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

Abstract

We present a theoretical study of the $\gamma {\gamma }^{\ast }\to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ processes from the threshold through the $f_2(1270)$ region in the $\pi \pi$ invariant mass. We adopt the Omnès 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.

Comments: 8 pages, 4 figures (journal version)