Determination of the S-wave π π scattering lengths from a study of K ±→π ± π 0 π 0 decays

We report the results from a study of the full sample of ∼6.031×107 K ±→π ± π 0 π 0 decays recorded by the NA48/2 experiment at the CERN SPS. As first observed in this experiment, the π 0 π 0 invariant mass (M 00) distribution shows a cusp-like anomaly in the region around M 00=2m +, where m + is the charged pion mass. This anomaly has been interpreted as an effect due mainly to the final state charge exchange scattering process π + π −→π 0 π 0 in K ±→π ± π + π − decay. Fits to the M 00 distribution using two different theoretical formulations provide the presently most precise determination of a 0−a 2, the difference between the π π S-wave scattering lengths in the isospin I=0 and I=2 states. Higher-order π π rescattering terms, included in the two formulations, allow also an independent, though less precise, determination of a 2.