Search for the proton decay mode $p \rightarrow \overline{\nu} K^{+}$ 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 $\tau / B(p \rightarrow \overline{\nu} K^{+}) > 5.4 \times 10^{32}$ years at 90% C.L.