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.

arXiv commentAccepted by Chinese Physics C

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Cited by in corpus (2)

• Measurement of ${\Gamma }_{ee}(J/\psi )$ with KEDR detector
• Analytic forms for the $e^{+}{e}^{-}$ annihilation cross sections around a resonance including initial state radiation