Radiative corrections in image decays Original Research Article

We investigate radiative corrections to image decays. In particular, we extend the non-relativistic framework developed recently to include real and virtual photons and show that, in a well-defined power counting scheme, the results reproduce corrections obtained in the relativistic calculation. Real photons are included exactly, beyond the soft-photon approximation, and we compare the result with the latter. The singularities generated by pionium near threshold are investigated, and a region is identified where standard perturbation theory in the fine structure constant α may be applied. We expect that the formulae provided allow one to extract S-wave ππ scattering lengths from the cusp effect in these decays with high precision.