Two-photon exchange effects in $e^+ e^-\rightarrow\pi^+\pi^-$ at small $ \sqrt{s}$

TL;DR

This paper investigates the two-photon exchange effects in electron-positron to pion pair production at low energies using a hadronic model, providing numerical results and a fitting function for experimental analysis.

Contribution

It introduces a scalar function to describe TPE effects in the process and offers a practical fitting function for experimental data interpretation.

Findings

TPE effects cause about -4% asymmetry in differential cross sections at 0.7 GeV.

Numerical ratio of TPE to one-photon exchange contributions is presented.

A fitting function for TPE corrections is proposed for experimental use.

Abstract

In this work, the two-photon-exchange (TPE) effects in $e^+e^- \rightarrow \pi^+ \pi^-$ at small $\sqrt{s}$ are discussed within a hadronic model. In the limit $m_e\rightarrow 0$, the TPE contribution to the amplitude can be described by one scalar function $\overline{c}_{1}^{(2\gamma)}$. The ratio between this function and the corresponding contribution in one-photon exchange $c_{1}^{(1\gamma)}$ reflects all the information of the TPE corrections. The numerical results on this ratio are presented and an artificial function is used to fit the numerical results. The latter can be used conveniently in the further experimental data analysis. The numerical results show the asymmetry of the differential cross sections in $e^+e^- \rightarrow \pi^+ \pi^-$ is about $-4\%$ at $\sqrt{s}\sim 0.7$ GeV.