$O(\alpha_s v^2)$ correction to $e^+e^-\to J/\psi+\eta_c$ at $B$ factories

TL;DR

This paper calculates the combined alpha_s and v^2 corrections to the e+e- to J/psi+eta_c process within NRQCD, finding only mild effects on predictions and clarifying the origin of certain logarithmic terms.

Contribution

It provides the first detailed analysis of the ${ m O}( ext{alpha}_s v^2)$ correction to this process and derives asymptotic expressions for the relevant short-distance coefficients.

Findings

The ${ m O}( ext{alpha}_s v^2)$ correction mildly enhances NRQCD predictions.

Asymptotic expressions for short-distance coefficients are obtained.

Double logarithms are linked to helicity-suppressed channels.

Abstract

We investigate the ${\mathcal O}(\alpha_s v^2)$ correction to the $e^+e^-\to J/\psi+\eta_c$ process in the nonrelativistic QCD (NRQCD) factorization approach. Within some reasonable choices of the relative order-$v^2$ NRQCD matrix elements, we find that including this new ingredient of correction only mildly enhances the existing NRQCD predictions. We have also deduced the asymptotic expressions for the ${\mathcal O}(\alpha_s v^2)$ short-distance coefficients, and reconfirm the early speculation that at next-to-leading order in $\alpha_s$, the double logarithm of type $\ln^2 (s/m_c^2)$ appearing in various NRQCD short-distance coefficients is always associated with the helicity-suppressed channels.