New Results in Kaon Physics from NA48 and KTEV

In the recent year many new results from kaon decays have been reported from both the NA48 experiment at CERN and the KTeV experiment at Fermilab. Both experiments have new and improved measurements of the parameter Re(epsilon'/epsilon) of direct CP violation in the neutral kaon system. Also several new results on rare and very rare K_L decays were reported. In addition, the NA48 collaboration has performed special high-intensity K_S run periods, with the first results now being available.Comment: Invited talk at the XXIII Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003, 14 pages, LaTeX, 12 eps figures. PSN FRAT0

New Results on Kaon Decays from NA48

New measurements of K_L and K_S decays from the NA48 experiment are presented. From data taken in the year 2001, the value of the K_e3 charge asymmetry has been determined to delta_L(e) = (3.317 +- 0.070(stat) +- 0.072 (syst)) x 10^-3. From a special high-intensity K_S run period performed in 2000, NA48 has found a limit of 1.4 x 10^-6 on the K_S -> 3 pi0 branching ratio and measured the parameter eta_000. The same data sample also leads to the first observation of the rare decay K_S -> pi0 gamma gamma. All results are still preliminary.Comment: 6 pages, 9 figures, to appear in the proceedings of the 38th Rencontres de Moriond, Electro-Weak Interactions and Unified Theories, Les Arcs, France, March 200

New NA48 Results on Kaon and Hyperon Decays

The NA48 Collaboration has obtained several new results on kaon and neutral hyperon decays. For hyperons we present new, very precise measurements on the Xi0 lifetime and the decay asymmetries of Xi0 -> Lamda gamma and Xi0 -> Sigma0 gamma. On kaon decays, we report on the first observation of the interference term between Inner Bremsstrahlung and Direct Emission in K+- -> pi+- pi0 gamma and on a new, accurate measurement of the form factor slopes in the semileptonic decay KL -> pi+- mu-+ nu.Comment: To appear in the proceedings of ICHEP06, 4 page

Wigner-Cusp in Kaon Decays and Determination of pi pi Scattering Lengths

In the last few years it has become possible to study low energy pi pi scattering in kaon decays to three pions, thanks to the high statistics measurement of K+- -> pi+- pi0 pi0 decays performed by the NA48/2 experiment at the CERN SPS. At the pi+ pi- threshold, the pi0 pi0 mass spectrum exhibits a Wigner-cusp, from which the S-wave pi pi scattering lengths are extracted with high precision. This measurement is complementary to the extraction of the scattering lengths from K_e4 decays, which is also performed by the NA48/2 experiment.Comment: 10 pages, proceedings of plenary talk at MENU 2007, FZ Juelich, Sep 2007 (final version after referee's comments

A Bishop surface with a vanishing Bishop invariant

We derive a complete set of invariants for a formal Bishop surface near a point of complex tangent with a vanishing Bishop invariant under the action of formal transformations. We prove that the modular space of Bishop surfaces with a vanishing Bishop invariant and with a fixed Moser invariant $s<\infty$ is of infinite dimension. We also prove that the equivalence class of the germ of a generic real analytic Bishop surface near a complex tangent with a vanishing Bishop invariant can not be determined by a finite part of the Taylor expansion of its defining equation. This answers, in the negative, a problem raised by J. Moser in 1985 after his joint work with Webster in 1983 and his own work in 1985