A discussion on vacuum polarization correction to the cross-section of e ⁺ e ⁻ → γ ^* / ψ → μ ⁺ μ ⁻

Abstract

Vacuum polarization is a part of the initial-state radiative correction for the cross-section of e + e − annihilation processes. In the energy region in the vicinity of narrow resonances J/ψ and ψ(3686), the vacuum polarization contribution from the resonant component has a significant effect on the line-shape of the lepton pair production cross-section. This paper discusses some basic concepts and describes an analytical calculation of the cross-section of e + e − → γ * /ψ → µ + µ − considering the single and double vacuum polarization effect of the virtual photon propagator. Moreover, it presents some numerical comparisons with the traditional treatments.