Search for Proton Decay through<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">p</mml:mi><mml:mspace/><mml:mo>→</mml:mo><mml:mspace/><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi mathvariant="italic">ν</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>in a Large Water Cherenkov Detector

We present results of a search for proton decays, $p\ensuremath{\rightarrow}\overline{\ensuremath{\nu}}{K}^{+}$, using data from a $33\mathrm{kt}\ifmmode \dot{}\else \.{}\fi{}\mathrm{yr}$ exposure of the Super-Kamiokande detector. Two decay modes of the kaon, ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$, were studied. The data were consistent with the background expected from atmospheric neutrinos; therefore a lower limit on the partial lifetime of the proton $\ensuremath{\tau}/B(p\ensuremath{\rightarrow}\overline{\ensuremath{\nu}}{K}^{+})$ was found to be $6.7\ifmmode\times\else\texttimes\fi{}{10}^{32}\mathrm{years}$ at $90%$ confidence level.