Charged lepton flavour violation and (g-2)_μ 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_jγ, τ→ℓπ, τ→ℓη, τ→ℓη′, μ ^-→e^-e⁺e^-, the six three body leptonic decays τ^-→ℓ_i ^-ℓ_j⁺ℓ_k^- and the rate for μ-e conversion in nuclei in the Littlest Higgs model with T-parity (LHT). We also calculate the rates for K_L,S→μe, K _L,S→π⁰μe and B _d,s→ℓ_iℓ_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 μ→eγ and μ^-→e^-e⁺e^- decay rates and the μ-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)_μ and find the new contributions to a _μ below 110^-10 and consequently negligible. We compare our results with those present in the literature.