Soft rescattering in the timelike proton form factor within a spacetime scheme

TL;DR

This paper investigates how soft rescattering effects influence the timelike proton form factor, especially near the proton-antiproton threshold, using a spacetime formalism to account for annihilation and meson production processes.

Contribution

It introduces a spacetime-based analysis of soft rescattering corrections to the timelike proton form factor, including effects of proton-antiproton annihilation into mesons.

Findings

Soft rescattering affects the real and imaginary parts of the form factor.

Proton-antiproton annihilation into mesons influences the phase of the form factor.

Near the threshold, the form factor's phase may differ between production and annihilation processes.

Abstract

The annihilation of a lepton pair into a proton-antiproton pair, and the reverse process, allow for a measurement of the timelike proton form factors. This work aims at studying the corrections due to direct soft interactions between the proton and the antiproton before their annihilation or after their creation. The analysis is carried on in the spacetime formalism used by us in a series of recent works on timelike FFs. In particular the effect of $\bar{p}p$ annihilation into many-meson states is considered. We expect it to determine similar real and imaginary parts for the form factor near the $\bar{p}p$ channel threshold. We also discuss the possibility that the timelike FF differ by a phase in the hadron pair production and annihilation.