Observation of a cusp-like structure in the π0π 0 invariant mass distribution from K±→π ±π0π0 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 π π 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).