Eur. Phys. J. C (2025) 85: 880
https://doi.org/10.1140/epjc/s10052-025-14599-8

Regular Article - Theoretical Physics

$V_{\mathit{cb}}$ puzzle in semi-leptonic $B\to D^{\ast }$ decays revisited

¹ School of Physics, Beihang University, 102206, Beijing, China
² Department of Physics, Guangxi Normal University, 541004, Guilin, China
³ Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University, 541004, Guilin, China
⁴ Sino-French Carbon Neutrality Research Center, École Centrale de Pékin/School of General Engineering, Beihang University, 100191, Beijing, China
⁵ Peng Huanwu Collaborative Center for Research and Education, Beihang University, 100191, Beijing, China
⁶ Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, 102206, Beijing, China
⁷ Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, 516000, Huizhou, China

^a ruixiang.shi@gxnu.edu.cn
^b lisheng.geng@buaa.edu.cn

Received: 16 March 2025
Accepted: 31 July 2025
Published online: 16 August 2025

Abstract

Inspired by the newly reported $B\to D^{\ast }(\to D\pi )\ell {\overline{\nu }}_{\ell }$ differential decay rates by the Belle and Belle II Collaborations, we revisit the $V_{\mathit{cb}}$ puzzle in semi-leptonic $B\to D^{\ast }$ decays, considering the latest lattice QCD (LQCD) simulations and light-cone sum rule (LCSR) results. We examine the commonly used Caprini–Lellouch–Neubert (CLN), Boyd–Grinstein–Lebed (BGL), and heavy quark effective theory (HQET) parameterizations. We demonstrate that these three parameterizations yield consistent results and reconfirm the $V_{\mathit{cb}}$ puzzle. Then, we use a state-of-the-art Bayesian method to estimate the impact of higher-order terms beyond the present HQET expansion on the uncertainty of $V_{\mathit{cb}}.$ We show that higher-order effects cannot eliminate the deviation between the exclusive and inclusive determinations of $V_{\mathit{cb}}.$ Finally, utilizing the best-fit results obtained in the HQET parameterization via fitting LQCD and LCSR data only as inputs, we predict the relevant observables, i.e., $R_{D^{\ast }},$$F_L^{D^{\ast }},$ and $P_{\tau }^{D^{\ast }},$ sensitive to new physics in the $B\to D^{\ast }\ell {\overline{\nu }}_{\ell }$ decays. We conclude that lepton-flavour universality violations still exist in the $b\to c\tau \nu$ transitions.