Abstract: In 1988 the NA31 experiment presented the first evidence of direct CP violation in the K-0 -> pi pi decay amplitudes. A clear signal with a 7.2 sigma statistical significance was later established with the full data samples from the NA31, E731, NA48 and KTeV experiments, confirming that CP violation is associated with a Delta S = 1 quark transition, as predicted by the Standard Model. However, the theoretical prediction for the measured ratio epsilon'/epsilon has been a subject of strong controversy along the years. Although the underlying physics was already clarified in 2001, the recent release of improved lattice data has revived again the theoretical debate. We review the current status, discussing in detail the different ingredients that enter into the calculation of this observable and the reasons why seemingly contradictory predictions were obtained in the past by several groups. An update of the Standard Model prediction is presented and the prospects for future improvements are analysed. Taking into account all known short-distance and long-distance contributions, one obtains Re (epsilon' / epsilon) = (15 +/- 7) . 10(-4), in good agreement with the experimental measurement.

Abstract: A bonus of the framed Standard Model (FSM), constructed initially to explain the mass and mixing patterns of quarks and leptons, is a solution (without axions) of the strong CP problem by cancelling the theta-angle term theta(I) Tr(H-mu v H-mu v*) in coloura by a chiral transformation on a quark zero mode which is inherent in FSM, and produces thereby a CP-violating phase in the CKM matrix similar in size to what is observed.' Extending here to flavour, one finds that there are two terms proportional to Tr(G(mu v) G(mu v)*): (a) in the action from flavour instantons with unknown coefficient, say theta(I)', (b) induced by the above FSM solution to the strong CP-problem with therefore known coefficient theta(C)'. Both terms can be cancelled in the FSM by a chiral transformation on the lepton zero mode to give a Jarlskog invariant J' in the PMNS matrix for leptons of order 10(-2), as is hinted by the experiment. But if, as suggested in Ref. 2, the term theta(I)' is to be cancelled by a chiral transformation in the predicted hidden sector to solve the strong CP problem therein, leaving only the term theta(C)' to be cancelled by the chiral transformation on leptons, then the following prediction results: J' similar to -0.012 (delta(CP)'similar to (1.11)pi) which is (i) of the right order, (ii) of the right sign and (iii) in the range favoured by the present experiment. Together with the earlier result for quarks, this offers an attractive unified treatment of all known CP physics.

Abstract: We study resonant CP-violating Einstein-Podolsky-Rosen correlations that may take place in the production and decay of unstable scalar particles at high-energy colliders. We show that as a consequence of unitarity and CPT invariance of the S-matrix, in 2 -> 2 scatterings mediated by mixed scalar particles, at least three linearly independent decay matrices associated with the unstable scalar states are needed to obtain non-zero CP-odd observables that are also odd under C-conjugation. Instead, for the correlated production and decay of two unstable particle systems in 2 -> 4 processes, we find that only two independent decay matrices are sufficient to induce a net non-vanishing CP-violating phenomenon. As an application of this theorem, we present numerical estimates of CP asymmetries for the correlated production and decay of supersymmetric scalar top anti-top pairs at the LHC, and demonstrate that these could reach values of order one. As a byproduct of our analysis, we develop a novel spinorial trace technique, which enables us to efficiently evaluate lengthy expressions of squared amplitudes describing the resonant scalar transitions.