Polarization phenomena in process $e^++e^-\rightarrow N+\bar N+\gamma $

TL;DR

This paper investigates polarization effects and differential cross sections in electron-positron collisions producing nucleon-antinucleon pairs with an initial state photon, including collinear photon emission and various hadronic final states.

Contribution

It provides detailed calculations of polarization observables, cross sections, and photon energy distributions for different hadronic channels in $e^+e^-$ annihilation with initial state radiation.

Findings

Calculated nucleon polarization and correlation coefficients.

Derived photon energy distributions for multiple hadronic channels.

Analyzed effects of collinear photon emission on cross sections.

Abstract

The emission of the hard photon by the initial state is considered. The nucleon polarization and the differential cross sections for some experimental conditions have been calculated. The case of the emission of the collinear (with respect to the direction of the electron beam momentum) photon is considered separately. The differential cross section, the nucleon polarization, the correlation coefficients for both polarized nucleons (provided the electron beam is unpolarized or longitudinally polarized), the transfer polarization from the longitudinally polarized electron beam to the nucleon have been calculated. The photon energy distribution for the reaction $e^+e^-\to h_1h_2\gamma $, where $h_1 $ and $h_2$ are some hadrons for the case of the collinear photon, emitted in the initial state, has been calculated. As $h_1h_2$ final state we considered some channels, namely: two spinless mesons (for example, $\pi^+\pi^-, K^+K^-$), two spin--one particles (for example, $\rho^+\rho^-, d\bar d$), the $\pi a_1(1260)$ and $\Delta(1232)\bar N$ channels. The photon energy distributions are calculated in terms of the form factors of the $\gamma^*\to h_1h_2$ transition ($\gamma^*$ is the virtual photon).