Small-momentum expansion of heavy-quark correlators in the large-$\beta_0$ limit and $\alpha_s$ extractions

TL;DR

This paper computes the small-momentum expansion of heavy-quark correlators in the large-$eta_0$ limit, providing insights into the perturbative behavior of moments used for precise $ alpha_s$ extraction from quarkonium sum rules and lattice data.

Contribution

It extends the analysis of heavy-quark correlators beyond the vector current in the large-$eta_0$ limit, revealing partial renormalon cancellation and guiding improved moment combinations.

Findings

Ratios of moments show partial cancellation of renormalon singularities.

Results inform the design of moments with better perturbative convergence.

Analysis extends previous work to additional correlators.

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.