QCD radiative corrections to J/ψ leptonic decay by using the scalar-integral reduction method

We study the scalar-integral reduction method, which uses the integration-by-parts method, in calculating α _s corrections to heavy-quarkonium amplitudes. We apply this method to leptonic decay of the spin-triplet S-wave heavy quarkonium as an illustrative example. All possible scalar integrals are reduced into a single master integral in the J/ψ → ℓ ⁺ℓ ^- decay at this order. One drawback of this method is that one cannot avoid a mixture of ultraviolet (UV) and infrared (IR) poles during the reduction. We show a way to classify the origin of divergences in loop integrals in the scalar-integral reduction method. We expect this method to be useful in constructing a fast algebraic algorithm for QCD radiative corrections to quarkonium processes.