Determination of the branching fractions of $B_s^0\to D_s^{\mp }{K}^{\pm }$ and $B^0\to D_s^{-}{K}^{+}$

Abstract

Measurements are presented of the branching fractions of the decays $B_s^0\to D_s^{\mp }{K}^{\pm }$ and $B^0\to D_s^{-}{K}^{+}$ relative to the decays $B_s^0\to D_s^{-}\ddot{I}{€}^{+}$ and $B^0\to D^{-}\ddot{I}{€}^{+}$, respectively. The data used correspond to an integrated luminosity of 3.0 fb${}^{-1}$ of proton-proton collisions. The ratios of branching fractions are $\frac{\mathcal{B}(B_s^0\to D_s^{\mp }{K}^{\pm })}{\mathcal{B}(B_s^0\to D_s^{-}\ddot{I}{€}^{+})}=0.0752\pm 0.0015\pm 0.0019$ and $\frac{\mathcal{B}(B^0\to D_s^{-}{K}^{+})}{\mathcal{B}(B^0\to D^{-}\ddot{I}{€}^{+})}=0.0129\pm 0.0005\pm 0.0008,$ where the uncertainties are statistical and systematic, respectively.