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

We discuss the recent Cabibbo's proposal to measure the pi pi scattering lengths combination a(0) - a(2) from the cusp effect in the pi(0)pi(0) energy spectrum at threshold for K+ -> pi(0)pi(0)pi(+) and K-L -> pi(0)pi(0)pi(0). We estimate the theoretical uncertainty of the a(0) - a(2) determination at NLO in our approach and obtain that it is not smaller than 5% for K+ -> pi(0)pi(0)pi(+). One gets similar theoretical uncertainties if the neutral K-L -> pi(0)pi(0)pi(0) decay data below threshold axe used instead. For this decay, there axe very large theoretical uncertainties above threshold due to cancellations and data above threshold cannot be used to get the scattering lengths.