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

By Monika Blanke A, Andrzej J. Buras A, Stefan Recksiegel A, Cecilia Tarantino A and Selma Uhlig A

Abstract

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 KL → π 0 ν¯ν, KL → π 0 ℓ + ℓ − and K + → π + ν¯ν. The resulting correlations are rather strong in the case of KL decays, but less pronounced in the case of K + → π + ν¯ν. 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 Q6 (gluon penguin) and Q8 (electroweak penguin) evaluated in the large-N limit and mMS s (2GeV) = 100MeV from lattice QCD, (ε′/ε)SM turns out to be close to the data so that significant departures of Br(KL → π0ν¯ν) and Br(KL → π 0 ℓ + ℓ − ) from the SM expectations are unlikely, while Br(K + → π + ν¯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 ε ′ /ε within the LHT model accompanied by large enhancements of Br(KL → π 0 ν¯ν) and Br(KL → π 0 ℓ + ℓ −), but only modest enhancements o

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