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The standard model (SM) of particle physics describes how the Universe works at a fundamental level. Even though this theory has proven to be very successful over the past 50 years, we know it is incomplete. Many theories that go beyond the SM predict the occurrence of certain processes that are forbidden by the SM, such as muon to electron conversion. This paper will briefly review the history of muon to electron conversion and focus on the high-precision experiments currently being proposed, COMET (Coherent Muon to Electron Transition) and Mu2e, and a next-generation experiment, PRISM. The PRISM experiment intends to use a novel type of accelerator called a fixed-field alternating-gradient (FFAG) accelerator. There has recently been renewed interest in FFAGs for the Neutrino Factory and the Muon Collider, and because they have applications in many areas outside of particle physics, such as energy production and cancer therapy. The synergies between these particle physics experiments and other applications will also be discussed.

Muon to electron conversion: how to find an electron in a muon haystack