Branching fraction and CP asymmetry of the decays $B^{+}\to K_{\mathrm{S}}^0\ddot{I}{€}^{+}$ and $B^{+}\to K_{\mathrm{S}}^0{K}^{+}$

Abstract

An analysis of $B^{+}\to K_{\mathrm{S}}^0\ddot{I}{€}^{+}$ and $B^{+}\to K_{\mathrm{S}}^0{K}^{+}$ decays is performed with the LHCb experiment. The $pp$ collision data used correspond to integrated luminosities of $1{fb}^{-1}$ and $2{fb}^{-1}$ collected at centre-of-mass energies of $\sqrt{s}=7\mathrm{Te}\mathrm{V}$ and $\sqrt{s}=8\mathrm{Te}\mathrm{V}$, respectively. The ratio of branching fractions and the direct {\it CP} asymmetries are measured to be $\mathcal{B}(B^{+}\to K_{\mathrm{S}}^0{K}^{+})/\mathcal{B}(B^{+}\to K_{\mathrm{S}}^0\ddot{I}{€}^{+})=0.064\pm 0.009\text{(stat.)}\pm 0.004\text{(syst.)}$, ${\mathcal{A}}^{CP}(B^{+}\to K_{\mathrm{S}}^0\ddot{I}{€}^{+})=-0.022\pm 0.025\text{(stat.)}\pm 0.010\text{(syst.)}$ and ${\mathcal{A}}^{CP}(B^{+}\to K_{\mathrm{S}}^0{K}^{+})=-0.21\pm 0.14\text{(stat.)}\pm 0.01\text{(syst.)}$. The data sample taken at $\sqrt{s}=7\mathrm{Te}\mathrm{V}$ is used to search for $B_c^{+}\to K_{\mathrm{S}}^0{K}^{+}$ decays and results in the upper limit $(f_c\cdot\mathcal{B}(B_c^+ \to K_{\rm \scriptscriptstyle S}^0 K^+))/(f_u\cdot\mathcal{B}(B^+ \to K_{\rm \scriptscriptstyle S}^0 π^+)) < 5.8\times10^{-2}\textrm{at 90% confidence level}$, where $f_c$ and $f_u$ denote the hadronisation fractions of a $\bar{b}$ quark into a $B_c^{+}$ or a $B^{+}$ meson, respectively.

13 pages, 2 figures