General analysis and numerical estimations of polarization observables in $\bar N+N\to \pi+ e^++e^-$ reaction in an exclusive experimental setup

TL;DR

This paper derives general formulas for polarization observables in the ar N + N f reaction, analyzing their dependence on kinematic variables and applying the results to probe proton form factors in an exclusive experimental setup.

Contribution

It provides a comprehensive theoretical framework for polarization observables in ar N + N f reactions, including explicit dependence on kinematic variables and application to form factor analysis.

Findings

Derived general expressions for polarization observables.

Explicit dependence on azimuthal angle and virtual photon parameter.

Application to proton form factors in the Born approximation.

Abstract

The dependence of the differential cross section and polarization observables in the $\bar N+N\to \pi +e^++e^-$ reaction on the polarizations of the proton target and antiproton beam (the produced electron may be unpolarized or longitudinally polarized) have been derived in a general form using hadron electromagnetic current conservation and $P-$ invariance of the hadron electromagnetic interaction. The analysis was done for the case of an exclusive experimental setup where the produced electron and pion are detected in coincidence. The explicit dependence of all polarization observables on two, from five, kinematic variables (the azimuthal angle $\varphi$ and the virtual-photon parameter $\epsilon$), have been obtained assuming one-photon-exchange. The application to the particular case of a mechanism which contains information on time-like proton form factors in the unphysical region is considered in the Born approximation.