Disintegration of beauty: a precision study

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}_dright)=left({0.63}_{-0.07}^{+0.11}right){textrm{ps}}^{-1},Gamma left({B}_sright)=left({0.63}_{-0.07}^{+0.11}right){textrm{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}^2left({B}_dright),{mu}_G^2left({B}_dright) , and {rho}_D^3left({B}_dright) 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^3left({B}_dright) and of the SU(3)F breaking effects in {mu}_{pi}^2,{mu}_G^2 and {rho}_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}^2left({B}_sright),{mu}_G^2left({B}_sright),{rho}_D^3left({B}_sright) 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) extracted from fits to inclusive semileptonic B-decays, would be very helpful in reducing the corresponding theory uncertainties.