Small-momentum expansion of heavy-quark correlators in the large-β0 limit and αs extractions

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.

Automated summary

We calculate the small-momentum expansion of heavy-quark current correlators in QCD large-beta(0) limit, extending previous analysis. Our results are utilized to study the higher-order behavior of dimensionless ratios for the extraction of strong coupling alpha(s). These ratios show partial cancellation of leading renormalon singularities, guiding the design of combinations of moments with improved perturbative behavior.