FCNC processes in the littlest higgs model with T-parity: An update

We update our 2006-2007 results for FCNC processes in the Littlest Higgs model with T-parity (LHT). The removal of the logarithmic UV cutoff dependence in our previous results through a new contribution to the Z⁰-penguin diagrams identified by Goto et al. and del Aguila et al., while making the deviations from the SM expectations in the quark sector less spectacular, still allows for sizable new physics effects in K → πvv̄ and K _l → π⁰l+l- decays and in the CP-asymmetry S χφ with the latter unaffected by the new contribution. We extend our analysis by a study of the fine-tuning required to fit the data on K and by the inclusion of the decay K_l → μ+μ-. A number of correlations can distinguish this model from the custodially protected Randall-Sundrum model analysed recently. We also reconsider lepton flavour violating decays, including now a discussion of fine-tuning. While the l_i → l _jγ decays are unaffected by the removal of the logarithmic cutoff dependence, the branching ratios for decays with three leptons in the final state, like μ → 3e are lowered by almost an order of magnitude. In spite of this, the pattern of lepton flavour violation in the LHT model can still be distinguished from the one in supersymmetric models.