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,K-S -> mu e, K-L,K-S -> pi(0)mu e and B-d,B-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 the pattern of the LFV branching rations in the LHT model differs significantly from the one encountered in the MSSM, allowing in a transparent manner to distinguish these two models with help of LFV processes. We also calculate (g-2)(mu) and find the new contributions to alpha(mu) below 1.10(-10) and consequently negligible. We compare our results with those present in the literature.