The recent discovery of a large CP violating asymmetry in KL-->pi+pi-e+e- mode has prompted us to seach for the associated KL-->pi 0 pi 0 e+e- decay mode in the KTeV-E799 experiment at Fermilab. In 2.7 x 10(11) K(L) decays, one candidate event has been observed with an expected background of 0.3 event, resulting in an upper limit for the KL-->pi 0 pi 0 e+e- branching ratio of 6.6 x 10(-9) at the 90% C.L.

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The KTeV/E799 experiment at Fermilab has searched for the rare kaon decay K(L)-->pi(0)e(+)e(-). This mode is expected to have a significant CP violating component. The measurement of its branching ratio could support the standard model or could indicate the existence of new physics. This Letter reports new results from the 1999-2000 data set. One event is observed with an expected background at 0.99+/-0.35 events. We set a limit on the branching ratio of 3.5x10(-10) at the 90% confidence level. Combining with the previous result based on the data set taken in 1997 yields the final KTeV result: BR(K(L)-->pi(0)e(+)e(-))<2.8x10(-10) at 90% C.L.

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We present a measurement of the charge asymmetry δ L in the mode K L → π ± e ∓ ν based on 298 million analyzed decays. We measure a value of δ L = (3322 ± 58(stat) ± 47(sys)) · 10 −6 , in good agreement with previous measurements and 2.4 times more precise than the current best published result. The result is used to place more stringent limits on CPT and ∆S = ∆Q violation in the neutral kaon system. PACS numbers: 11.30. Er, 13.25.Es, The charge asymmetry in K L semileptonic decays is deeply related to CP violation through neutral kaon mixing. TheBR(e + π − ) + BR(e − π + ) . Assuming ∆S = ∆Q and no CPT violation in the decayTo first order in the parameters that violate CP and CPT,The terms Y and Re(x −x) parameterize CPT violation in the ∆S = ∆Q and ∆S = −∆Q transitions respectively[1, 2]:In the Standard Model, the ∆S = ∆Q violation is CPTconserving and occurs in 2nd order weak decays. Estimates for |x| are in the range 10 −7 [3]. δ L is modified to order |x| 2 and will not be considered in this letter.

We present a series of measurements based on KL,S → π + π − and KL,S → π 0 π 0 decays collected in 1996-1997 by the KTeV experiment (E832) at Fermilab. We compare these four K → ππ decay rates to measure the direct CP violation parameter Re(ǫ ′ /ǫ) = (20.7 ± 2.8) × 10 −4 . We also test CPT symmetry by measuring the relative phase between the CP violating and CP conserving decay amplitudes for K → π + π − (φ+−) and for K → π 0 π 0 (φ00). We find the difference between the relative phases to be ∆φ ≡ φ00 − φ+− = (+0.39 ± 0.50)• , and the deviation of φ+− from the superweak phase to be φ+− − φSW = (+0.61 ± 1.19)• ; both results are consistent with CPT symmetry. In addition, we present new measurements of the KL-KS mass difference and KS lifetime: ∆m = (5261 ± 15)×10 6h s −1 and τS = (89.65 ± 0.07)×10 −12 s .

The KTeV experiment at Fermilab has isolated a total of 132 events from the rare decay KL → e + e − µ + µ − , with an estimated background of 0.8 events. The branching ratio of this mode is determined to be (2.69±0.24stat ±0.12syst)×10 −9 , with a radiative cutoff of M 2 eeµµ /M 2 K > 0.95. The first measurement using this mode of the parameter α from the D'Ambrosio, Isidori, and Portolès model of the KL γ * γ * vertex yields a result of −1.59 ± 0.37, consistent with values obtained from other decay modes. Because of the limited statistics, no sensitivity is found to the DIP parameter β. The magnitude of the angular distribution asymmetry between the e + e − and µ + µ − planes, indicative of a CP −violating contribution to the decay, is found to be consistent with zero. We set a 90% C.L. upper limit of 4.12 × 10 −11 on the branching ratio of the lepton flavor-violating mode KL → e ± e ± µ ∓ µ ∓ , a factor of three improvement over the current limit from the KTeV experiment.PACS numbers: 13.20. Eb, 14.40.Aq, 12.15.Hh, 11.30.Er, 11.30.Fs The rare decay K L → e + e − µ + µ − offers the most direct means for studying the dynamics of the K L γ * γ * vertex. This information is useful for models that relate the K L → µ + µ − branching ratio to ρ, the real part of the CKM matrix element V td [1,2,3]. This decay mode can also be used to determine the presence of any CP −violating contributions to the K L γ * γ * interaction [4]. Additionally, a search for the lepton flavorviolating counterpart K L → e ± e ± µ ∓ µ ∓ provides a constraint on physics beyond the Standard Model.In the model of D'Ambrosio, Isidori, and Portolès (DIP) [5], the K L γ * γ * form factor can be written asHere, q 1 and q 2 are the momenta of the two virtual photons, and M ρ is the mass of the ρ vector meson. In this model, α and β are two arbitrary real parameters and are expected to be of order one. The determination of both α and β is possible through the decay K L → e + e − µ + µ − by examining the dilepton invariant masses and the integrated decay rate. Knowledge of the K L γ * γ * form factor is important for understanding the long distance contributions to K L → µ + µ − and extracting the value of ρ [5].Two measurements have been made of the linear DIP parameter α to date, both by the KTeV collaboration. From the mode K L → µ + µ − γ , the shape of the dimuon invariant mass distribution (M µµ ) and the measured branching ratio have been used to determine α = −1. 54 ± 0.10 [6]. A fit to the dielectron mass distribution (M ee ) from K L → e + e − e + e − determines α = −1.1 ± 0.6 [7], where the larger error results from the smaller q 2 of the dielectron distribution. No measurements have yet been made of the quadratic DIP pa-

We present the first measurement of the form factor ratios g(1)/f(1) (direct axial vector to vector), g(2)/f(1) (second class current), and f(2)/f(1) (weak magnetism) for the decay Xi(0)-->Sigma(+)e(-)nu macro(e) using the KTeV (E799) beam line and detector at Fermilab. From the Sigma(+) polarization measured with the decay Sigma(+)-->p pi(0) and the e(-)-nu; correlation, we measure g(1)/f(1) to be 1.32+/-(0.21)(0.17)(stat)+/-0.05(syst), assuming the SU(3)(f) (flavor) values for g(2)/f(1) and f(2)/f(1). Our results are all consistent with exact SU(3)(f) symmetry.