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.
Highlights
As one of the most simple bound states of strong interaction, the pion plays an important role in studying the strong interaction
The precise measurements of the structures such as the electromagnetic (EM) form factors (FFs) of the pion and the nucleon provide a precise test of our understanding of QCD
It is well known that the two-photon-exchange (TPE) contributions are important to be considered in the precise extraction of the EM FFs of the proton via the unpolarized elastic ep scattering [1,2,3,4,5,6]
Summary
As one of the most simple bound states of strong interaction, the pion plays an important role in studying the strong interaction. The ratio between this function and the corresponding contribution in one-photon exchange c1(1γ ) reflects all the information of the TPE corrections.
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