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.