Observation of a cusp-like structure in the π0π0 invariant mass distribution from K± -> π± π0 π0 decay and determination of the ππ scattering lengths

We report the results from a study of a partial sample of ∼2.3×10^7 K±→π±π0 π0 decays recorded by the NA48/2 experiment at the CERN SPS, showing an anomaly in the π0 π0 invariant mass (M00) distribution in the region around M00 =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 π+ π-→ π0 π0 in K± →π±π+ π-decay [N. Cabibbo, Phys. Rev. Lett. 93 (2004) 121801]. It provides a precise determination of a0 − a2, 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 (a0−a2) 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 a0 and a2 predicted by chiral symmetry is taken into account, this result becomes (a0 −a2)m+ = 0.264±0.006(stat)± 0.004(syst) ±0.013(ext).