Rare Pionium Decays and Pion Polarizability

TL;DR

This paper calculates the decay rate of pionium into two photons, highlighting how pion polarizability affects this process and proposing a method to measure pion polarizability differences through future experiments.

Contribution

It introduces a correction to pionium decay width accounting for pion polarizability and suggests a way to determine pion polarizability differences via branching fraction measurements.

Findings

Pion polarizability causes a 10% correction to decay width.

Future measurements could determine pion polarizability differences.

The decay into b3b3 is influenced by axial anomaly contributions.

Abstract

We calculate the decay of pionium atoms into two photons. The pion polarizability gives 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.