Final State Interactions and Khuri-Treiman Equations in η → 3π decays 1

Abstract

Using extended Khuri-Treiman equations, we evaluate the final state interactions due to two-pion rescatterings to the decays η → π0π + π − and η → π0π0π0. As subtraction to the dispersion relation we take the one-loop chiral perturbation theory result of Gasser and Leutwyler. The calculated corrections are moderate and amount to about 14 % in the amplitude at the center of the decay region. A careful analysis of the errors inherent to our approach is given. As a consequence, the experimental rate of the decay can only be reproduced if the double quark mass ratio Q−2 ≡ md−mu md+mu ms − ˆm ms+ ˆm is increased from the usual value of 1/(24.1) 2 to 1/(22.4 ± 0.9) 2. We have also calculated the ratio of the rates of the two decays and various Dalitz Plot parameters. In particular, the linear slope a in the charged decay is different from the one-loop value and agrees better with experiment.