μ–e conversion in nuclei versus μ→e γ: an effective field theory point of view

Using an effective lagrangian description we analyze possible new physics contributions to the most relevant muon number violating processes: μ→e γ and μ–e conversion in nuclei. We identify a general class of models in which those processes are generated at one loop level and in which μ–e conversion is enhanced with respect to μ→e γ by a large ln(m2μ/Λ2), where Λ is the scale responsible for the new physics. For this wide class of models bounds on μ–e conversion constrain the scale of new physics more stringently than μ→e γ already at present and, with the expected improvements in μ–e conversion experiments, will push it upwards by about one order of magnitude more. To illustrate this general result we give an explicit model containing a doubly charged scalar and derive new bounds on its couplings to the leptons.