Analytical Forms for Cross Sections of Di-lepton Production from $e^+e^-$ Collisions around the $J/ψ$ Resonance
A detailed theoretical derivation of the cross sections of $e^+e^- \to e^+e^-$ and $e^+e^- \to μ^+μ^-$ around the $J/ψ$ resonance is reported. The resonance and interference parts of the cross sections, related to $J/ψ$ 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 $ψ(3686)$ resonance.
hep-ph↗