Isospin breaking in pion Compton scattering

Using chiral perturbation theory we calculate for pion Compton scattering the isospin-breaking effects induced by the difference between the charged and neutral pion mass. At one-loop order this correction is directly proportional to m²_π± -m²_π0 and free of (electromagnetic) counterterm contributions. The differential cross-section for charged pion Compton scattering π^-γ → π^-γ gets affected (in backward directions) at the level of a few permille. At the same time the isospin-breaking correction leads to a small shift of the pion polarizabilities by δ(α_π-β_π) ≃ 1.3 ̇ 10^-5 fm³. In case of the low-energy γ γ → π⁰π⁰ reaction isospin breaking manifests itself through a cusp effect at the π⁺ π^- threshold. We give an improved estimate for it based on the empirical π π -scattering length difference a₀-a₂.