Branching fraction measurement of $B^0 \to D^+_s \pi^-$

This analysis presents a new measurement of $\mathcal{B}(B^0 \to D^+_s \pi^-)$, using LHCb data taken in 2011, 2012, 2015, and 2016. The $B^0 \to D^+_s \pi^-$ decay is described by a single tree diagram and probes the u→ b quark transition |Vub| and non- factorisable effects |aNF|. Measuring the $B^0 \to D^+_s \pi^-$ signal yield is challenging, due to a large number of background events and the tail of the $B^0 \to D^-_s \pi^+$ signal around the $B^0 \to D^+_s \pi^-$ signal peak. Therefore, the $B^0 \to D^-_s \pi^+$ signal shape and the backgrounds are studied in detail. The branching fraction of $B^0 \to D^+_s \pi^-$ is found to be $\mathcal{B}(B^0 \to D^+_s \pi^-) = (23.1 ± 1.7 \ (\rm{stat}) ± 1.6 (\mathcal{B})) · 10^{−6}$, which is the single world’s best measurement and in agreement with the current world average. The non-factorisable effects are found to be compatible with |aNF| = 1.0, i.e. naive factorisation. On top of this, the parameter rDπ and the dependence of the hadronisation fraction $f_s/f_d$ on collision energy are measured with high precision.