Reconciling charmonium production and polarization data within the nonrelativistic QCD framework

TL;DR

This paper demonstrates that by focusing on a key ratio of long-distance matrix elements, the nonrelativistic QCD framework can simultaneously explain charmonium production rates and polarization measurements, resolving previous inconsistencies.

Contribution

The authors introduce a universal method for determining LDMEs that successfully reconciles production and polarization data within the NRQCD framework.

Findings

Key polarization parameter is the ratio of specific LDMEs.

Fitted LDMEs produce consistent production and polarization results.

Theoretical corrections affect LDMEs but not phenomenological outcomes.

Abstract

A thorough study reveals that the only key parameter for $\psi$ ($J/\psi$, $\psi'$) polarization is the ratio $\langle O^\psi(^3S_1^{[8]})\rangle/\langle O^\psi(^3P_0^{[8]})\rangle$, if the velocity scaling rule holds. The fit of the yield data is incapable of the determination of this parameter. We provide a universal approach to fixing the long-distance matrix elements (LDMEs) for the $J/\psi$ and $\psi'$ production. Further, with the existing data, we implement this approach, and obtain a favorable set of the LDMEs, and manage to reconcile the charmonia production and polarization experiment. A quantitative analysis indicates that theoretical corrections to the short-distance coefficients change only the values of the LDMEs but not the phenomenological results.