Determination of the S-wave π π scattering lengths from a study of K±→ π± π0 π0 decays.

We report the results from a study of the full sample of ∼6.031×10⁷ K^±→ π^± π⁰ π⁰ decays recorded by the NA48/2 experiment at the CERN SPS. As first observed in this experiment, the π⁰ π⁰ invariant mass ( M₀₀) distribution shows a cusp-like anomaly in the region around M₀₀=2 m₊, 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⁻→ π⁰ π⁰ in K^±→ π^± π⁺ π⁻ decay. Fits to the M₀₀ distribution using two different theoretical formulations provide the presently most precise determination of a₀− a₂, 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 a₂. [ABSTRACT FROM AUTHOR]