Periodic interference structures in the time-like proton form factor

TL;DR

This paper identifies sinusoidal patterns in the proton timelike form factor data, suggesting rescattering processes at specific distances that contribute to the imaginary part of the form factor, revealing complex inelastic interactions.

Contribution

It provides the first evidence of periodic interference structures in the timelike proton form factor linked to rescattering effects at sub-femtometer scales.

Findings

Sinusoidal modulation observed in form factor data near threshold.

Rescattering processes occur at 0.7-1.5 fm distance.

Large inelastic contributions inferred from the imaginary part.

Abstract

An intriguing and elusive feature of the timelike hadron form factor is the possible presence of an imaginary part associated to rescattering processes. We find evidence of that in the recent and precise data on the proton timelike form factor measured by the BABAR collaboration. By plotting these data as a function of the 3-momentum of the relative motion of the final proton and antiproton, a systematic sinusoidal modulation is highlighted in the near-threshold region. Our analysis attributes this pattern to rescattering processes at a relative distance of 0.7-1.5 fm between the centers of the forming hadrons. This distance implies a large fraction of inelastic processes in $\bar{p}p$ interactions, and a large imaginary part in the related $e^+e^- \rightarrow \bar{p}p$ reaction because of unitarity.