Correlations between έ/ε and rare K decays in the Littlest Higgs model with T-parity

We calculate the CP-violating ratio ′/ in the Littlest Higgs model with T-parity (LHT) and investigate its correlations with the branching ratios for K_L→π⁰ν, K_L→π ⁰ℓ⁺ℓ^- and K⁺→π ⁺ν. The resulting correlations are rather strong in the case of K_L decays, but less pronounced in the case of K⁺→π ⁺ν. Unfortunately, they are subject to large hadronic uncertainties present in ′/, whose theoretical prediction in the Standard Model (SM) is reviewed and updated here. With the matrix elements of ₆ (gluon penguin) and ₈ (electroweak penguin) evaluated in the large-N limit and (2 GeV) ≤ 100 MeV from lattice QCD, (′/) _SM turns out to be close to the data so that significant departures of Br(K_L→π⁰ν) and Br(K_L→π ⁰ℓ⁺ℓ^-) from the SM expectations are unlikely, while Br(K⁺→π⁺ν) can be enhanced even by a factor 5. On the other hand, modest departures of the relevant hadronic matrix elements from their large-N values allow for a consistent description of ′/ within the LHT model accompanied by large enhancements of Br(K _L→π⁰ν) and Br(K_L→π ⁰ℓ⁺ℓ^-), but only modest enhancements of Br(K⁺→π⁺ν).