Disintegration of beauty: a precision study

Abstract

Abstract We update the Standard Model (SM) predictions for B-meson lifetimes within the heavy quark expansion (HQE). Including for the first time the contribution of the Darwin operator, SU(3)F breaking corrections to the matrix element of dimension-six four-quark operators and the so-called eye-contractions, we obtain for the total widths $$ \Gamma \left({B}^{+}\right)=\left({0.58}_{-0.07}^{+0.11}\right){\textrm{ps}}^{-1},\Gamma \left({B}_d\right)=\left({0.63}_{-0.07}^{+0.11}\right){\textrm{ps}}^{-1},\Gamma \left({B}_s\right)=\left({0.63}_{-0.07}^{+0.11}\right){\textrm{ps}}^{-1} $$ Γ B + = 0.58 − 0.07 + 0.11 ps − 1 , Γ B d = 0.63 − 0.07 + 0.11 ps − 1 , Γ B s = 0.63 − 0.07 + 0.11 ps − 1 , and for the lifetime ratios τ(B+)/τ(Bd) = 1.086 ± 0.022, τ(Bs)/τ(Bd) = 1.003 ± 0.006 (1.028 ± 0.011). The two values for the last observable arise from using two different sets of input for the non-perturbative parameters $$ {\mu}_{\pi}^2\left({B}_d\right),{\mu}_G^2\left({B}_d\right) $$ μ π 2 B d , μ G 2 B d , and $$ {\rho}_D^3\left({B}_d\right) $$ ρ D 3 B d as well as from different estimates of the SU(3)F breaking in these parameters. Our results are overall in very good agreement with the corresponding experimental data, however, there seems to emerge a tension in τ(Bs)/τ(Bd) when considering the second set of input parameters. Specifically, this observable is extremely sensitive to the size of the parameter $$ {\rho}_D^3\left({B}_d\right) $$ ρ D 3 B d and of the SU(3)F breaking effects in $$ {\mu}_{\pi}^2,{\mu}_G^2 $$ μ π 2 , μ G 2 and $$ {\rho}_D^3 $$ ρ D 3 ; hence, it is of utmost importance to be able to better constrain all these parameters. In this respect, an extraction of $$ {\mu}_{\pi}^2\left({B}_s\right),{\mu}_G^2\left({B}_s\right),{\rho}_D^3\left({B}_s\right) $$ μ π 2 B s , μ G 2 B s , ρ D 3 B s from future experimental data on inclusive semileptonic Bs-meson decays or from direct non-perturbative calculations, as well as more insights about the value of $$ {\rho}_D^3(B) $$ ρ D 3 B extracted from fits to inclusive semileptonic B-decays, would be very helpful in reducing the corresponding theory uncertainties.