Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions

Abstract

We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-${\beta }_0$ limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our results are used to study the higher-order behaviour of dimensionless ratios of vector and pseudo-scalar moments used for the precise extraction of the strong coupling, ${\alpha }_s$, from relativistic quarkonium sum rules and lattice data, respectively. We show that these ratios benefit from a partial cancellation of the leading renormalon singularities. Our results can guide the design of combinations of moments with improved perturbative behaviour.

Comments: 27 pages, 7 figures. References added. Version to appear in JHEP