content_image/339201.jpg content_image/339202.jpg content_image/339203.jpg
and on the square of the SM lepton mixing with heavier vector-like fermions [46]. 

• Tree-level LFV . We have included the most relevant constraints following [42]. Ex- plicitly, we have studied the decays µ → e − e $^{+}$e − , τ → µ − µ $^{+}$µ − , τ → e − e $^{+}$e − , τ → µ − e $^{+}$e − , τ → µ − e $^{+}$µ − and the µ − e nuclear conversion rate. The tri-lepton decays l → l$_{1}$ ¯ l$_{2}$l$_{3}$ are mediated by LFV tree-level couplings to the physical Z gauge boson and its KK excitations. (The effects due to fermion mixing are negligible). 7 At low energies, these contributions can be parameterized by the following effective Lagrangian, 

<img src='content_image/339201.jpg'>

where α = e, µ, τ . In terms of this effective Lagrangian, the branching ratios for these decays read 

<img src='content_image/339202.jpg'>

For the µ − e conversion rate we have applied the usual expression 

where g µe L,R are the corresponding off-diagonal Z ¯ eµ couplings, G$_{F}$ is the Fermi constant and α the QED coupling strength, while the other terms are atomic physics constants defined in [48]. We shall use the current PDG [45] bounds for the tri-lepton decays and the titanium bound B$_{conv}$ < 6 . 1 × 10 − 13 from the SINDRUM II experiment [49] for µ − e conversion. 

<img src='content_image/339203.jpg'>

