Leptonic widths of heavy quarkonia: QCD/NRQCD matching for the electromagnetic current at O(alpha_s v^2)

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Scientific paper

We construct the S-wave part of the electromagnetic vector annihilation current to O(αs v2 ), where v is the non-relativistic quark velocity, for heavy quarks whose dynamics are described by the ¯ NRQCD action on the lattice. The NRQCD vector current for QQ annihilation is expressed as a linear combination of lattice operators with quantum numbers L = 0, J P = 1- , and the coefficients are determined by matching to the corresponding continuum current in QCD to O(v2 ) at one- loop. The annihilation channel gives a complex amplitude with Coulomb-exchange and infrared singularities, making a careful choice for the contours of integration and infrared subtraction functions in the numerical integration necessary. 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 is applicable to simulations of electromagnetic decays of heavy quarkonia, notably the ϒ meson.

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