Dispersive analysis of the decay η → 3π

Abstract

We demonstrate that the decay η → 3π represents a sensitive probe for the breaking of chiral symmetry by the quark masses. The transition amplitude is proportional to the mass ratio (m d 2 − m u 2) (m s 2 − m ̂ 2) . The factor of proportionality is calculated by means of dispersion relations, using chiral perturbation theory to determine the subtraction constants. The theoretical uncertainties in the result are shown to be remarkably small, so that η-decay may be used to accurately measure this ratio of quark masses.