One-loop scalar integrals contributing to resummation of relativistic corrections to Γ[J/ψ → e⁺e^-]

We evaluate the scalar integrals that are necessary to compute the relativistic corrections to the QCD one-loop vertex corrections to the leptonic decay of the spin-triplet S-wave heavy quarkonium H resummed to all orders in the heavy-quark velocity v. Ultraviolet and infrared divergences are regularized by using dimensional regularization. A relativistic expansion of the results reproduces previous results for the order-v² corrections. Our results will be very useful in determining the color-singlet nonrelativistic quantum chromodynamics matrix elements for the spin-triplet S-wave heavy quarkonia.