Search for proton decay via $p\to \nu K^{+}$ using $260\mathrm{kiloton}·\mathrm{year}$ data of Super-Kamiokande

We have searched for proton decay via $p\to \nu K^{+}$ using Super-Kamiokande data from April 1996 to February 2013, $260\mathrm{kiloton}·\mathrm{year}$ exposure in total. No evidence for this proton decay mode is found. A lower limit of the proton lifetime is set to $\tau /B(p\to \nu K^{+})>5.9\times 10^{33}$ years at 90% confidence level.

Figure 1

The upper figure shows the decaying proton mass distribution in ${}^{16}\mathrm{O}$ and the lower figure shows the $K^{+}$ momentum distribution from the simulation of $p\to \nu K^{+}$. In the upper figure, the single-bin histogram shows the free proton case and the broad histogram shows the bound proton case. The rightmost peak in the bound proton case corresponds to the $p$-state, located slightly lower than the proton mass by 15.5 MeV of binding energy; the second rightmost peak is the $s$-state (39 MeV in binding energy). The correlated nucleon decay makes the longer tail in the lower mass region. In the lower figure, the single-bin histogram shows the free proton case ($339\mathrm{MeV}/\mathrm{c}$) and the broad histogram shows the bound proton case which is smeared by Fermi motion.

Figure 2

Cross sections of the single K-meson productions via resonances calculated by NEUT. Upper plots show neutrino interactions and lower show antineutrino interactions.

Figure 3

An example graphical event display of a simulated proton decay passing all of the criteria for Method 1. The single Cherenkov ring was produced by the muon from kaon decay and fit with momentum $231\mathrm{MeV}/c$. The color of the hit PMTs represents the residual hit time after subtracting the time-of-flight of Cherenkov light in water from the vertex to the PMT. The hit PMTs associated with a 6 MeV prompt gamma are colored cyan. The decay electron was detected after the displayed event.

Figure 4

Number of hits versus hit time for a typical proton decay MC event selected by Method 1. In the upper figure, three hit clusters due to prompt $\gamma$, the $\mu$ from kaon decay ($\tau =12\mathrm{ns}$), and the muon-decay electron ($\tau =2.2\mu \sec$) can be seen in order. The lower figure is expanded around the $\mu$ hit cluster and $t_{\gamma }$, $t_0$, and $t_{\mu }$ are shown as a demonstration.

Figure 5

The likelihood distribution to separate $\mu$ and proton. The negative region is $\mu$-like and positive is protonlike. In the upper figure, the atmospheric $\nu$ MC (red boxes) is compared with data merging SK-I/III/IV (black bars) requiring cuts (A-1) through (A-5), and they are in good agreement. The lower figure shows the same distributions after $\gamma$-tagging cuts; is reduced by the likelihood cut. The blue histogram overlays the proton decay MC with arbitrary normalization.

Figure 6

Number of $\gamma$ ray hit distributions. The upper figure shows sum of SK-I, III, and IV which have 40% photo coverage, the lower figure corresponds to SK-II with 19% photo coverage. Bars, squares, and histogram correspond to data, atmospheric $\nu$ MC normalized to livetime of data, and proton decay MC with arbitrary normalization, respectively. The signal regions are indicated by arrows. The peaks at small numbers of hits are due to dark hits of the PMTs.

Figure 7

Muon momentum distribution for $260\mathrm{kton}·\mathrm{year}$. Dots, boxes, and histogram correspond to data, atmospheric $\nu$ MC, and proton decay MC, respectively. The data are fit by the background plus signal by free normalization. No excess above the expected background is observed. The normalization of the proton decay MC histogram shown is at the upper limit allowed by the fit.

Figure 8

An example graphical event display of a simulated proton decay passing all of the criteria for Method 3. The two Cherenkov rings were produced by gamma rays from ${\pi }^0$ decay and reconstructed to an invariant mass of $155\mathrm{MeV}/c^2$ and momentum of $209\mathrm{MeV}/c$. The color of the hit PMTs represents the residual hit time after subtracting the time-of-flight of Cherenkov light in water from the vertex to the PMT. The ${\pi }^{+}$ does not make a Cherenkov ring that is reconstructed, however PMT hits due to this particle are present opposite to the ${\pi }^0$ direction, visible in the upper left of the ID barrel region.

Figure 9

Charge distribution as a function of angle to the ${\pi }^{+}$ direction which is defined as opposite the reconstructed ${\pi }^0$ direction. The upper figure shows the distribution for the signal MC in which $K^{+}$ decays into ${\pi }^{+}$ and ${\pi }^0$. The bump around 23° in the signal is made by Cherenkov light of ${\pi }^{+}$. The lower figure shows only the region from 0° to 60° for signal MC (blue) and atmospheric $\nu$ MC (hatched red) after the (C-1)-(C-5) criteria are required. These histograms show the average response from numerous Monte Carlo events.

Figure 10

An illustration showing each region for $K^{+}\to {\pi }^{+}{\pi }^0$. Region (1) is an area which is inside of 90° from each $\gamma$ direction, region (2) is an area which is inside of 35° from backward of reconstructed ${\pi }^0$ direction, and region (3) is defined as residual part.

Figure 11

$E_{\mathrm{res}}$ (upper), $L_{\text{shape}}$ (middle), and $E_{\mathrm{bk}}$ (lower) distributions for the two-ring sample in SK-I,III, and IV after cuts from (C-1) through (C-4). Black crosses correspond to data and red histograms show the atmospheric $\nu$ MC normalized by livetime.

Figure 12

$E_{\mathrm{res}}$ distributions for the two-ring (upper) and single-ring (lower) samples after all cuts except (C-5) in all periods. Red histograms are atmospheric $\nu$ MC, and blue histograms are proton decay MC, respectively. No data remain after cuts. Arrows in the figures show signal regions.

Figure 13

$L_{\text{shape}}$ distributions for the two-ring (upper) and single-ring (lower) samples for SK-I,III, and IV, after all cuts except (C-6). Black dots correspond to data, red histograms are atmospheric $\nu$ MC normalized to the livetime of data, and blue histograms are proton decay MC, respectively. Arrows in the figures show signal regions.

Figure 14

$L_{\text{shape}}$ distributions for the two-ring (upper) and single-ring (lower) samples for SK-II after all cuts except (C-6), respectively. Red histograms are atmospheric $\nu$ MC, and blue histograms are proton decay MC. No data remain after cuts. Arrows in the figures show signal regions.

Figure 15

$E_{\mathrm{bk}}$ distributions for the two-ring (upper) and single-ring (lower) samples after all cuts except (C-7) in all periods. Black dots correspond to data, red histograms are atmospheric $\nu$ MC, and blue histograms are proton decay MC, respectively. Arrows in the figures show signal regions.