Search for proton decay into three charged leptons in 0.37 megaton-years exposure of the Super-Kamiokande

A search for proton decay into three charged leptons has been performed by using $0.37\mathrm{Mton}·\mathrm{years}$ of data collected in Super-Kamiokande. All possible combinations of electrons, muons, and their antiparticles consistent with charge conservation were considered as decay modes. No significant excess of events has been found over the background, and lower limits on the proton lifetime divided by the branching ratio have been obtained. The limits range between $9.2\times {10}^{33}$ and $3.4\times {10}^{34}\mathrm{years}$ at 90% confidence level, improving by more than an order of magnitude upon limits from previous experiments. A first limit has been set for the $p\to {\mu }^{-}{e}^{+}{e}^{+}$ mode.

Figure 1

Signal efficiency (top, blue dots), data (bottom, black dots), and expected background events (bottom, red line) at each cut step in each mode. In upper column, from left to right for the $p\to e^{+}{e}^{+}{e}^{-}$, $p\to {\mu }^{+}{e}^{+}{e}^{-}$, and $p\to {\mu }^{-}{e}^{+}{e}^{+}$ modes, respectively. In lower column, from left to right for the $p\to e^{+}{\mu }^{+}{\mu }^{-}$, $p\to e^{-}{\mu }^{+}{\mu }^{+}$, and $p\to {\mu }^{+}{\mu }^{+}{\mu }^{-}$ modes, respectively. The background MC is normalized by live time. SK-I to SK-IV are combined in signal MC, background MC, and data. Note that both the data and background MC plots for the $p\to {\mu }^{+}{e}^{+}{e}^{-}$ and $p\to {\mu }^{-}{e}^{+}{e}^{+}$ modes are the same, since SK cannot identify the charge sign of the leptons. For the same reason, the data and background MC plots are the same for the $p\to e^{+}{\mu }^{+}{\mu }^{-}$ and $p\to e^{-}{\mu }^{+}{\mu }^{+}$ modes as well.

Figure 2

Two-dimensional plots of total mass and momentum for signal (left), background (center), and measured data (right) after the selections C1–C3 and C5 are applied. From the top to the bottom, for the $p\to e^{+}{e}^{+}{e}^{-}$, $p\to {\mu }^{+}{e}^{+}{e}^{-}$, $p\to e^{-}{\mu }^{+}{\mu }^{+}$, and $p\to {\mu }^{+}{\mu }^{+}{\mu }^{-}$ modes, respectively. Light blue shows free proton and dark blue shows bound proton in the signal plot. Two black squares show the lower and upper signal boxes. The dot size is enlarged in the signal box only for background. SK-I to SK-IV are combined in signal MC, background MC ($4\times 500\mathrm{years}$), and data. For the $p\to {\mu }^{-}{e}^{+}{e}^{+}$ mode, the number of signal MC points is lower than that of $p\to {\mu }^{+}{e}^{+}{e}^{-}$ by 19%, due to the different effective lifetimes (and therefore different decay electron production probabilities) of the ${\mu }^{-}$ and ${\mu }^{+}$ in water. Similarly, the signal MC for $p\to e^{+}{\mu }^{+}{\mu }^{-}$ has 20% fewer events than that for the $p\to e^{-}{\mu }^{+}{\mu }^{+}$ mode. As in Fig. 1, the data and background MC figures are the same for modes that differ only by the charge sign of the leptons.

Figure 3

Data (black dots) and background (red line) comparison for total mass (left) and momentum (right) after the selections C1–C3 and C5 are applied. The shape of the signal (free proton only) distribution is shown by the blue line (filled cyan histogram). Additionally, a $P_{\text{tot}}<250\mathrm{MeV}/\mathrm{c}$ cut is applied on the total mass plot and an $800<M_{\text{tot}}<1050\mathrm{MeV}/{\mathrm{c}}^2$ cut is applied on the total momentum plot. From the top to the bottom, the $p\to e^{+}{e}^{+}{e}^{-}$, $p\to {\mu }^{+}{e}^{+}{e}^{-}$, $p\to e^{-}{\mu }^{+}{\mu }^{+}$, and $p\to {\mu }^{+}{\mu }^{+}{\mu }^{-}$ modes are shown, respectively. Dotted black lines show the boundary of the signal box. SK-I to SK-IV are combined in signal, background MC, and data. Background MC is normalized by atmospheric neutrino flux, oscillation probability, and live time. Signal MC is normalized to the partial proton lifetime limit calculated in Sec. 8. The number of signal MC events for the $p\to {\mu }^{-}{e}^{+}{e}^{+}$ mode is lower than that of $p\to {\mu }^{+}{e}^{+}{e}^{-}$ by 19%, due to the different effective lifetimes (and therefore different decay electron production probabilities) of the ${\mu }^{-}$ and ${\mu }^{+}$ in water. Similarly, the signal MC for $p\to e^{+}{\mu }^{+}{\mu }^{-}$ has 20% fewer events than that for the $p\to e^{-}{\mu }^{+}{\mu }^{+}$ mode. As in Fig. 1, the data and background MC figures are the same for modes that differ only by the charge sign of the leptons.

Figure 4

Estimated partial lifetime lower limit for each mode of proton decay into three charged leptons by this analysis (red histogram), IMB-3 (star) [9], and HPW (circle) [10] experiments. The $p\to {\mu }^{-}{e}^{+}{e}^{+}$ channel was not searched for by IMB-3 and HPW experiments.