Two loop QCD corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ in asymptotic expansion

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 $\overline{\mathrm{MS}}$ mass scheme, with the uncertainty arising from the renormalization scale ${\mu }_R$ included. The ${\mu }_R$ uncertainty for predictions from the $\overline{\mathrm{MS}}$ 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.

arXiv comment9 pages, 4 figures, 1 tables, 1 attached file. Matches journal version

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