Disintegration of beauty: a precision study

A bstract 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 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 ( B d ) = 1 . 086 ± 0 . 022, τ ( B s ) /τ ( B d ) = 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 μ π 2 B d , μ G 2 B d , and 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 ( B s ) /τ ( B d ) when considering the second set of input parameters. Specifically, this observable is extremely sensitive to the size of the parameter ρ D 3 B d and of the SU(3) F breaking effects in μ π 2 , μ G 2 and ρ D 3 ; hence, it is of utmost importance to be able to better constrain all these parameters. In this respect, an extraction of μ π 2 B s , μ G 2 B s , ρ D 3 B s from future experimental data on inclusive semileptonic B s -meson decays or from direct non-perturbative calculations, as well as more insights about the value of ρ D 3 B extracted from fits to inclusive semileptonic B -decays, would be very helpful in reducing the corresponding theory uncertainties.