Dispersive analysis of the $\gamma\gamma^{*} \to \pi \pi$ process

TL;DR

This paper develops a dispersive theoretical framework for analyzing the gamma gamma* to pi pi processes, incorporating rescattering effects and coupled-channel unitarity, to interpret experimental data and aid in muon g-2 calculations.

Contribution

It introduces a comprehensive dispersive approach using Omnès representation and coupled-channel unitarity for the first time in this context.

Findings

Provides a detailed amplitude analysis of gamma gamma* to pi pi processes.

Offers a framework compatible with current experimental data from BESIII.

Contributes to the theoretical input for muon g-2 hadronic light-by-light scattering estimates.

Abstract

We present a theoretical study of the $\gamma\gamma^{*} \to \pi^+\pi^-, \pi^0\pi^0$ processes from the threshold through the $f_2(1270)$ region in the $\pi\pi$ invariant mass. We adopt the Omn\`es representation in order to account for rescattering effects in both s- and d-partial waves. For the description of the $f_0(980)$ resonance, we implement a coupled-channel unitarity. The constructed amplitudes serve as an essential framework to interpret the current experimental two-photon fusion program at BESIII. They also provide an important input for the dispersive analyses of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment.