Correlations between epsilon'/epsilon and Rare K Decays in the Littlest Higgs Model with T-Parity

Understand

We calculate the CP-violating ratio epsilon'/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^+ l^- and K^+ -> pi^+ nu {bar nu}.

• The resulting correlations are rather strong in the case of K_L decays, but less pronounced in the case of K^+ -> pi^+ nu {bar nu}.
• Unfortunately, they are subject to large hadronic uncertainties present in epsilon'/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'/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^+ l^-) from the SM expectations are unlikely, while Br(K^+ -> pi^+ nu {bar nu}) can be enhanced even by a factor 5.