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

Abstract

We compute in order ${\ensuremath{\alpha}}_{s}$ 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 $J/\ensuremath{\psi}$ operator matrix elements.