Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium

We present a new computation of S-wave color-singlet nonrelativistic QCD matrix elements for the J/ψ and the ηc. We compute the matrix elements of leading order in the heavy-quark velocity v and the matrix elements of relative order v2. Our computation is based on the electromagnetic decay rates of the J/ψ and the ηc and on a potential model that employs the Cornell potential. We include relativistic corrections to the electromagnetic decay rates, resumming a class of corrections to all orders in v, and find that they significantly increase the values of the matrix elements of leading order in v. This increase could have important implications for theoretical predictions for a number of quarkonium decay and production processes. The values that we find for the matrix elements of relative order v2 are somewhat smaller than the values that one obtains from estimates that are based on the velocity-scaling rules of nonrelativistic QCD.