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

AbstractWe present an updated determination of the values of $$\vert V_{cb} \vert ,$$ | V cb | , $$R(D^*)$$ R ( D ∗ ) and $$\vert V_{ub} \vert /\vert V_{cb} \vert $$ | V ub | / | V cb | based on the new data on semileptonic $$B \rightarrow D^* \ell \nu _\ell $$ B → D ∗ ℓ ν ℓ decays by the Belle and Belle-II Collaborations and on the recent theoretical progress in the calculation of the form factors relevant for semileptonic $$B \rightarrow D^* \ell \nu _\ell $$ B → D ∗ ℓ ν ℓ and $$B_s \rightarrow K \ell \nu _\ell $$ B s → K ℓ ν ℓ 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 $$R^{\textrm{th}}(D^*) = 0.262 \pm 0.009$$ R th ( D ∗ ) = 0.262 ± 0.009 and we extract from a bin-per-bin analysis of the experimental data the value $$\vert V_{cb} \vert = (39.92 \pm 0.64) \cdot 10^{-3}.$$ | V cb | = ( 39.92 ± 0.64 ) · 10 - 3 . Our result for $$R(D^*)$$ R ( D ∗ ) is consistent with the latest experimental world average $$R^{\textrm{exp}}(D^*) = 0.284 \pm 0.012$$ R exp ( D ∗ ) = 0.284 ± 0.012 (HFLAV Collaboration in Preliminary average of R(D) and $$R(D^*)$$ R ( D ∗ ) as for Summer 2023. See https://hflav-eos.web.cern.ch/hflav-eos/semi/summer23/html/RDsDsstar/RDRDs.html) at the $$\simeq 1.5\,\sigma $$ ≃ 1.5 σ level. Our value for $$\vert V_{cb} \vert $$ | V cb | is compatible with the latest inclusive determinations $$\vert V_{cb} \vert ^{\textrm{incl}} = (41.97 \pm 0.48) \cdot 10^{-3}$$ | V cb | incl = ( 41.97 ± 0.48 ) · 10 - 3 (Finauri and Gambino in The $$q^2$$ q 2 moments in inclusive semileptonic B decays. arXiv:2310.20324) and $$\vert V_{cb} \vert ^{\textrm{incl}} = (41.69\pm 0.63) \cdot 10^{-3}$$ | V cb | incl = ( 41.69 ± 0.63 ) · 10 - 3 (Bernlochner et al. in JHEP 10:068, 2022) within $$\simeq 2.6$$ ≃ 2.6 and $$\simeq 2.0$$ ≃ 2.0 standard deviations, respectively. From a reappraisal of the calculations of $$\vert V_{ub} \vert / \vert V_{cb} \vert ,$$ | V ub | / | V cb | , we also obtain $$\vert V_{ub} \vert / \vert V_{cb} \vert = 0.087\pm 0.009$$ | V ub | / | V cb | = 0.087 ± 0.009 in good agreement with the result $$\vert V_{ub} \vert / \vert V_{cb} \vert = 0.0844\pm 0.0056$$ | V ub | / | V cb | = 0.0844 ± 0.0056 from the latest FLAG review (Flavour Lattice Averaging Group (FLAG) Collaboration in Phys J C 82:869, 2022).