Abstract
Applying an operator product expansion approach we update the Standard Model prediction of the Bc 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 overline{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 Bc decay.
Highlights
Since both valence quarks in the Bc meson are heavy, the state is similar in structure to it’s quarkonium cousins, the ηc and ηb pseudoscalar mesons, the lightest members of the
This circumstance allows for an effective treatment in terms of Non-Relativistic QCD (NRQCD), where the anti-quark corresponding to the valence quark, or the quark corresponding to the valence anti-quark, is integrated out at the respective scale
Since we have chosen to match the Operator Product Expansion (OPE) directly to NRQCD the fields indicated should be those for NRQCD; by a slight abuse of notation, and in order to make the long expression more legible, we have denoted the fields in eq (5.25) and below in eq (5.26) as those of the full theory, but it should be understood that they really stand for fields in the effective theory, i.e., c → Ψ(+c) and b → X−(b)
Summary
The largest source of uncertainty in the calculation of the inclusive rate of the Bc decay is in the value of the pole mass. Pole masses are convenient for the perturbative calculations, but are beset by both computational and conceptual difficulties: their perturbative expansion is poorly convergent and suffers from a renormalon ambiguity. When expressed in terms of the pole mass, the perturbative rate suffers from a renormalon ambiguity. Eliminating the pole mass in favour of well defined (e.g., short distance) masses, gives a perturbative expansion of the rate that is free of renormalon ambiguities [38,39,40,41]. The leading term in the OPE for the decay width of Bc mesons is the perturbative Γb+Γc The corrections to those are expressed as products of non-perturbative matrix elements and Wilson coefficients. In the calculations below we use the same scheme choice for these sub-leading terms as for the leading ones
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