A discussion on vacuum polarization correction to the cross-section of $e^{+}{e}^{-}\to {\gamma }^{\ast }/\psi \to {\mu }^{+}{\mu }^{-}$

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 $J/\psi$ and $\psi (3686)$, 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 $e^{+}{e}^{-}\to {\gamma }^{\ast }/\psi \to {\mu }^{+}{\mu }^{-}$ considering the single and double vacuum polarization effect of the virtual photon propagator. Moreover, it presents some numerical comparisons with the traditional treatments.

15 pages,14 figures