Two-photon exchange effects in e+e−→π+π− and timelike pion electromagnetic form factor

Hong-Yu Chen,Hai-Qing Zhou

doi:10.1103/physrevd.98.054003

Hong-Yu Chen, Hai-Qing Zhou

Open Access

https://doi.org/10.1103/physrevd.98.054003

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Abstract

The two-photon-exchange (TPE) effects in the process $e^+e^- \rightarrow \pi^+\pi^-$ at large momentum transfer are discussed within the perturbative QCD (pQCD). The contributions from the twist-2 and twist-3 distribution amplitudes (DAs) of pion are considered in the estimation. Different with the results under the one-photon-exchange (OPE) approximation, the TPE effects result in an asymmetry of the differential cross section on the scattering angle. The precise measurement of this asymmetry by the further experiment is an precise test of pQCD at large momentum transfer. The time-like electromagnetic form factor of pion at the leading order of pQCD is re-discussed and the comparison of our results with those in the references are presented.

Highlights

The pion and the proton are the most elemental bound states due to the strong interaction
Since our focus is on the TPE effects in eþe− → πþπ−, we do not discuss the details of the dependence of the pion form factor Q2jFπðQ2Þj on the input distribution amplitudes (DAs)
The red dashed curves refer to the contribution from twist-2 DA, the blue dotted curves refer to the contribution from twist-3 DAs, the black solid curves refer to the contribution from their sum and the Exdata sets are taken from Ref. [41]

Summary

INTRODUCTION

The pion and the proton are the most elemental bound states due to the strong interaction. In 2000, the measurements of the ratio of the EM form factors of the proton by the polarized method [1,2] gave very different results from those given by the Rosenbluth method [3,4] This suggests the extraction of the EM form factors from the experimental data is a nontrivial problem. We arrange our work as follows: in Sec. II, we give a simple introduction on the cross section of eþe− → πþπ− and the timelike EM form factor of the pion by pQCD under the one-photon-exchange (OPE) approximation; in Sec. III we discuss the TPE effects in this process; in Sec. IV, we discuss the input used in our practical estimation; and in Sec. V, we give the numerical results and our conclusion

Published by the American Physical Society

Using the approximation me

NUMERICAL RESULTS AND DISCUSSION

This conclusion is very different from that given by