Correlations between epsilon_s14/epsilon and Rare K Decays in the Littlest Higgs Model with T-Parity

Abstract

We calculate the CP-violating ratio epsilon_s14/epsilon in the Littlest Higgs model with T-parity (LHT) and investigate its correlations with the branching ratios for K_L -> pi^0 nu {bar nu}, K_L -> pi^0 l^_s16 l^- and K^_s16 -> pi^_s16 nu {bar nu}. The resulting correlations are rather strong in the case of K_L decays, but less pronounced in the case of K^_s16 -> pi^_s16 nu {bar nu}. Unfortunately, they are subject to large hadronic uncertainties present in epsilon_s14/epsilon, 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_s^MS(2 GeV) = 100 MeV from lattice QCD, (epsilon_s14/epsilon)_SM turns out to be close to the data so that significant departures of Br(K_L -> pi^0 nu {bar nu}) and Br(K_L -> pi^0 l^_s16 l^-) from the SM expectations are unlikely, while Br(K^_s16 -> pi^_s16 nu {bar nu}) 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_s14/epsilon within the LHT model accompanied by large enhancements of Br(K_L -> pi^0 nu {bar nu}) and Br(K_L -> pi^0 l^_s16 l^-), but only modest enhancements of Br(K^_s16 -> pi^_s16 nu {bar nu}).