Polarization phenomena in the reaction $e^+ + e^- \to p + \bar p +\pi^0$ in frame of the non-resonant mechanism

TL;DR

This paper derives the nucleon polarization dependence in the reaction $e^+ + e^- o p + ar p + ext{pi}^0$ within a non-resonant framework, providing theoretical expressions and numerical estimates relevant for experimental analysis.

Contribution

It presents a theoretical derivation of nucleon polarization in the specified reaction using six invariant amplitudes, assuming electromagnetic current conservation and P-invariance, with numerical estimates for normal polarization.

Findings

Derived polarization dependence on invariant variables.

Expressed polarization in terms of six complex amplitudes.

Numerical estimates for normal polarization up to 16 GeV$^2$.

Abstract

The dependence of the nucleon polarization in the reaction $e^+ + e^- \to N + \bar{N} +\pi^0 $ over different invariant variables in frame of the non-resonant mechanism, has been derived. The nucleon polarization is expressed in terms of six invariant complex amplitudes, assuming the conservation of the hadron electromagnetic currents and the P-invariance of the hadron electromagnetic interaction. An inclusive experimental setup when the proton (or the antiproton) and the pion are detected in coincidence is considered. Numerical estimations were performed for the so called normal polarization in the energy range from threshold up to $s=16$ GeV$^2$, using a specific parametrization of the nucleon electromagnetic form factors and taking into account the unpolarized differential cross section of the non-resonant mechanism, as previously calculated.