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Searches for charged lepton flavor violation (CLFV) offer deep probes for arange of new physics scenarios, such as super-symmetric models, theoriesinvolving scalar leptoquarks or additional Higgs doublets, and modelsexplaining the neutrino mass hierarchy and the matter-antimatter asymmetry ofthe universe via leptogenesis. The coherent, neutrinoless conversion of a muonto an electron in the field of a nucleus, $\mu^{-}+N\rightarrow e^{-} +N$, isone example of a muonic CLFV process which has sensitivity to this new physics.This paper details three experiments: COMET, DeeMe and Mu2e which will searchfor $\mu^{-}+N\rightarrow e^{-} +N$ in the coming decade. These experimentsoffer sensitivity up to an effective new physics mass scale of$\mathcal{O}(10^{4}$ TeV/c$^{2}$), going far beyond what can be achieved indirect, collider-based, searches. The theoretical motivation, designs andanticipated timelines for these three experiments are presented. Theseexperiments are a crucial part of a global search for CLFV. Continued supportfor all planned experimental searches for muonic CLFV is strongly encouraged.

Experimental Searches for Muon to Electron Conversion in a Nucleus: COMET, DeeMe, and Mu2e. A Contributed paper for Snowmass 21