Determination of the S-wave pi pi scattering lengths from a study of K+- ---> pi+- pi0 pi0 decays

We report the results from a study of the full sample of similar to 6.031 x 10(7) K(+/-) -> pi(+/-)pi(0)pi(0) decays recorded by the NA48/2 experiment at the CERN SPS. As first observed in this experiment, the pi(0)pi(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 pi(+)pi(-) -> pi(0)pi(0) in K(+/-) -> pi(+/-)pi(+)pi(-) 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 pi pi S-wave scattering lengths in the isospin I = 0 and I = 2 states. Higher-order pi pi rescattering terms, included in the two formulations, allow also an independent, though less precise, determination of a(2).