Unified dispersive approach to ${\gamma }^{\ast }\to \gamma \pi \pi$ and $\gamma \gamma \to \pi \pi$

Abstract

A representation of the amplitude ${\gamma }^{\ast }(q^2)\to \gamma \pi \pi$ is proposed which combines large $N_c$ chiral resonance Lagrangian modelling with general unitarity and analyticity properties. The amplitude is constrained from $\gamma \gamma$ scattering results and $e^{+}{e}^{-}\to \gamma {\pi }^0{\pi }^0$ measurements by the CMD-2 and SND collaborations. As an application, the contribution of the $\pi \pi +\gamma$ states in the HVP contribution to the muon $g-2$ are reconsidered, taking into account the effect of the strong $S$-wave $\pi \pi$ rescattering in a model independent way.

Comments: 5 pages. To appear in the proceedings of "The International Workshop on e+e- collisions from Phi to Psi 2013", Rome sept. 2013