Measuring the a0–a2 pion scattering lengths through K→3π decays

We discuss the recent Cabibbo's proposal to measure the ππ scattering lengths combination a0–a2 from the cusp effect in the π0π0 energy spectrum at threshold for K+→π0π0π+ and KL→π0π0π0. We estimate the theoretical uncertainty of the a0–a2 determination at NLO in our approach and obtain that it is not smaller than 5 % for K+→π0π0π+. One gets similar theoretical uncertainties if the neutral KL→π0π0π0 decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations and data above threshold cannot be used to get the scattering lengths.