B s → K (*)ℓ$ \overline{\nu} $, angular analysis, S-wave contributions and |V ub |

Abstract

Abstract We analyse the $ \overline{B}_s^0\to {K^{+}}{l^{-}}\overline{\nu} $ and $ \overline{B}_s^0\to {K^{*+ }}\left( {\to K\pi } \right){\ell^{-}}\overline{\nu} $ decays that are valuable for extracting the CKM matrix element |V ub|. We calculate the differential and integrated partial widths in units of |V ub|2 based on various calculations of hadronic form factors and in particular the latest Lattice QCD calculation of the B s → K * form factors. For the decay $ \overline{B}_s^0\to K\pi \ell \overline{\nu} $ , we formulate the general angular distributions with the inclusion of the various partial-wave Kπ contributions. Using the results for the Kπ scalar form factor calculated from unitarized chiral perturbation theory, we explore the S-wave effects on angular distribution variables and demonstrate that they may not be negligible, considering the high precision expected in future measurements. We also briefly discuss the impact of the S-wave ππ contributions in the $ {B^{-}}\to {\pi^{+}}{\pi^{-}}\ell \overline{v} $ decay and provide estimates for the mode $ {B^{-}}\to {K^{+}}{K^{-}}\ell \overline{\nu} $ . The studies of these channels in future can not only be used to determine |V ub|, but may also provide valuable information on the Kπ and ππ phase shifts.