Supersymmetric Explanation of CP Violation in K→ππ Decays

Exploring the flavour structure of the high-scale MSSM

We analyse the sensitivity of quark flavour-changing observables to the MSSM, in a regime of heavy superpartners. We analyse four distinct and motivated frameworks characterising the structure of the soft-breaking terms by means of approximate flavour symmetries. We show that a set of six low-energy observables with realistic chances of improvement in the near future, namely Δ M s , d , ϵ K ,ϵ K ' / ϵ K , B ( K → π ν ν ¯ ) , and the phase of D-D ¯ mixing, could play a very important role in characterising these frameworks for superpartner masses up to O ( 100 )  TeV. We show that these observables remain very interesting even in a long-term perspective, i.e. even taking into account the direct mass reach of the most ambitious future high-energy colliders.

Direct CP violation in [Formula: see text]: Standard Model Status

In 1988 the NA31 experiment presented the first evidence of direct CP violation in the [Formula: see text] decay amplitudes. A clear signal with a [Formula: see text] 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 [Formula: see text] quark transition, as predicted by the Standard Model. However, the theoretical prediction for the measured ratio [Formula: see text] 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 [Formula: see text], in good agreement with the experimental measurement.

Theory of rare K decays

I review rare kaon decays. I introduce the flavor problem and possible solutions. Very rare kaon decays like K → πvv¯ are very important to this purpose: we study also K → πl+l-, K → ππee where chiral dynamics is important to disentangle short distance effects. We discuss also the decays K0 → μ+μ-, which have received recently some attention due to the measurement by LHCB.

Standard Model and New physics for ε′k/εk

The first result of the lattice simulation and improved perturbative calculations have pointed to a discrepancy between data on ε′k/εk and the standard-model (SM) prediction. Several new physics (NP) models can explain this discrepancy, and such NP models are likely to predict deviations of ℬ(K → πvv) from the SM predictions, which can be probed precisely in the near future by NA62 and KOTO experiments. We present correlations between ε′k/εk and ℬ(K → πvv) in two types of NP scenarios: a box dominated scenario and a Z-penguin dominated one. It is shown that different correlations are predicted and the future precision measurements of K → πvv can distinguish both scenarios.

Direct CP Violation in K→μ^{+}μ^{-}

A rare decay K_{L}→μ^{+}μ^{-} has been measured precisely, while a rare decay K_{S}→μ^{+}μ^{-} will be observed by an upgrade of the LHCb experiment. Although both processes are almost CP-conserving decays, we point out that an interference contribution between K_{L} and K_{S} in the kaon beam emerges from a genuine direct CP violation. It is found that the interference contribution can change K_{S}→μ^{+}μ^{-} standard-model predictions at O(60%). We also stress that an unknown sign of A(K_{L}→γγ) can be determined by a measurement of the interference, which can much reduce a theoretical uncertainty of B(K_{L}→μ^{+}μ^{-}). We also investigate the interference in a new physics model, where the ε_{K}^{'}/ε_{K} tension is explained by an additional Z-penguin contribution.

Final state interactions in [Formula: see text] decays: [Formula: see text] rule vs. [Formula: see text]

Dispersive effects from strong [Formula: see text] rescattering in the final state interaction (FSI) of weak [Formula: see text] decays are revisited with the goal to have a global view on their relative importance for the [Formula: see text] rule and the ratio [Formula: see text] in the standard model (SM). We point out that this goal cannot be reached within a pure effective (meson) field approach like chiral perturbation theory in which the dominant current-current operators governing the [Formula: see text] rule and the dominant density-density (four-quark) operators governing [Formula: see text] cannot be disentangled from each other. But in the context of a dual QCD approach, which includes both long-distance dynamics and the UV completion, that is, QCD at short-distance scales, such a distinction is possible. We find then that beyond the strict large N limit, N being the number of colours, FSIs are likely to be important for the [Formula: see text] rule but much less relevant for [Formula: see text]. The latter finding diminishes significantly hopes that improved calculations of [Formula: see text] would bring its SM prediction to agree with the experimental data, opening thereby an arena for important new physics contributions to this ratio.