Disintegration of beauty: a precision study

TL;DR

This paper refines Standard Model predictions for B-meson lifetimes by including new contributions and corrections, achieving good agreement with experimental data but highlighting the need for better parameter constraints.

Contribution

First to incorporate the Darwin operator and SU(3)$_F$ breaking corrections into B-meson lifetime calculations within the heavy quark expansion.

Findings

Predicted B-meson widths and lifetime ratios closely match experimental data.

Identified sensitivity of $ au(B_s)/ au(B_d)$ to non-perturbative parameters.

Highlighted the importance of constraining non-perturbative parameters for accurate predictions.

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 $\Gamma (B^+) = (0.58^{+0.11}_{-0.07}) \, \mbox{ps}^{-1}$, $\Gamma (B_d) = (0.63^{+0.11}_{-0.07}) \, \mbox{ps}^{-1}$, $\Gamma (B_s) = (0.63^{+0.11}_{-0.07}) \, \mbox{ps}^{-1}$, 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.