Final state interactions and Khuri-Treiman equations in,ν → 3π decays Original Research Article

Using extended Khuri-Treiman equations, we evaluate the final state interactions due to two-pion rescatterings to the decays ν → π0π+π− and ν → 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 − m.)(ms − m)̂]·[(md + mu)(ms + m)̂] 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.