Agradecimentos: We gratefully acknowledge the support and effort of the Fermilab staff and the technical staffs of the participating institutions for their vital contributions. This work was supported in part by the U.S. Department of Energy, The National Science Foundation, The Ministry of Education and Science of Japan, Fundacao de Amparo a Pesquisa do Estado de Sao Paulo-FAPESP, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico-CNPq and CAPES-Ministerio Educao. We also wish to thank Gino Isidori for helpful discussions on implementing the CI3PI model for K-L ->pi(0)pi(0)pi(0) decays Ver menos

Abstract: Using a sample of 68.3x10(6) K-L ->pi(0)pi(0)pi(0) decays collected in 1996-1999 by the KTeV (E832) experiment at Fermilab, we present a detailed study of the K-L ->pi(0)pi(0)pi(0) Dalitz plot density. We report the first observation of interference from K-L ->pi(+)pi(-)pi(0) decays in which pi(+)pi(-) rescatters to pi(0)pi(0) in a final-state interaction. This rescattering effect is described by the Cabibbo-Isidori model, and it depends on the difference in pion scattering lengths between the isospin I=0 and I=2 states, a(0)-a(2). Using the Cabibbo-Isidori model, and fixing (a(0)-a(2))m(pi)(+)=0.268 +/- 0.017 as measured by the CERN-NA48 collaboration, we present the first measurement of the K-L ->pi(0)pi(0)pi(0) quadratic slope parameter that accounts for the rescattering effect: h(000)=(+0.59 +/- 0.20(stat)+/- 0.48(syst)+/- 1.06(ext))x10(-3), where the uncertainties are from data statistics, KTeV systematic errors, and external systematic errors. Fitting for both h(000) and a(0)-a(2), we find h(000)=(-2.09 +/- 0.62(stat)+/- 0.72(syst)+/- 0.28(ext))x10(-3), and m(pi)(+)(a(0)-a(2))=0.215 +/- 0.014(stat)+/- 0.025(syst)+/- 0.006(ext); our value for a(0)-a(2) is consistent with that from NA48 Ver menos