Leptonic widths of heavy quarkonia: S-wave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current at O({alpha}{sub s}v{sup 2})

We construct the S-wave part of the electromagnetic vector annihilation current to O({alpha}{sub s}v{sup 2}) on the lattice for heavy quarks whose dynamics are described by the NRQCD action, and v is the nonrelativistic quark velocity inside the meson. The lattice vector current for QQ annihilation is expressed as a linear combination of lattice operators with quantum numbers L=0, J{sup P}=1{sup -}, and the coefficients are determined by matching this lattice current to the corresponding continuum current in QCD to O(v{sup 2}) at one-loop. The annihilation channel gives a complex amplitude and a proper choice for the contours of integration is needed; a simple Wick rotation is not possible. In this way, and with a careful choice of subtraction functions in the numerical integration, the Coulomb-exchange and infrared singularities appearing in the amplitudes are successfully treated. The matching coefficients are given as a function of the heavy quark mass Ma in lattice units. An automated vertex generation program written in Python is employed, allowing us to use a realistic NRQCD action and an improved gluon lattice action. A change in the definition of either action is easily accommodated in this procedure. The final result, when combined with lattice simulation results,more » describes the electromagnetic decays of heavy quarkonia, notably the {upsilon} meson.« less