Detailed study of the KL→π0π0π0 Dalitz plot

Using a sample of 68.3×106 KL→π0π0π0 decays collected in 1996-1999 by the KTeV (E832) experiment at Fermilab, we present a detailed study of the KL→π0π0π0 Dalitz plot density. We report the first observation of interference from KL→π+π-π0 decays in which π+π- rescatters to π0π0 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, a0-a2. Using the Cabibbo-Isidori model, and fixing (a0-a2)mπ+=0. 268±0.017 as measured by the CERN-NA48 collaboration, we present the first measurement of the KL→π0π0π0 quadratic slope parameter that accounts for the rescattering effect: h000=(+0.59±0.20stat±0. 48syst±1.06ext)×10-3, where the uncertainties are from data statistics, KTeV systematic errors, and external systematic errors. Fitting for both h000 and a0-a2, we find h000=(-2.09±0.62stat±0. 72syst±0.28ext)×10-3, and mπ+(a0-a2)=0.215±0. 014stat±0.025syst±0.006ext; our value for a0-a2 is consistent with that from NA48.