On the measurement of $\chi_2(^3P_2)$ quarkonium state in the processes $e^++e^-\to \bar p+p$ and $\bar p+p\to e^++e^-$

TL;DR

This paper investigates the backward-forward asymmetry in electron-positron and proton-antiproton annihilation processes mediated by the $ ext{chi}_2(^3P_2)$ quarkonium state, using dispersion relations to relate asymmetry to decay widths.

Contribution

It introduces a method to calculate asymmetry effects near the resonance using dispersion relations and compares these effects with those involving the Z-boson.

Findings

Asymmetry effects are less than 10^{-3} near the resonance.

Main source of asymmetry is pure QED, around 10^{-2}.

The energy dependence of asymmetry is characterized near the resonance.

Abstract

The intermediate quarkonium state $\chi_2(^3P_2)$ in electron-positron annihilation to proton and antiproton as well as in antiproton-proton annihilation to electron and positron can produce backward-forward asymmetry, when populated through two photon exchange. We use the dispersion relation method, which permits to express the asymmetry in terms of partial widths of quarkonium decay. The asymmetry dependence on the center of mass energy in the range near the resonance is presented. The comparison with a similar effect in these reactions with the neutral $Z$-boson in the intermediate state is given. We show that these effects are $\le 10^{-3}$. The main source of asymmetry is of pure QED origin ($\sim 10^{-2}$) which arises from the interference between initial and final state real photon emission.