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: The simple m(2)phi(2) potential as an inflationary model is coming under increasing tension with limits on the tensor-to-scalar ratio r and measurements of the scalar spectral index n(s). Cubic Galileon interactions in the context of the Horndeski action can potentially reconcile the observables. However, we show that this cannot be achieved with only a constant Galileon mass scale because the interactions turn off too slowly, leading also to gradient instabilities after inflation ends. Allowing for a more rapid transition can reconcile the observables but moderately breaks the slow-roll approximation leading to a relatively large and negative running of the tilt alpha(s) that can be of order n(s) – 1. We show that the observables on CMB and large scale structure scales can be predicted accurately using the optimized slow-roll approach instead of the traditional slow-roll expansion. Upper limits on vertical bar alpha(s)vertical bar place a lower bound of r greater than or similar to 0.005 and, conversely, a given r places a lower bound on vertical bar alpha(s)vertical bar, both of which are potentially observable with next generation CMB and large scale structure surveys.

Abstract: Within the framework of xenon-based double beta decay experiments, we propose the possibility to improve the background rejection of an electroluminescent Time Projection Chamber (EL TPC) by reducing the diffusion of the drifting electrons while keeping nearly intact the energy resolution of a pure xenon EL TPC. Based on state-of-the-art microscopic simulations, a substantial addition of helium, around 10 or 15 %, may reduce drastically the transverse diffusion down to 2.5 mm/root m from the 10.5 mm/root m of pure xenon. The longitudinal diffusion remains around 4 mm/root m. Light production studies have been performed as well. They show that the relative variation in energy resolution introduced by such a change does not exceed a few percent, which leaves the energy resolution practically unchanged. The technical caveats of using photomultipliers close to an helium atmosphere are also discussed in detail.