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 $J/\psi$ and the ${\eta }_c$. We compute the matrix elements of leading order in the heavy-quark velocity $v$ and the matrix elements of relative order $v^2$. Our computation is based on the electromagnetic decay rates of the $J/\psi$ and the ${\eta }_c$ 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 $v^2$ are somewhat smaller than the values that one obtains from estimates that are based on the velocity-scaling rules of nonrelativistic QCD.