Correlations between epsilon '/epsilon and rare K decays in the Littlest Higgs model with T-parity

We calculate the CP-violating ratio epsilon'/epsilon in the Littlest Higgs model with T-parity (LHT) and investigate its correlations with the braching ratios for K-L -> pi(0)vv,, K-L -> pi(0)l(+)l(-) and K+ -> pi(+)vv. The resulting correlations are rather strong in the case of K-L decays, but less pronounced in the case of K+ -> pi(0)vv. Unfortunately, they are subject to large hadronic uncertainties present in epsilon(')/epsilon, whose theoretical prediction in the Standard Model (SM) is reviewed and update here. With the matrix elements of Q(6) (gluon penguin) and Q(8) (electroweak penguin) evaluated in the large-N limit and m(s)(MS) (2 GeV) = 100 MeV from lattice QCD, (epsilon'/epsilon)(SM) turns out to be close to the data so that significant departures of Br(K-L -> pi(0)vv) and Br(K-L -> pi l(+)l(-)) from the SM expectations are unlikely, while Br(K+ -> pi(+)vv) 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 epsilon(')/epsilon within the LHT model accompanied by large enhancements of Br(K-L -> pi(0)l(+)l(-)) and Br(K-L -> pi(0)l(+)l(-)), but only modest enhancement of Br(K+ -> pi(+)vv).