We report on a new measurement of the branching ratio B(KL → π 0 γγ) using the KTeV detector. We reconstruct 1982 events with an estimated background of 608, that results in B(KL → π 0 γγ) = (1.29 ± 0.03stat ± 0.05syst) × 10 −6. We also measure the parameter, aV , which characterizes the strength of vector meson exchange terms in this decay. We find aV = −0.31 ± 0.05stat ± 0.07syst. These results utilize the full KTeV data set collected from 1997 to 2000 and supersede earlier KTeV measurements of the branching ratio and aV .

The branching ratio of the rare decay 0 ! e e ÿ has been measured precisely, using the complete data set from the KTeV E799-II experiment at Fermilab. We observe 794 candidate 0 ! e e ÿ events using K L ! 3 0 as a source of tagged 0 s. The expected background is 52:7 11:2 events, predominantly from high e e ÿ mass 0 ! e e ÿ decays. We have measured B 0 ! e e ÿ ; m e e ÿ =m 0 2 > 0:95 6:44 0:25 stat 0:22 syst 10 ÿ8 , which is above the unitary bound from 0 ! and within the range of theoretical expectations from the standard model.

We present precise tests of CP and CPT symmetry based on the full dataset of K → ππ decays collected by the KTeV experiment at Fermi National Accelerator Laboratory during 1996, 1997, and 1999. This dataset contains 16 million K → π 0 π 0 and 69 million K → π + π − decays. We measure the direct CP violation parameter Re(ǫ−4 . We find the KL-KS mass difference ∆m = (5270 ± 12)×10 6 s −1 and the KS lifetime τS = (89.62 ± 0.05)×10 −12 s. We also measure several parameters that test CPT invariance. We find the difference between the phase of the indirect CP violation parameter, ǫ, and the superweak phase, φǫ − φSW = (0.40 ± 0.56)• . We measure the difference of the relative phases between the CP violating and CP conserving decay amplitudes for K → π + π − (φ+−) and for K → π 0 π 0 (φ00), ∆φ = (0.30 ± 0.35)• . From these phase measurements, we place a limit on the mass difference between K 0 and K 0 , ∆M < 4.8 × 10 −19 GeV/c 2 at 95% C.L. These results are consistent with those of other experiments, our own earlier measurements, and CPT symmetry.

Based on a large number of smearing steps, we classify SU͑3͒ gauge field configurations in different topological sectors. For each sector we compare the exact analytical predictions for the microscopic Dirac operator spectrum of quenched staggered fermions. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero, showing explicitly that the smallest Dirac operator eigenvalues of staggered fermions at presently realistic lattice couplings are insensitive to gauge field topology. On the smeared configurations, 4 eigenvalues clearly separate out from the rest on configurations of topological charge , and move towards zero in agreement with the index theorem.