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\,\text {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} {\rightarrow }{{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 $b{\rightarrow }u$ 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 ${{\overline{B}} {}^0_{s}} {\rightarrow }{{D} ^+_{s}} {{\pi } ^-} $ and ${{B} ^0} {\rightarrow }{{D} ^-} {{\pi } ^+} $ decays.