Observation of a cusp-like structure in the ππ invariant mass distribution from K→πππ decay and determination of the ππ scattering lengths

We report the results from a study of a partial sample of ∼2.3×10K→πππ decays recorded by the NA48/2 experiment at the CERN SPS, showing an anomaly in the ππ invariant mass (M) distribution in the region around M=2m, where m is the charged pion mass. This anomaly, never observed in previous experiments, can be interpreted as an effect due mainly to the final state charge exchange scattering process ππ→ππ in K→πππ decay [N. Cabibbo, Phys. Rev. Lett. 93 (2004) 121801]. It provides a precise determination of a-a, the difference between the ππ scattering lengths in the isospin I=0 and I=2 states. A best fit to a rescattering model [N. Cabibbo, G. Isidori, JHEP 0503 (2005) 21] corrected for isospin symmetry breaking gives (a-a)m=0.268±0.010(stat)±0.004(syst), with additional external uncertainties of ±0.013 from branching ratio and theoretical uncertainties. If the correlation between a and a predicted by chiral symmetry is taken into account, this result becomes (a-a)m=0.264±0.006(stat)±0.004(syst)±0.013(ext).