Eur. Phys. J. C (2024) 84: 400
https://doi.org/10.1140/epjc/s10052-024-12742-5

Regular Article - Theoretical Physics

Updates on the determination of $|V_{\mathit{cb}}|,$$R(D^{\ast })$ and $|V_{\mathit{ub}}|/|V_{\mathit{cb}}|$

¹ Physics Department, INFN Sezione di Roma La Sapienza, Piazzale Aldo Moro 5, 00185, Rome, Italy
² Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
³ LAPTh, Université Savoie Mont-Blanc and CNRS, 74941, Annecy, France

^b simula@roma3.infn.it

Received: 23 November 2023
Accepted: 29 March 2024
Published online: 17 April 2024

Abstract

We present an updated determination of the values of $|V_{\mathit{cb}}|,$$R(D^{\ast })$ and $|V_{\mathit{ub}}|/|V_{\mathit{cb}}|$ based on the new data on semileptonic $B\to D^{\ast }\ell {\nu }_{\ell }$ decays by the Belle and Belle-II Collaborations and on the recent theoretical progress in the calculation of the form factors relevant for semileptonic $B\to D^{\ast }\ell {\nu }_{\ell }$ and $B_s\to K\ell {\nu }_{\ell }$ decays. In particular we present results derived by applying either the Dispersive Matrix (DM) method of Di Carlo et al. (Phys Rev D 104:054502, 2021), Martinelli et al. (Phys Rev D 104:094512, 2021), Martinelli et al. (Phys Rev D 105:034503, 2022), Martinelli et al. (Eur Phys J C 82:1083, 2022), Martinelli et al. (JHEP 08:022, 2022) and Martinelli et al. (Phys Rev D 106:093002, 2022) or the more standard Boyd–Grinstein–Lebed (BGL) (Boyd et al. in Phys Rev D 56:6895, 1997) approach to the most recent values of the form factors determined in lattice QCD. Using all the available lattice results for the form factors from the DM method we get the theoretical value $R^{\text{th}}(D^{\ast })=0.262\pm 0.009$ and we extract from a bin-per-bin analysis of the experimental data the value $|V_{\mathit{cb}}|=(39.92\pm 0.64)·{10}^{-3}.$ Our result for $R(D^{\ast })$ is consistent with the latest experimental world average $R^{\text{exp}}(D^{\ast })=0.284\pm 0.012$ (HFLAV Collaboration in Preliminary average of R(D) and $R(D^{\ast })$ as for Summer 2023. See https://hflav-eos.web.cern.ch/hflav-eos/semi/summer23/html/RDsDsstar/RDRDs.html) at the $\simeq 1.5\sigma$ level. Our value for $|V_{\mathit{cb}}|$ is compatible with the latest inclusive determinations $|V_{\mathit{cb}}{|}^{\text{incl}}=(41.97\pm 0.48)·{10}^{-3}$ (Finauri and Gambino in The $q^2$ moments in inclusive semileptonic B decays. arXiv:2310.20324) and $|V_{\mathit{cb}}{|}^{\text{incl}}=(41.69\pm 0.63)·{10}^{-3}$ (Bernlochner et al. in JHEP 10:068, 2022) within $\simeq 2.6$ and $\simeq 2.0$ standard deviations, respectively. From a reappraisal of the calculations of $|V_{\mathit{ub}}|/|V_{\mathit{cb}}|,$ we also obtain $|V_{\mathit{ub}}|/|V_{\mathit{cb}}|=0.087\pm 0.009$ in good agreement with the result $|V_{\mathit{ub}}|/|V_{\mathit{cb}}|=0.0844\pm 0.0056$ from the latest FLAG review (Flavour Lattice Averaging Group (FLAG) Collaboration in Phys J C 82:869, 2022).