Charged lepton flavour violation and (g−2)_μin 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 1 ⋅ 10⁻¹⁰ and consequently negligible. We compare our results with those present in the literature.