This paper reports world averages of measurements of b-hadron, c-hadron, and τ -lepton properties obtained by the Heavy Flavour Averaging Group using results available before April 2021. In rare cases, significant results obtained several months later are also used. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, CP violation parameters, parameters of semileptonic decays, and Cabibbo-Kobayashi-Maskawa matrix elements. Selected world averages -continued from previous page. ∆Γ d /Γ d 0.001 ± 0.010 |q d /p d | 1.0010 ± 0.0008 ∆m s 17.765 ± 0.006 ps −1 ∆Γ s +0.084 ± 0.005 ps −1 |q s /p s | 1.0003 ± 0.0014 φ ccs s −0.049 ± 0.019 rad Unitarity-Triangle angle parameters sin2β ≡ sin2φ 1 0.699 ± 0.017 β ≡ φ 1 (22.2 ± 0.7) • −ηS φK 0 S 0.74 +0.11 −0.13 −ηS η K 0 0.63 ± 0.06 −ηS K 0 S K 0 S K 0 S 0.83 ± 0.17 φ s (φφ) −0.073 ± 0.115 ± 0.027 rad S B 0 s →K + K − , C B 0 s →K + K − (0.14 ± 0.03, 0.17 ± 0.03) −ηS J/ψ π 0 0.86 ± 0.14 −ηS D + D − 0.84 ± 0.12 −ηS J/ψ ρ 0 0.66 +0.13 −0.12 +0.09 −0.03(0.343 ± 0.002)% τ parameters, lepton universality, and |V us | g τ /g µ 1.0009 ± 0.0014 g τ /g e 1.0027 ± 0.0014 g µ /g e 1.0019 ± 0.0014* )0 s B ( * )0 s ) = (87.0 ± 1.7)% [34] measured as described in Ref. [35]. The proportions of the various production channels for non-strange B mesons have also been measured [22]. 4.3 b-hadron production fractions at high energy At high energy, all species of weakly decaying b hadrons may be produced, either directly or in strong and electromagnetic decays of excited b hadrons. Before 2010, it was assumed that the fractions of different species in unbiased samples of high-p T b-hadron jets where independent of whether they originated from Z decays, pp collisions at the Tevatron, or pp collisions at the LHC. This hypothesis was plausible under the condition Q 2 Λ 2 QCD , namely, that the square of the momentum transfer to the produced b quarks is large compared with the square of the hadronization energy scale. This hypothesis is correct in the limit p T → ∞, in which the production mechanism of a b hadron is completely described by the fragmentation of the b quark. For finite p T , however, there are interference effects of the production mechanism of the b quark and its hadronization. While formally suppressed by inverse powers of p T , these effects may be sizable, especially when the fragmentation probabilities are small as, e.g., in the case of b baryons. In fact, the available data show that the fractions depend on the kinematics of the produced b hadron. Both CDF and LHCb reported a p T dependence of the fractions, with the fraction of Λ 0 b baryons observed at low p T being enhanced with respect to that seen at LEP at higher p T . In our previous publication [1], we presented two sets of averages, one including only measurements performed at LEP, and another including only measurements performed ...

We report a measurement of the branching fraction ratios R(D ( * ) ) ofB → D ( * ) τ −ν τ relative tō B → D ( * ) −ν (where = e or µ) using the full Belle data sample of 772 × 10 6 BB pairs collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. The measured values are R(D) = 0.375 ± 0.064(stat.) ± 0.026(syst.) and R(D * ) = 0.293 ± 0.038(stat.) ± 0.015(syst.). The analysis uses hadronic reconstruction of the tag-side B meson and purely leptonic τ decays. The results are consistent with earlier measurements and do not show a significant deviation from the standard model prediction.

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