We calculate the CP-violating ratio ε ′ /ε in the Littlest Higgs model with T-parity (LHT) and investigate its correlations with the branching ratios for K L → π 0 νν, K L → π 0 ℓ + ℓ − and K + → π + νν. The resulting correlations are rather strong in the case of K L decays, but less pronounced in the case of K + → π + νν. Unfortunately, they are subject to large hadronic uncertainties present in ε ′ /ε, whose theoretical prediction in the Standard Model (SM) is reviewed and updated here. With the matrix elements of Q 6 (gluon penguin) and Q 8 (electroweak penguin) evaluated in the large-N limit and m MS s (2 GeV) = 100 MeV from lattice QCD, (ε ′ /ε) SM turns out to be close to the data so that significant departures of Br(K L → π 0 νν) and Br(K L → π 0 ℓ + ℓ − ) from the SM expectations are unlikely, while Br(K + → π + νν) 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 ε ′ /ε within the LHT model accompanied by large enhancements of Br(K L → π 0 νν) and Br(K L → π 0 ℓ + ℓ − ), but only modest enhancements of Br(K + → π + νν).
Note addedAn additional contribution to the Z penguin in the Littlest Higgs model with T-parity has been pointed out in [1,2], which has been overlooked in the present analysis. This contribution leads to the cancellation of the left-over quadratic divergence in the calculation of some rare decay amplitudes. Instead of presenting separate errata to the present work and our papers [3][4][5][6] partially affected by this omission, we have presented a corrected and updated analysis of flavour changing neutral current processes in the Littlest Higgs model with T-parity in [7].