A Search for the Neutrinoless Conversion of Negative Muons into Positrons with the Mu2e Experiment*

The primary physics goal of the Mu2e Experiment is to search for Charged Lepton Flavor Violation (CLFV) in the process of a coherent neutrinoless  $\mu^{-} N \rightarrow e^{-} N$  transition.   This process is allowed under the Standard Model albeit at unobservable rates.   Another interesting process that  Mu2e  will search for is the neutrinoless conversion of stopped negative muons into positrons.  This process violates both lepton flavor and lepton number.   Observation of either process would be an unambiguous indication of New Physics.  In addition, the observation of  $\mu^{-} N \rightarrow e^{+} N’$ would be proof that  neutrinos are Majorana particles. We discuss the status and prospects of this search.