Determination of pion-pion scattering length from pionium decay

The s-wave π - π scattering lengths (αo and α2 for isospin 0 and 2, respectively) are fundamental manifestations of the breaking of chiral symmetry in the low-energy limit of QCD. We describe a model-independent method for determining the difference |αo - α2| from measurements of decay branching ratios of pionium, a bound atomic system of π+ and π-. The ratio of decay rates for atomic s-states to 2 γ vs. 2π0 (expected to be ∼ 0.5%) is directly related to |α0 - α 2|, in a way independent of principal quantum number or strong interaction corrections to the atomic wave functions. An optimal experimental determination would involve measurement of the 2γ decay probability for a tagged sample of pionium, produced in any bound or low-lying continuum state via reactions in a target of very low density (to inhibit collisional breakup of the atom). The need for low target density and clean tagging make such an experiment well suited to a cooled beam storage ring