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

TL;DR

The paper advances the determination of color-singlet S-wave NRQCD matrix elements for J/ψ and ηc by combining electromagnetic decay widths with a Cornell-potential-based input and by resumming a class of relativistic corrections via a generalized Gremm-Kapustin relation. It solves coupled nonlinear equations to extract both leading-order and relativistic (v^2) matrix elements, and performs a rigorous covariance analysis to quantify correlated uncertainties. The results show an increase in leading-order matrix elements due to relativistic effects, while the order-v^2 elements remain broadly consistent with velocity-scaling expectations; ηc values are obtained via two methods and averaged with spin-symmetry considerations. The study provides refined, correlated NRQCD inputs that should improve predictions for a wide range of charmonium decay and production processes and offers a comprehensive uncertainty framework for future work.

Abstract

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.