Search for Nucleon Decay in Super-Kamiokande

Searches for nucleon decays are performed by Super-Kamiokande, a large water cherenkov detecor. The total exposure is 141 kton·year which includes 1489 days data of SuperKamiokande-I (SK-1) and 799 days of Super-Kamiokande-II (SK-2). We have not observed any evidence of nucleon decay yet. The lower limit of proton life time decay into eπ, which is dominant mode predicted by non-SUSY model, is 8.2×10 years with 90 % confidence level. The lower limit of proton life time decay into νK, which is dominant mode predicted by SUSY model, is 2.8×10 years with 90 % confidence level.


GUTs and Nucleon decays
The standard model based on the gauge group has been successful in accounting for many experimental results. However, the standard model has a lot of unanswered questions, such as why there are so many parameters. Various attempts have been made to resolve the shortcoming by unifying the electroweak and the strong interactions in the context of Grand Unified Theory (GUTs). GUTs is motivated by the apparent merging of the coupling constants of the strong, weak, and electromagnetic forces at a large energy scale (∼ 10 16 GeV ), which is out of the reach of accelerators, when low energy measurements extrapolated. One of the other general features of GUTs is that they allow lepton and baryon number violations and they predict instability of nucleons. Then nucleon decay experiments are the direct probe for GUTs.
In GUTs, nucleon decay can proceed via an exchange of a massive boson between two quarks in a nucleon, and one quark transforms into a lepton and another into an anti-quark which binds a spectator quark creating a meson. The favored decay mode in GUTs based on SU(5) symmetry is p → e + π 0 . On the other hand, GUTs model incorporating supersymmetry (SUSY-GUTs) suppress the decay mode p → e + π 0 but favor the other mode p → νK + via dimension five operator interactions with the exchange of a heavy supersymmetric color triplet

Super-Kamiokande detector
The The results of p → e + π 0 and p → νK + for SK-1 data were already published 7 8 and they excluded minimal SU(5) and minimal SUSY SU (5). In this paper, the results of combined analysis of SK-1 and SK-2 are reported.

MC simulations
A Monte Carlo simulation is used to estimate detection efficiencies of proton decay occurring in water (H 2 O). For the case of a free proton decay in hydrogen, the momentum of the decay particles are uniquely determined by two-body kinematics. For the case of a bound proton in oxygen, Fermi motion of the protons, the nuclear binding energy, and meson-nuclear interactions are taken into account.
Backgrounds to the proton decay search arise from atmospheric neutrino interactions. The neutrino interactions in water are simulated by neut 9 with an input atmospheric neutrino flux calculated by Honda, et al. 10 , which are used for neutrino oscillation analysis.
Particles produced in the simulations of proton decay and atmospheric neutrino are passed through a detector simulation which is based on GEANT-3 to model Cherenkov light emission from charged particles, propagation of particles and lights through the matter, detector geometry response of the PMTs and electronics.
If a proton decays into e + and π 0 , they are emitted back-to-back in the proton rest frame. The π 0 immediately decays into two gamma rays. Then we may observe 2 or 3 e-like cherenkov rings, and we can reconstruct π 0 mass from two gamma rays and also proton mass from all rings if we succeed to reconstruct all of the rings. In p → e + π 0 mode, the following selection criteria are applied: (A1) the vertex is in the fiducial volume described in Sec 1. The detection efficiencies are estimated to be 44.6 and 43.5 % for SK-1 and SK-2, respectively. The difference of efficiency is 1 % and it implies SK-2 has a similar performance with SK-1 even though the photo coverage of SK-2 is almost a half of SK-1. The inefficiency is mainly due to nuclear interaction effects of pions in oxygen. The total systematic uncertainties are estimated to be 19 % both for SK-1 and SK-2, and the largest contribution is the uncertainty of the cross section for pion-nuclear effects (15 %).
The remaining backgrounds are estimated to be 0.2 and 0.1 events for SK-1 and SK-2, respectively. The dominant sources of neutrino interaction are charged current (CC) singlepion production (32 %), CC multi-pion production (19 %), and CC quasi-elastic scattering (28 %). The systematic uncertainty comes from reconstruction performance, hadron propagation in water, pion-nuclear effect, cross sections and flux of neutrinos are taken into account and the uncertainty of the background is estimated to be 37 %. Figures 2 show the reconstructed π 0 mass, the total momentum, and the total invariant mass distributions of SK-2 data and the atmospheric neutrino MC. The data agrees with the atmospheric neutrino MC. The number of observed data in the signal box in Figure 1 are 0 both for SK-1 and SK-2. The life time limit calculated by a method based on Bayes theorem 11 is τ /B p→e + π 0 > 8.2 × 10 33 years at 90 % confidence level.
If a proton decays into K + and ν, the momentum of K + is below cherenkov threshold and it cannot emit cherenkov light. Most of K + are stopped in water and decay into other particles. For p → νK + mode, three methods are employed to analyze and merged results are shown later section. If the data is fitted by the atmospheric neutrino MC and the proton decay MC, the upper limit of contamination of the proton decay can be obtained and the lifetime limit can be calculated.
There are much background events in single ring µ sample as shown in the previous section.
To eliminate the background, further cuts are applied. If a proton decays in the oxygen, the remaining nitrogen nucleus left in excited states emit γ rays immediately. The most significant branch is the 6.32 MeV γ ray from p 3/2 hole state with 41 % probability 12 . Thus the signal of γ ray may be observed before µ and it is very powerful tool to eliminate the backgrounds.
To select K + → µ + ν µ with prompt γ, the following selection criteria are applied after (B1)-(B3) in section 4.1; (B4) the distance between µ and decay electron is less than 200 cm, (B5) the goodness of vertex fit is grater than 0.6. The cuts (B4) and (B5) are helpful to reject proton ring which mainly comes from charged current quasi-elastic interaction (n + ν → p + µ) and the case µ is below cherenkov threshold. To determine initial vertex, time information of each PMT is used (TDC fit). Then a precise vertex fitter which uses opening angle and hit pattern of a cherenkov ring is applied assuming particle type (e-like/µ-like) in the analysis. If a proton ring is taken as a µ-like ring, the precise fitter may fail to fit the vertex because the actual opening angle is smaller than expectation as µ. Further proton rejection cut is applied; (B6) the difference of goodness between precise fit and TDC fit is less than 0.1. Then number of hit versus time distribution is made for an event and a time window with 12 nsec is opened before muon peak and is slid to earlier time to find a maximum hit cluster which may be produced by γ ray. N γ and T γ are defined as the maximum number of hit in the time window and the time of middle of the time window. (B7) 8 < N γ < 60 for SK-1 and 4 < N γ < 30 for SK-2, (B8) T µ − T γ < 75 nsec. Figures 4 show N γ versus T µ − T γ distributions for the proton decay MC, the atmospheric neutrino MC, and the data. The detection efficiencies are estimated to be 7.2 % and 5.8 % for SK-1 and SK-2, respectively. Event though the photo coverage of SK-2 is almost a half of SK-1, the detection efficiency keeps about 80 % of SK-1. That is useful information to design a large water cherenkov detector of the next generation. The systematic uncertainties are estimated to be 22 % both for SK-1 and SK-2, which are dominated by the uncertainty of the γ ray emission probability (20 %). The background events for each livetime are estimated to be 0.16 and 0.08 events for SK-1 (1489 days) and SK-2 (799 days), respectively. The most dominant neutrino interaction in the background is that the neutrino interacts with nuclei and makes resonance N(1650) and it decays into K + Λ. On the other hand, there are no candidates in both SK-1 and SK-2.
4.3 K + → π 0 π + A K + decays into π 0 π + with 21.5 % fraction, and most of them have monochromatic momentum. The momentum of π + is just above cherenkov threshold and its cherenkov ring cannot be observed clearly. The π + decays into µ with momentum below cherenkov threshold. As a result, two γs from a π 0 and PMT activities in the backward of π 0 direction, and a decay electron can be observed if a proton decays in this mode. The selection criteria is required; (C1) FC 2 rings and both are e-like, (C2) one decay electron, (C3) reconstructed π 0 mass is grater than 85 MeV/c 2 and less than 185 MeV/c 2 , (C4) reconstructed π 0 momentum is grater than 175 MeV/c and less than 250 MeV/c. Then a backward charge, Q bk and a residual charge, Q res are defined as sum of the charges in 140 • ∼ 180 • and 90 • ∼ 140 • from the π 0 direction. (C5) 40(20) < Q bk < 100(50) pe for SK-1 (SK-2), (C6) 70(35)pe < Q res for SK-1 (SK-2).
Figures 5 shows Q bk versus Q res plots for the proton decay MC, the atmospheric neutrino MC, and the SK-2 data. The detection efficiencies are estimated to be 6.2 % and 4.8 % for SK-1 and SK-2, respectively. The detection efficiency of SK-2 also keeps about 80 % of SK-1. The systematic uncertainties are 8.6 % both for SK-1 and SK-2 and the most dominant error comes from uncertainty of N-π cross section in water (5.0 %). The numbers of backgrounds are estimated to be 0.43 and 0.31 for SK-1 and SK-2, respectively. The large contributions are single π production in charged and neutral current interactions. There are no candidates in the data.

Combined limit for p → νK +
The three methods are used to calculate lifetime limit for the proton decay mode p → νK + based on the Bayes theorem. Detail descriptions can be found in reference 8 . The obtained lower limit of the proton lifetime via p → νK + is 2.8×10 33 years at 90 % confidence level.

Summary
We have searched for nucleon decay via p → e + π 0 , which is dominant mode in the non-SUSY GUTs, and p → νK + , which is dominant mode in the SUSY-GUTs mode, from an exposure of 141 kton year. No significant excess above background of the atmospheric neutrino interactions is observed. The lower limits of the partial nucleon lifetime at 90 % confidence level are 8.2×10 33 years and 2.8 × 10 33 years, respectively.