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

35 pages, 5 figures, 7 tables

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Cited by in corpus (10)

• Study of singly heavy baryon lifetimes
• The heavy quark expansion for lifetimes: Towards the QCD corrections to power suppressed terms
• Dispersive constraints on fermion masses
• Quark-hadron duality at work: lifetimes of bottom baryons
• Revisiting lifetimes of doubly charmed baryons
• Collider-Flavour Complementarity from the bottom to the top
• ${\tau }_{B_s}/{\tau }_{B_d}$ and $\Delta {\Gamma }_s$ confront new physics in $b\to s\tau \tau$
• HQET sum rules for matrix elements of dimension-six four-quark operators for meson lifetimes within and beyond the Standard Model
• Precision measurement of the $B^0$ meson lifetime using $B^0\to J/\psi K^{\ast 0}$ decays with the ATLAS detector
• $B\to X_c\ell \bar{\nu }$ Decay as a Probe of Complex Conjugate Poles