Exclusive determinations of $|V_{cb}|$ and $R(D^{\ast })$ through unitarity

Abstract

In this work we apply the Dispersive Matrix (DM) method of Refs. [1,2] to the lattice computations of the Form Factors (FFs) entering the semileptonic $B\to D^{\ast }\ell {\nu }_{\ell }$ decays, recently produced by the FNAL/MILC Collaborations [3] at small, but non-vanishing values of the recoil variable ($w-1$). Thanks to the DM method we obtain the FFs in the whole kinematical range accessible to the decay in a completely model-independent and non-perturbative way, implementing exactly both unitarity and kinematical constraints. Using our theoretical bands of the FFs we extract $|V_{cb}|$ from the experimental data and compute the theoretical value of $R(D^{\ast })$. Our final result for $|V_{cb}|$ reads $|V_{cb}|=(41.3\pm 1.7)\cdot 10^{-3}$, compatible with the most recent inclusive estimate at the $0.5\sigma$ level. Moreover, we obtain the pure theoretical value $R(D^{\ast })=0.275\pm 0.008$, which is compatible with the experimental world average at the $\sim 1.3\sigma$ level.

20 pages, 5 figures, 2 tables. Revised version including appendices describing the DM method, the application of the unitarity filters and the implementation of the kinematical constraints. Results and conclusions unchanged. Matches published version in EPJC

References in corpus (4)

• $R(D^{\ast })$, $|V_{cb}|$, and the Heavy Quark Symmetry relations between form factors
• Extraction of $|V_{cb}|$ from $B\to D^{(\ast )}\ell {\nu }_{\ell }$ and the Standard Model predictions of $R(D^{(\ast )})$
• 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

Cited by in corpus (11)

• 50 Years of Quantum Chromodynamics
• Revisiting $B\to K^{(\ast )}\nu \bar{\nu }$ decays in the Standard Model and beyond
• Global fit to $b\to c\tau \nu$ anomalies as of Spring 2024
• Review of Semileptonic $B$ Anomalies
• Discriminating $B\to D^{\ast }\ell \nu$ form factors via polarization observables and asymmetries
• Coup de grace to the charged Higgs solution of $P_5^{\prime }$ and $R_{D^{(\ast )}}$ discrepancies
• Insights on the current semi-leptonic $B$-decay discrepancies -- and how $B_s\to {\mu }^{+}{\mu }^{-}\gamma$ can help
• Extractions of $|V_{ub}|/|V_{cb}|$ from a combined study of the exclusive $b\to u(c)\ell {\nu }_{\ell }$ decays
• New physics contributions to moments of inclusive $b\to c$ semileptonic decays
• An Imperative study of the angular observables in ${\Lambda }_b\to {\Lambda }_c^{+}(\to \Lambda {\pi }^{+}){\ell }^{-}{\bar{\nu }}_{\ell }$ decay and probing the footprint of new physics
• Constraints on lepton-flavor mixing with third-generation new physics