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.
Blanke, M., Buras Andrzej, J., Duling, B., Poschenrieder, A., Tarantino, C. (2007). Charged lepton flavour violation and (g-2)mu in the littlest Higgs model with T-parity: a clear distinction from supersymmetry. JOURNAL OF HIGH ENERGY PHYSICS(5) [10.1088/1126-6708/2007/05/013].