Exclusive semileptonic $B\to \pi \ell {\nu }_{\ell }$ and $B_s\to K\ell {\nu }_{\ell }$ decays through unitarity and lattice QCD

Abstract

The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{ub}|$ is obtained from exclusive semileptonic $B\to \pi \ell {\nu }_{\ell }$ and $B_s\to K\ell {\nu }_{\ell }$ decays adopting the unitarity-based dispersion matrix approach for the determination of the hadronic form factors (FFs) in the whole kinematical range. We use lattice computations of the relevant susceptibilities and of the FFs in the large-$q^2$ regime in order to derive their behavior in the low-$q^2$ region without assuming any specific momentum dependence and without constraining their shape using experimental data. Then, we address the extraction of $|V_{ub}|$ from the experimental data, obtaining $|V_{ub}|=(3.62\pm 0.47)\cdot 10^{-3}$ from $B\to \pi$ and $|V_{ub}|=(3.77\pm 0.48)\cdot 10^{-3}$ from $B_s\to K$, which after averaging yield $|V_{ub}|=(3.69\pm 0.34)\cdot 10^{-3}$. These results are compatible with the most recent inclusive value $|V_{ub}{|}_{incl}=4.13(26)\cdot 10^{-3}$ at the 1$\sigma$ level. We also present purely theoretical estimates of the ratio of the $\tau /\mu$ decay rates $R_{\pi (K)}^{\tau /\mu }$, the normalized forward-backward asymmetry ${\bar{\mathcal{A}}}_{FB}^{\ell ,\pi (K)}$ and the normalized lepton polarization asymmetry ${\bar{\mathcal{A}}}_{polar}^{\ell ,\pi (K)}$.

Comments: 46 pages, 9 figures, 9 tables. Version improved by the referee's suggestions. Conclusions unchanged. To appear in JHEP. arXiv admin note: text overlap with arXiv:2105.07851