${\mathbf{B}}_{\mathbf{s}}\to {\mathbf{K}}^{(\ast )}\mathbf{\ell }\bar{\nu }$, Angular Analysis, S-wave Contributions and $|{\mathbf{V}}_{\mathbf{ub}}|$

Abstract

We analyse the ${\overline{B}}_s^0\to K^{+}{l}^{-}\bar{\nu }$ and ${\overline{B}}_s^0\to K^{\ast +}(\to K\pi ){\ell }^{-}\bar{\nu }$ 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 $B_s\to K^{\ast }$ form factors. For the decay ${\overline{B}}_s^0\to K\pi \ell \bar{\nu }$, we formulate the general angular distributions with the inclusion of the various partial-wave $K\pi$ contributions. Using the results for the $K\pi$ 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 $\pi \pi$ contributions in the $B^{-}\to {\pi }^{+}{\pi }^{-}\ell \bar{\nu }$ decay and provide estimates for the mode $B^{-}\to K^{+}{K}^{-}\ell \bar{\nu }$. The studies of these channels in future can not only be used to determine $|V_{ub}|$, but may also provide valuable information on the $K\pi$ and $\pi \pi$ phase shifts.

Comments: 1+30 pages, 13 figures, modified discussion on the B to \pi \pi l\nu