Observation of a cusp-like structure in the π 0 π 0 invariant mass distribution from K ± → π ± π 0 π 0 decay and determination of the ππ scattering lengths

Abstract We report the results from a study of a partial sample of ∼ 2.3 × 10 7 K ± → π ± π 0 π 0 decays recorded by the NA48/2 experiment at the CERN SPS, showing an anomaly in the π 0 π 0 invariant mass ( M 00 ) distribution in the region around M 00 = 2 m + , 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 − → π 0 π 0 in K ± → π ± π + π − decay [N. Cabibbo, Phys. Rev. Lett. 93 (2004) 121801]. It provides a precise determination of a 0 − a 2 , 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 0 − a 2 ) 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 0 and a 2 predicted by chiral symmetry is taken into account, this result becomes ( a 0 − a 2 ) m + = 0.264 ± 0.006 ( stat ) ± 0.004 ( syst ) ± 0.013 ( ext ) .