K→πνν and ε'/ε in Simplified New Physics Models

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The decays K+→π+νν and Kₗ→π⁰νν, being the theoretically cleanest rare decays of mesons, are very sensitive probes of New Physics. In view of the excellent prospects of reaching the Standard Model sensitivity for K+→π+νν by the NA62 experiment at CERN and for Kₗ→π⁰νν by the KOTO experiment at J-PARC, we study them in the simplest extensions of the SM in which stringent correlations between these two decays and other flavour observables are present. We first consider simple models with tree-level Z and Z' contributions in which either MFV or a U(2)³ symmetry is imposed on the quark flavour-violating couplings. We then compare the resulting correlations with those present in generic models in which the latter couplings are arbitrary, subject to constraints from ΔF=2 processes, electroweak and collider data. Of particular interest are the correlations with ε'/ε and Kₗ→μ+μ- which limit the size of NP contributions to K+→π+νν and Kₗ→π⁰νν, depending on the Dirac structure of couplings and the relevant operators. But in MFV also the constraint from Bₛ→μ+μ- turns out to be important. We take into account the recent results from lattice QCD and large N approach that indicate ε'/ε in the SM to be significantly below the data. While in many models the enhancement of ε'/ε implies a suppression of Kₗ→π⁰νν, we present two models in which these observables can be simultaneously enhanced relative to SM predictions. A correlation between K+→π+νν and B→ K(K*)μ+μ-, found by us in the simple models considered here, should be of interest for NA62 and LHCb experimentalists at CERN in the coming years. The one with B→ K(K*)νν will be tested at Belle II.