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

TL;DR

This paper analyzes how vacuum polarization corrections, especially near narrow resonances like J/ψ, significantly affect the cross-section of muon pair production in electron-positron annihilation, providing analytical calculations and numerical comparisons.

Contribution

It offers an analytical approach to calculating vacuum polarization effects on the cross-section near narrow resonances, including single and double polarization effects, with numerical comparisons to traditional methods.

Findings

Vacuum polarization significantly influences the cross-section near resonances.

Analytical formulas for single and double vacuum polarization effects are derived.

Numerical comparisons show differences from traditional treatments.

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.