experiment was built and has been operated with funding from the Japanese Ministry of Education, Culture, Sports, Science and Technology, the U.S. Department of Energy, and the U.S. National Science Foundation.

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