μ-e conversion in nuclei versus μ-->e γ: an effective field theory point of view

Abstract

Using an effective lagrangian description we analyze possible new physics contributions to the most relevant muon number violating processes: $μ\to e γ$ 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 $μ\to e γ$ by a large $\ln(m^2_μ/Λ^2),$ 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 $μ\to e γ$ 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.