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 $\Gamma (B^+) = (0.58^{+0.11}_{-0.07}) \, \mbox{ps}^{-1}$, $\Gamma (B_d) = (0.63^{+0.11}_{-0.07}) \, \mbox{ps}^{-1}$, $\Gamma (B_s) = (0.63^{+0.11}_{-0.07}) \, \mbox{ps}^{-1}$, and for the lifetime ratios $\tau (B^+) / \tau (B_d) = 1.086 \pm 0.022$, $\tau (B_s) / \tau (B_d) = 1.003 \pm 0.006 \, (1.028 \pm 0.011)$. The two values for the last observable arise from using two different sets of input for the non-perturbative parameters $\mu_\pi^2(B_d)$, $\mu_G^2(B_d)$, and $\rho_D^3(B_d)$ 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 $\tau (B_s)/\tau (B_d)$ when considering the second set of input parameters. Specifically, this observable is extremely sensitive to the size of the parameter $\rho_D^3 (B_d)$ 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 $\mu_\pi^2 (B_s), \mu_G^2 (B_s), \rho_D^3 (B_s)$ 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 $\rho_D^3 (B)$ extracted from fit, would be very helpful in reducing the corresponding theory uncertainties.