Rare pionium decays and pion polarizability

H.-W. Hammer; J.N. Ng

doi:doi:10.1007/s100500050324

EPJ

Rare pionium decays and pion polarizability

H.-W. Hammer - J.N. Ng

TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., V6T 2A3 Canada

Received: 1 March 1999 / Revised version: 31 May 1999 Communicated by W. Weise

Abstract
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 $\pi\pi$ -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 $\gamma\pi^0$ .

PACS
36.10.Gv Mesonic atoms and molecules, hyperonic atoms and molecules - 14.40.Aq $\pi$ , K and $\eta$ mesons - 13.40.-f Electromagnetic processes and properties

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