Color-octet nonrelativistic QCD matrix elements for heavy quarkonium decays in the refined Gribov-Zwanziger theory

Abstract

We determine color-octet nonrelativistic QCD matrix elements for quarkonium decays from moments of the two-point correlation function of the QCD field-strength tensor computed in the refined Gribov-Zwanziger theory. We find that a tree-level calculation in the refined Gribov-Zwanziger theory can give a suitable description of the QCD field-strength correlation function at both short and long distances, which leads to moments that are infrared finite and can be properly renormalized. By using the color-octet matrix elements we obtain, we quantitatively improve the nonrelativistic effective field theory description of quarkonium decay rates, especially for the $\chi_{QJ}$ and $\eta_Q$ states, where $Q =c$ or $b$.