Exploiting Perpendicular Momentum Distributions of Semileptonic Decays: $\bar{B}_s^0\to D_s^+\mu^-\bar\nu$ as a Case Study

Abstract

We derive the differential distribution of semileptonic decays with respect to the perpendicular momentum component of the final state hadron. The benefits and shortfalls arising from measurements of these distributions are discussed. Our approach is illustrated on the LHCb measurement of the $\bar{B}_s^0\to D_s^+\mu^-\bar\nu$ decay distribution where the publicly available data by the LHCb experiment is used in an independent phenomenological analysis for the first time. We extract the CKM element $|V_{cb}|$ and information on the shape of the relevant hadronic form factors from the measurement of the binned rate in the perpendicular momentum component of the hadron.