Unified dispersive approach to $γ^*\toγππ$ and $γγ\toππ$

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

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