Lepton Flavour Violation in the Presence of a Fourth Generation of Quarks and Leptons

We calculate the rates for the charged lepton flavour violating (LFV) decays l_i -> l_j gamma, tau -> l pi, 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 Standard Model (SM3) extended by a fourth generation of quarks and leptons (SM4), assuming that neutrinos are Dirac particles. We also calculate branching ratios for K_L -> mu e, K_L -> pi^0 mu e, B_{d,s} -> mu e, B_{d,s} -> tau e and B_{d,s} -> tau mu. We find that the pattern of the LFV branching ratios in the SM4 differs significantly from the one encountered in the MSSM, allowing to distinguish these two models with the help of LFV processes in a transparent manner. Also differences with respect to the Littlest Higgs model with T-parity are found. Most importantly the branching ratios for l_i -> l_j gamma, tau -> l pi, tau -> l eta('), mu^- -> e^-e^+e^-, tau^- -> e^-e^+e^-, tau^- -> mu^- mu^+ mu^-, tau^- -> e^- mu^+ mu^- and tau^- -> mu^- e^+ e^- can all still be as large as the present experimental upper bounds but not necessarily simultaneously. Also the rate for mu-e conversion in nuclei can reach the corresponding upper bound.