Search for proton decay via $p \to e^{+}\pi^{0}\pi^{0}$ and $p \to \mu^{+}\pi^{0}\pi^{0}$ in 0.401 megaton-years exposure of Super-Kamiokande I-V

We searched for proton decay via $p \to e^{+}\pi^{0}\pi^{0}$ and $p \to \mu^{+}\pi^{0}\pi^{0}$ in 0.401 megaton-years of data collected in all pure water detector phases of Super-Kamiokande (SK) I-V. A theoretical study predicts proton decay rates without assuming a particular grand unified theory and suggests that three-body proton decays involving two pions can have decay rates comparable to those of $p \to e^{+}\pi^{0}$ and $p \to \mu^{+}\pi^{0}$. This is the first search for proton decay into a charged anti-lepton and two neutral pions in SK. One data candidate event was found for each of the two decay modes, which is consistent with the expected atmospheric neutrino background. We set lower limits on the lifetime of $\tau/B(p \to e^{+}\pi^{0}\pi^{0}) > 7.2 \times 10^{33}$ years and $\tau/B(p \to \mu^{+}\pi^{0}\pi^{0}) > 4.5 \times 10^{33}$ years at 90 $\%$ confidence level. These limits are more than one order of magnitude higher than those of the previous experiment.