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Charged Lepton Flavour Violation and (g-2)_mu in the Littlest Higgs Model with T-Parity: a clear Distinction from Supersymmetry

We calculate the rates for the charged lepton flavour violating decays l_i -> l_j gamma, tau -> l pi, tau -> l eta, tau -> l eta', mu^- -> e^- e^+ e^-, the six three body leptonic decays tau^- -> l_i^- l_j^+ l_k^- and the rate for mu-e conversion in nuclei in the Littlest Higgs model with T-Parity (LHT). We also calculate the rates for K_{L,S} -> mu e, K_{L,S} -> pi^0 mu e and B_{d,s} -> l_i l_j. We find that the relative effects of mirror leptons in these transitions are by many orders of magnitude larger than analogous mirror quark effects in rare K and B decays analyzed recently. In particular, in order to suppress the mu -> e gamma and mu^- -> e^- e^+ e^- decay rates and the mu-e conversion rate below the experimental upper bounds, the relevant mixing matrix in the mirror lepton sector V_Hl must be rather hierarchical, unless the spectrum of mirror leptons is quasi-degenerate. We find that the pattern of the LFV branching ratios in the LHT model differs significantly from the one encountered in the MSSM, allowing in a transparent manner to distinguish these two models with the help of LFV processes. We also calculate (g-2)_mu and find the new contributions to a_mu below 10^{-10} and consequently negligible. We compare our results with those present in the literature.