Improved determination of color-singlet nonrelativistic QCD matrix elements for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-wave charmonium

Abstract

We present a new computation of $S$-wave color-singlet nonrelativistic QCD matrix elements for the $J/\ensuremath{\psi}$ and the ${\ensuremath{\eta}}_{c}$. 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 $J/\ensuremath{\psi}$ and the ${\ensuremath{\eta}}_{c}$ 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.