B decays in the upsilon expansion

TL;DR

The paper introduces the upsilon expansion, a modified perturbative framework that rewrites B-decay predictions in terms of the Υ(1S) mass rather than the $b$-quark mass. By using ε counting that treats αs corrections differently in the Υ mass and in decay rates, the approach achieves renormalon cancellation and improved convergence for both inclusive and exclusive observables. The method yields more stable extractions of CKM elements $|V_{cb}|$ and $|V_{ub}|$, tighter control over nonperturbative uncertainties, and consistent predictions for form-factor ratios like $R_1(1)$, semileptonic branching ratios, and charm counting. The dominant remaining theoretical uncertainty lies in nonperturbative contributions to the Υ mass, which can be constrained by experimental data on shape variables and exclusive form factors.

Abstract

Theoretical predictions for B decay rates are rewritten in terms of the Upsilon(1S) meson mass instead of the b quark mass, using a modified perturbation expansion. The theoretical consistency of this expansion is shown both at low and high orders. Our method improves the behavior of the perturbation series for semileptonic and nonleptonic inclusive decay modes, as well as for exclusive decay form factors. The results are applied to the determination of the semileptonic B branching ratio, charm counting, the ratio of B -> X tau nu and B -> X e nu decay rates, and form factor ratios in B -> D* e nu decay. We also comment on why it is not possible to separate perturbative and nonperturbative effects in QCD.

Figures (1)

• Figure 1: One-loop correction to the heavy quark self energy, and the tree-level contribution to the $Q\bar{Q}$ potential.