Standard Model prediction of the $B_c$ lifetime

Abstract

Applying an operator product expansion approach we update the Standard Model prediction of the $B_c$ lifetime from over 20 years ago. The non-perturbative velocity expansion is carried out up to third order in the relative velocity of the heavy quarks. The scheme dependence is studied using three different mass schemes for the $\bar{b}$ and $c$ quarks, resulting in three different values consistent with each other and with experiment. Special focus has been laid on renormalon cancellation in the computation. Uncertainties resulting from scale dependence, neglecting the strange quark mass, non-perturbative matrix elements and parametric uncertainties are discussed in detail. The resulting uncertainties are still rather large compared to the experimental ones, and therefore do not allow for clear-cut conclusions concerning New Physics effects in the $B_c$ decay.

42 pages, 1 figure

References in corpus (7)

• Big-Bang Nucleosynthesis
• Measurement of the branching ratio of ${\bar{B}}^0\to D^{\ast +}{\tau }^{-}{\bar{\nu }}_{\tau }$ relative to ${\bar{B}}^0\to D^{\ast +}{\ell }^{-}{\bar{\nu }}_{\ell }$ decays with a semileptonic tagging method
• The lifetime of the $B_c^{-}$ meson and the anomalies in $B\to D^{(\ast )}\tau \nu$
• The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD
• Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order
• Heavy-to-heavy quark decays at NNLO
• Third order corrections to the semi-leptonic \boldmath{$b\to c$} and the muon decays

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