Two loop QCD corrections to $e^+ e^- \to J/\psi + \eta_c$ in asymptotic expansion

TL;DR

This paper calculates two-loop QCD corrections to the process $e^+ e^- o J/ au + au_c$ using asymptotic expansion, providing reliable predictions for cross sections across various energies and comparing different mass schemes.

Contribution

The paper derives NNLO short-distance coefficients for $e^+ e^- o J/ au + au_c$ in asymptotic expansion, extending previous calculations and enabling accurate phenomenological predictions.

Findings

Asymptotic expressions approximate full results within 3% for $r<0.8$.

Predicted cross sections are consistent with experimental data.

Uncertainty from renormalization scale is quantified in both mass schemes.

Abstract

Within the framework of NRQCD, the short-distance coefficients (SDCs) for the process $e^+e^-\to J/\psi+\eta_c$ have been obtained up to NNLO in asymptotic expansions over $r={16m_c^2}/{s}$ up to $r^{15}$. Although these asymptotic expressions are deviated from the full results near the threshold $r= 1$, they provide excellent approximations to the full results for $r<0.8$, with deviations less than $3\%$. Therefore, these asymptotic expressions offer reliable applications for phenomenological predictions across a wide range of center-of-mass energies $\sqrt{s}$. Utilizing these asymptotic expressions, we present phenomenological predictions for the cross sections in both the on-shell mass scheme and the $\overline{\rm MS}$ mass scheme, with the uncertainty arising from the renormalization scale $\mu_R$ included. The $\mu_R$ uncertainty for predictions from the $\overline{\rm MS}$ mass scheme is slightly larger than that from the on-shell mass scheme, which is partly attributed to the helicity flip in the process $e^+e^-\to J/\psi+\eta_c$. We observe that both mass schemes yield quite similar predictions, and our theoretical results are consistent with the available experimental data.