Exploiting perpendicular momentum distributions of semileptonic decays: \( {\overline{B}}_s^0\to {D}_s^{+}{\mu}^{-}\overline{\nu} \) as a case study

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 ${\overline{B}}_s^0\to D_s^{+}{\mu }^{-}\overline{\nu }$ \( {\overline{B}}_s^0\to {D}_s^{+}{\mu}^{-}\overline{\nu} \) decay distribution, where the publicly available efficiency and resolution data from the LHCb experiment are 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. An independent determination of the form factor parameters from the LHCb data is achieved, enabling the inclusion of this measurement in global fits and providing stronger constraints on the underlying theoretical descriptions.