Search for the proton decay mode $p\to \bar{\nu }{K}^{+}$ with KamLAND

We present a search for the proton decay mode $p \rightarrow \overline{\nu} K^{+}$ based on an exposure of 8.97 kton-years in the KamLAND experiment. The liquid scintillator detector is sensitive to successive signals from $p \rightarrow \overline{\nu} K^{+}$ with unique kinematics, which allow us to achieve a detection efficiency of 44%, higher than previous searches in water Cherenkov detectors. We find no evidence of proton decays for this mode. The expected background, which is dominated by atmospheric neutrinos, is $0.9 \pm 0.2$ events. The nonbackground-subtracted limit on the partial proton lifetime is $\tau \mathrm{/}B(p\to \bar{\nu }{K}^{+})>5.4\times {10}^{32}$ years at 90% C.L.