Rare pionium decays and pion polarizability
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We calculate the decay of pionium atoms into two photons. The pion polarizabilities give rise to a 10% correction to the corresponding decay width for pointlike pions. This opens the possibility to obtain the difference between the electric and magnetic polarizability of the charged pion from a future measurement of the branching fraction of pionium into two photons. For such an experiment the ππ-scattering lengths would have to be known to better than 5% precision. We also comment on the contribution of the axial anomaly to the decay of pionium into γπ0.
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