Fine structure of the cross sections of $e^{+}e^{-}$ annihilation near the thresholds of $p\bar{p}$ and $n\bar{n}$ production

TL;DR

This paper investigates the detailed energy dependence of cross sections for proton-antiproton, neutron-antineutron, and meson production near threshold energies in electron-positron annihilation, considering Coulomb and mass difference effects.

Contribution

It provides a refined analysis of cross section behavior near thresholds, highlighting limitations of the factorization approach due to finite optical potential effects.

Findings

Cross sections are highly sensitive to optical potential parameters.

The factorization approach fails near thresholds due to finite potential size.

Coulomb and mass difference effects significantly influence cross section energy dependence.

Abstract

The energy dependence of the cross sections of $p\bar p$, $n\bar n$, and meson production in $e^+e^-$ annihilation in the vicinity of the $p\bar p$ and $n\bar n$ thresholds is studied. The proton-neutron mass difference and the $p\bar p$ Coulomb interaction are taken into account. The values of the cross sections are very sensitive to the parameters of the optical potential. It is shown that the commonly accepted factorization approach for the account of the Coulomb interaction does not work well enough in the vicinity of the threshold due to the finite size of the optical potential well.