Measurement of the fragmentation fraction ratio $f_s/f_d$ and its dependence on $B$ meson kinematics

Abstract

The relative production rate of $B_s^0$ and $B^0$ mesons is determined with the hadronic decays $B_s^0\to D_s^{-}\ddot{I}{€}^{+}$ and $B^0\to D^{-}{K}^{+}$. The measurement uses data corresponding to 1.0 fb${}^{-1}$ of $pp$ collisions at a centre-of-mass energy of $\sqrt{s}=7$ TeV recorded in the forward region with the LHCb experiment. The ratio of production rates, $f_s/f_d$, is measured to be $0.238\pm 0.004\pm 0.015\pm 0.021$, where the first uncertainty is statistical, the second systematic, and the third theoretical. This is combined with a previous LHCb measurement to obtain $f_s/f_d=0.256\pm 0.020$. The dependence of $f_s/f_d$ on the transverse momentum and pseudorapidity of the $B$ meson is determined using the decays $B_s^0\to D_s^{-}\ddot{I}{€}^{+}$ and $B^0\to D^{-}\ddot{I}{€}^{+}$. There is evidence for a decrease with increasing transverse momentum, whereas the ratio remains constant as a function of pseudorapidity. In addition, the ratio of branching fractions of the decays $B^0\to D^{-}{K}^{+}$ and $B^0\to D^{-}\ddot{I}{€}^{+}$ is measured to be $0.0822\pm 0.0011(\text{stat})\pm 0.0025(\text{syst})$.