(Formula Presented) and ε′/ε in simplified new physics models

Abstract: The decays K⁺→π⁺νν¯ and K_L→π⁰νν¯, being the theoretically cleanest rare decays of mesons, are very sensitive probes of New Physics (NP). In view of the excellent prospects of reaching the Standard Model (SM) sensitivity for K⁺→π⁺νν¯ by the NA62 experiment at CERN and for K_L→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 Minimal Flavour Violation (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 the constraints from ΔF = 2 processes, electroweak and collider data. Of particular interest are the correlations with ε′/ε and K_L → μ⁺μ⁻ which limit the size of NP contributions to K⁺→π⁺νν¯ and K_L→π⁰νν¯, depending on the Dirac structure of couplings and the relevant operators. But in MFV models also the constraint from B_s → 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 the suppression of K_L→π⁰νν¯, we present two models in which ε′/ε and K_L→π⁰νν¯ 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.