Updates on the determination of Vcb , R(D*) and Vub / Vcb

We present an updated determination of the values of Vcb , | V cb | , R(D^*) R ( D ∗ ) and Vub / Vcb | V ub | / | V cb | based on the new data on semileptonic B → D^* ν _ 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 → D^* ν _ B → D ∗ ℓ ν ℓ and Bₛ → K ν _ 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 Rᵗʰ(D^*) = 0.262 ± 0.009 R th ( D ∗ ) = 0.262 ± 0.009 and we extract from a bin-per-bin analysis of the experimental data the value Vcb = (39.92 ± 0.64) · 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 Rᵉˣᵖ(D^*) = 0.284 ± 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 1.5\,σ ≃ 1.5 σ level. Our value for Vcb | V cb | is compatible with the latest inclusive determinations Vcb ⁱⁿᶜˡ = (41.97 ± 0.48) · 10⁻³ | V cb | incl = ( 41.97 ± 0.48 ) · 10 - 3 (Finauri and Gambino in The q² q 2 moments in inclusive semileptonic B decays. arXiv:2310.20324 ) and Vcb ⁱⁿᶜˡ = (41.69± 0.63) · 10⁻³ | V cb | incl = ( 41.69 ± 0.63 ) · 10 - 3 (Bernlochner et al. in JHEP 10:068, 2022) within 2.6 ≃ 2.6 and 2.0 ≃ 2.0 standard deviations, respectively. From a reappraisal of the calculations of Vub / Vcb , | V ub | / | V cb | , we also obtain Vub / Vcb = 0.087± 0.009 | V ub | / | V cb | = 0.087 ± 0.009 in good agreement with the result Vub / Vcb = 0.0844± 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).