$O({\alpha }_s{v}^2)$ correction to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ at $B$ factories

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.

Comments: v3, 6 pages, 2 figures, 1 table; matching the published version