Indirect bounds on Z→μe, and lepton flavor violation at future colliders

Motivated by the interest in lepton number violating processes, we study the connection between the rate of Z→μe decay and those of the low-energy processes μ→3e, and μ→e conversion in nuclear field, assuming that the relevant form factors are constant or weakly q2 dependent. We show that if the vector or axial Z form factors are dominant, Br(Z→μe) is not observable, while if the Z dipole form factors are dominant, the relatively weak indirect bound Br(Z→μe)<7×10−9 does not fully preclude a signal at future colliders, as TESLA. We finally comment on the relation of Z→μe with Z→τe and Z→τμ decays, and suggest a simple scaling law for these three processes.