Measurement of the branching fraction of the $B^{0}\rightarrow D_{s}^{+}\pi^{-}$ decay

A branching fraction measurement of the $B^{0}\rightarrow D_{s}^{+}\pi^{-}$ decay is presented using proton-proton collision data collected with the LHCb experiment, corresponding to an integrated luminosity of $5.0\,$fb$^{-1}$. The branching fraction is found to be ${\mathcal{B}(B^{0}\rightarrow D_{s}^{+}\pi^{-}) = (19.4 \pm 1.8\pm 1.3 \pm 1.2)\times 10^{-6}}$, where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the $B^0 \to D^{-}\pi^{+}$, $D_{s}^{+}\rightarrow K^{+}K^{-}\pi^{+}$ and $D^{-}\rightarrow K^{+}\pi^{-}\pi^{-}$ branching fractions. This is the most precise single measurement of this quantity to date. As this decay proceeds through a single amplitude involving a $b \to u$ charged-current transition, the result provides information on non-factorisable strong interaction effects and the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$. Additionally, the collision energy dependence of the hadronisation-fraction ratio $f_s/f_d$ is measured through $\bar{B}{}_{s}^{0}\rightarrow D_{s}^{+}\pi^{-}$ and $B^0 \to D^{-}\pi^{+}$ decays.