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A representation of the amplitude $\gamma^*(q^2)\to\gamma\pi\pi$ is proposedwhich combines large $N_c$ chiral resonance Lagrangian modelling with generalunitarity 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, thecontribution 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.

Unified dispersive approach to $\gamma^*\to\gamma\pi\pi$ and $\gamma\gamma\to\pi\pi$