I shortly review the present status of the theoretical calculations of ε/ε and the comparison with the present experimental results. I discuss the role of higher order chiral corrections and in general of non-factorizable contributions for the explanation of the ∆I = 1/2 selection rule and direct CP violation in kaon decays. Still lacking satisfactory lattice calculations, analytic methods and ...

This paper deals with the passage from discrete to continuous in modeling the static elastic properties, in the setting of anti-planar linear elasticity, of vertical screw dislocations in a cylindrical crystal. We study, in the framework of Γ-convergence, the asymptotic behavior of the elastic stored energy induced by dislocations as the atomic scale ε tends to zero, in the regime of dilute dis...

CP violation occurs in the Standard Model through the imaginary phase in the CKM mixing matrix. An alternative mechanism, proposed shortly after the discovery of the effect, is a superweak interaction. The latter can be ruled out by experimental observation of direct CP violation, parametrized by ε. Theoretical calculations of ε within the Standard Model are hard, but most predictions give ε/ε ...

We present O(log logn)-round algorithms in the Massively Parallel Computation (MPC) model, with Õ(n) memory per machine, that compute a maximal independent set, a 1 + ε approximation of maximum matching, and a 2+ ε approximation of minimum vertex cover, for any n-vertex graph and any constant ε > 0. These improve the state of the art as follows: • Our MIS algorithm leads to a simple O(log log∆)...

ε-support vector regression (ε-SVR) can be converted into an unconstrained convex and non-smooth quadratic programming problem. It is not solved by the traditional algorithm. In order to solve this non-smooth problem, a class of piecewise smooth functions is introduced to approximate the ε-insensitive loss function of ε-SVR, which generates a ε-piecewise smooth support vector regression (ε-dPWS...

We review the theory of ε/ε and present an updated phenomenological analysis using hadronic matrix elements from lattice QCD. The present status of the computation of ε/ε, considering various approaches to the matrix-element evaluation, is critically discussed. ⋆ based on the talks given by M.C. at “Les Rencontres de Physique de la Vallée d’Aoste”, La Thuile (Italy), 27 February–4 March 2000 an...

The long-distance contributions to K → 2π amplitudes can be pinned down, using well established Chiral Perturbation Theory techniques. The strong S–wave rescattering of the two final pions generates sizeable chiral loop corrections, which have an important impact on the direct CP violation ratio ε/ε [1,2]. Including all large logarithmic corrections, both at short and long distances, the Standa...