In addition to the well-known $B\to D^{(*)}\ell {\nu }_{\ell }$ decays, semileptonic $B_s\to D_s^{(*)}\ell {\nu }_{\ell }$ processes offer the possibility to determine the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$. We implement the dispersive matrix approach to describe the hadronic form factors (FFs) for the $B_s\to D_s^{(*)}$ transition in the whole kinematical range, starting from recent lattice QCD computations at large values of the four-momentum transfer. We extract $|V_{cb}|$ from the experimental data, obtaining $|V_{cb}|\times {10}^3=(41.7\pm 1.9)$ from $B_s\to D_s\ell {\nu }_{\ell }$ and $|V_{cb}|\times {10}^3=(40.7\pm 2.4)$ from $B_s\to D_s^{*}\ell {\nu }_{\ell }$ decays. After averaging with the values of $|V_{cb}|$ obtained from the $B\to D^{(*)}$ channels [G. Martinelli et al., Phys. Rev. D 105, 034503 (2022); G. Martinelli et al., arXiv:2109.15248.], we get $|V_{cb}|\times {10}^3=(41.2\pm 0.8)$, which is compatible with the most recent inclusive estimate $|V_{cb}{|}_{\mathrm{incl}}\times {10}^3=42.16\pm 0.50$ [M. Bordone et al., Phys. Lett. B 822, 136679 (2021).] at the $1\sigma$ level. In addition we test the lepton flavor universality by computing the $\tau /\ell$ ratios of the total decay rates (where $\ell$ is a light lepton), obtaining $R(D_s)=0.298(5)$ and $R(D_s^{*})=0.250(6)$. We also address the issue of the $SU(3{)}_F$ symmetry breaking by comparing the hadronic FFs entering the semileptonic $B\to D^{(*)}$ and $B_s\to D_s^{(*)}$ channels.

• Received 3 May 2022
• Accepted 24 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.093002

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Published by the American Physical Society