Analytic forms for the $e^+e^-$ annihilation cross sections around a resonance including initial state radiation

TL;DR

This paper derives exact analytic formulas for $e^+e^-$ annihilation cross sections near a resonance, incorporating initial state radiation and other effects, to improve precision and computational efficiency in experimental physics.

Contribution

It provides new analytic expressions for cross sections including initial state radiation, vacuum polarization, and energy spread effects, enhancing measurement accuracy and computational speed.

Findings

Achieves precision below 0.1% for cross sections including radiative effects.

Improves the accuracy of physical parameter measurements like branching fractions.

Enhances computational efficiency in data analysis procedures.

Abstract

The exact analytic form of cross sections including initial state radiation with Kuraev-Fadin radiative function are obtained for $e^+e^-$ annihilation around a resonance. Despite accounting for vacuum polarization and center-of-mass energy spread effects, the precision remains below 0.1\%, meeting the accuracy requirements of quantum electrodynamics corrections up to $\mathcal{O}(\alpha^2)$. The analytic forms lead to an enhancement in the precision of experimental measurements of physical parameters, such as branching fractions, and demonstrate significantly improved computational efficiency in the regression procedures.