Resummation of relativistic corrections toe+e−→J/ψ+ηc

Abstract

We present a new calculation, in the nonrelativistic QCD (NRQCD) factorization formalism, of the relativistic corrections to the double-charmonium cross section $\ensuremath{\sigma}[{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c}]$ at the energy of the Belle and BABAR experiments. In comparison with previous work, our calculation contains several refinements. These include the use of the improved results for the nonperturbative NRQCD matrix elements, the resummation of a class of relativistic corrections, the use of the vector-meson-dominance method to calculate the fragmentation contribution to the pure QED amplitude, the inclusion of the effects of the running of $\ensuremath{\alpha}$, and the inclusion of the contribution that arises from the interference between the relativistic corrections and the corrections of next-to-leading order in ${\ensuremath{\alpha}}_{s}$. We also present a detailed estimate of the theoretical uncertainty. We conclude that the discrepancy between the theoretical prediction for $\ensuremath{\sigma}[{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c}]$ and the experimental measurements has been resolved.