Disintegration of beauty: a precision study

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.