Analytic 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^- → e⁺e^- and e⁺e^- → 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. (authors)