Indirect Bounds on Z-> mu e and Lepton Flavor Violation at Future Colliders

Abstract

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