Search for proton decay into a single charged antilepton and a massless invisible particle using the full pure water data set of Super-Kamiokande

A search for proton decay via $p\to l^{+}+X$, where $l^{+}$ is a positively charged lepton and $X$ is an invisible, massless, neutral particle, was performed using a 401~kton$\cdot$years exposure representing the entire pure water phase of Super-Kamiokande. No significant indication of a proton decay was observed beyond the expected atmospheric neutrino background. Lower limits on the partial lifetime of the proton were set to at $1.72\times {10}^{33}$ years for $p\to e^{+}+X$ and $0.61\times {10}^{33}$ years for $p\to {\mu }^{+}+X$ at the $90\mathrm{\%}$ confidence level. These results improve on previous limits by factors of 2 and 1.5, respectively.