Analytical Forms for Cross Sections of Di-lepton Production from $e^{+}{e}^{-}$ Collisions around the $J/\psi$ Resonance

Abstract

A detailed theoretical derivation of the cross sections of $e^{+}{e}^{-}\to e^{+}{e}^{-}$ and $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ around the $J/\psi$ resonance is reported. The resonance and interference parts of the cross sections, related to $J/\psi$ resonance parameters, are calculated. Higher-order corrections for vacuum polarization and initial-state radiation are considered. An arbitrary upper limit of radiative correction integration is involved. Full and simplified versions of analytic formulae are given with precision at the level of 0.1% and 0.2%, respectively. Moreover, the results obtained in the paper can be applied to the case of the $\psi (3686)$ resonance.

Accepted by Chinese Physics C