Observation of a cusp-like structure in the pi(0)pi(0) invariant mass distribution from K-+/-->pi(+/-)pi(0)pi(0) decay and determination of the pi pi scattering lengths

We report the results from a study of a partial sample of similar to 2.3 x 10(7) K+/- -> pi(+/-)pi(0)pi(0) decays recorded by the NA48/2 experiment at the CERN SPS, showing an anomaly in the pi(0)pi(0) invariant mass (M-00) distribution in the region around M-00 = 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 pi(+)pi(-) -> pi(0)pi(0) in K+/- -> pi(+/-)pi(+)pi(-) decay [N. Cabibbo, Phys. Rev. Lett. 93 (2004) 121801]. It provides a precise determination of a(0) - a(2), the difference between the pi pi 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 a2 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). (c) 2005 Elsevier B.V. All rights reserved.