The Littlest Higgs Model with T-Parity Facing CP-Violation in B_s - anti-B_s Mixing

The non-minimal flavour violating interactions of mirror quarks and new heavy gauge bosons in the Littlest Higgs model with T-parity (LHT) give rise to naturally large CP-violating effects in the B_s system. In view of a large new CP phase in B_s - anti-B_s mixing hinted by the CDF and D0 data and the recent UTfit analysis, we update our 2006 analysis of particle-antiparticle mixing and rare K and B decays in the LHT model, using the most recent values of a number of input parameters and performing a more careful error analysis. We find that the CP-asymmetry S_{psi phi} can easily reach values ~ 0.15-0.20, compared to the SM value ~ 0.04, while higher values are rather unlikely though not excluded. Large enhancements are also possible in the branching ratios for K_L -> pi0 nu anti-nu, K+ -> pi+ nu anti-nu and K_L -> pi0 l+ l- with much more modest effects in B_{s,d} -> mu+ mu-. We perform a detailed study of correlations between the latter decays and S_{psi phi} as well as of the correlation between S_{psi phi} and S_{psi K_S}. We also point out that the possible tension between epsilon_K and the tree level CKM determination recently hinted by various analyses can easily be resolved in the LHT model.