$|V_{cb}|$, Lepton Flavour Universality and $SU(3{)}_F$ symmetry breaking in $B_s\to D_s^{(\ast )}\ell \hat{I}{½}_{\ell }$ decays through unitarity and lattice QCD

Abstract

In addition to the well-known $B\to D^{(\ast )}\ell \hat{I}{½}_{\ell }$ decays, semileptonic $B_s\to D_s^{(\ast )}\ell \hat{I}{½}_{\ell }$ processes offer the possibility to determine the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cb}|$. We implement the Dispersive Matrix (DM) approach to describe the hadronic Form Factors (FFs) for the $B_s\to D_s^{(\ast )}$ transition in the whole kinematical range, starting from recent Lattice QCD computations at large values of the 4-momentum transfer. We extract $|V_{cb}|$ from the experimental data, obtaining $|V_{cb}|\cdot 10^3=(41.7\pm 1.9)$ from $B_s\to D_s\ell \hat{I}{½}_{\ell }$ and $|V_{cb}|\cdot 10^3=(40.7\pm 2.4)$ from $B_s\to D_s^{\ast }\ell \hat{I}{½}_{\ell }$ decays. After averaging with the values of $|V_{cb}|$ obtained from the $B\to D^{(\ast )}$ channels [1,2] we get $|V_{cb}|\cdot 10^3=(41.2\pm 0.8)$, which is compatible with the most recent inclusive estimate $|V_{cb}{|}_{\mathrm{incl}}\cdot 10^3=42.16\pm 0.50$ [3] at the $1\ddot{I}ƒ$ level. In addition we test the Lepton Flavour Universality (LFU) by computing the $\ddot{I}„/\ell$ ratios of the total decay rates (where $\ell$ is a light lepton), obtaining $R(D_s)=0.298(5)$ and $R(D_s^{\ast })=0.250(6)$. We also address the issue of the $SU(3{)}_F$ symmetry breaking by comparing the hadronic FFs entering the semileptonic $B\to D^{(\ast )}$ and $B_s\to D_s^{(\ast )}$ channels.

31 pages, 8 figures, 3 tables. Revised and reformatted version to appear in PRD. Results and conclusions unchanged