Convergence properties of $$eta rightarrow 3pi $$ decays in chiral perturbation theory

The convergence of the decay widths and some of the Dalitz plot parameters of the decay (eta rightarrow 3pi ) seems problematic in low energy QCD. In the framework of resummed chiral perturbation theory, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters a and d can be described very well too. When the parameters b and (alpha ) are concerned, we find a mild tension for the whole range of the free parameters, at less than 2(sigma ) C.L. This can be interpreted in two ways – either some of the higher order corrections are indeed unexpectedly large or there is a specific configuration of the remainders, which is, however, not completely improbable.