Order-alpha_s corrections to the quarkonium electromagnetic current at all orders in the heavy-quark velocity

TL;DR

This paper calculates order alpha_s corrections to the quarkonium electromagnetic current in NRQCD, introducing a new streamlined method for one-loop matching, and demonstrates the convergence of the velocity expansion for relevant matrix elements.

Contribution

It introduces a novel method using full-QCD expressions for one-loop NRQCD matching, simplifying calculations and confirming the convergence of the velocity expansion.

Findings

The new method streamlines one-loop NRQCD calculations.

The velocity expansion converges rapidly for J/psi operator matrix elements.

Results support the validity of the NRQCD velocity expansion under certain conditions.

Abstract

We compute in order alpha_s the nonrelativistic QCD (NRQCD) short-distance coefficients that match quark-antiquark operators of all orders in the heavy-quark velocity v to the electromagnetic current. We employ a new method to compute the one-loop NRQCD contribution to the matching condition. The new method uses full-QCD expressions as a starting point to obtain the NRQCD contribution, thus greatly streamlining the calculation. Our results show that, under a mild constraint on the NRQCD operator matrix elements, the NRQCD velocity expansion for the quark-antiquark-operator contributions to the electromagnetic current converges. The velocity expansion converges rapidly for approximate J/psi operator matrix elements.