Particle-antiparticle mixing, ε_K, ΔΓ _q, A_SL^q, A_CP(B_d → ψK_S), A_CP(B_s → ψφ) and B → X_s,dγ in the Littlest Higgs model with T-parity

We calculate a number of observables related to particle-antiparticle mixing in the Littlest Higgs model with T-parity (LHT). The resulting effective Hamiltonian for ΔF = 2 transitions agrees with the one of Hubisz et al., but our phenomenological analysis goes far beyond the one of these authors. In particular, we point out that the presence of mirror fermions with new flavour and CP-violating interactions allows to remove the possible Standard Model (SM) discrepancy between the CP asymmetry S_ψKS and large values of |V_ub| and to obtain for the mass difference ΔM_s < (ΔM_s)_SM as suggested by the recent result by the CDF collaboration. We also identify a scenario in which simultaneously significant enhancements of the CP asymmetries S_ψφ and A _SL^q relative to the SM are possible, while satisfying all existing constraints, in particular from the B → X_sγ decay and A_CP(B → X_sγ) that are presented in the LHT model here for the first time. In another scenario the second, non-SM, value for the angle γ = -(109 ± 16)° from tree level decays, although unlikely, can be made consistent with all existing data with the help of mirror fermions. We present a number of correlations between the observables in question and study the implications of our results for the mass spectrum and the weak mixing matrix of mirror fermions. In the most interesting scenarios, the latter one turns out to have a hierarchical structure that differs significantly from the CKM one.