Branching fraction and CP asymmetry of the decays B⁺→K<inf>S</inf>⁰π⁺ and B⁺→K<inf>S</inf>⁰K⁺

An analysis of B ⁺→K _S ⁰π ⁺ and B ⁺→K _S ⁰K ⁺ decays is performed with the LHCb experiment. The pp collision data used correspond to integrated luminosities of 1fb ^-1 and 2fb ^-1 collected at centre-of-mass energies of √s=7TeV and √s=8TeV, respectively. The ratio of branching fractions and the direct CP asymmetries are measured to be B(B ⁺→K _S0K ⁺)/B(B ⁺→K _S ⁰π ⁺)=0.064±0.009 (stat.)±0.004(syst.), A ^CP(B ⁺→K _S ⁰π ⁺)=-0.022±0.025(stat.)±0.010 (syst.) and A ^CP(B ⁺→K _S ⁰K ⁺)=-0.21±0.14 (stat.)±0.01 (syst.). The data sample taken at √s=7 TeV is used to search for B _c ⁺→K _S ⁰K ⁺ decays and results in the upper limit (f _c{dot operator}B(B _c ⁺→K _S ⁰K ⁺))/(fu{dot operator}B(B ⁺→K _S ⁰π ⁺))<5.8×10-2 at 90% confidence level, where f _c and f _u denote the hadronisation fractions of a b- quark into a Bc+ or a B ⁺ meson, respectively.