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

Abstract

In addition to the well-known $B\to D^{(\ast )}\ell {\nu }_{\ell }$ decays, semileptonic $B_s\to D_s^{(\ast )}\ell {\nu }_{\ell }$ 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 $B_s\to D_s\ell {\nu }_{\ell }$ and $|V_{cb}|\cdot 10^3=(40.7\pm 2.4)$ from $B_s\to D_s^{\ast }\ell {\nu }_{\ell }$ 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 $1\sigma$ level. In addition we test the Lepton Flavour Universality (LFU) 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 $R(D_s^{\ast })=0.250(6)$. 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

References in corpus (10)

• FLAG Review 2021
• Three loop calculations and inclusive $V_{cb}$
• Analyzing new physics in the decays ${\bar{B}}^0\to D^{(\ast )}{\tau }^{-}{\bar{\nu }}_{\tau }$ with form factors obtained from the covariant quark model
• Precise measurement of the $f_s/f_d$ ratio of fragmentation fractions and of $B_s^0$ decay branching fractions
• $|V_{cb}|$ and $R(D^{(\ast )})$ using lattice QCD and unitarity
• Unitarity Bounds for Semileptonic Decays in Lattice QCD
• Constraints for the semileptonic $B\to D^{(\ast )}$ form factors from lattice QCD simulations of two-point correlation functions
• $B_s\to D_s^{\ast }$ Form Factors for the full $q^2$ range from Lattice QCD
• Measurement of the shape of the $B_s^0\to D_s^{\ast -}{\mu }^{+}{\nu }_{\mu }$ differential decay rate
• Optimized Lepton Universality Tests in $B\to V\ell \bar{\nu }$ decays

Cited by in corpus (5)

• Impact of ${\Lambda }_b\to {\Lambda }_c\tau \nu$ measurement on New Physics in $b\to cl\nu$ transitions
• Discriminating $B\to D^{\ast }\ell \nu$ form factors via polarization observables and asymmetries
• Dispersive bounds for local form factors in ${\Lambda }_b\to \Lambda$ transitions
• Extractions of $|V_{ub}|/|V_{cb}|$ from a combined study of the exclusive $b\to u(c)\ell {\nu }_{\ell }$ decays
• Prediction of various observables for $B_s^0\to D_s^{(\ast )-}{\ell }^{+}{\nu }_{\ell }$ within covariant confined quark model