Mu$\chi$e -- A Search for Familons in Muon Decay Using HPGe Detectors

A broken lepton family symmetry can lead to muon decay to a Familon $$\mu \to {\chi _{Familon}} + e .$$ We propose to search for two body muon decay to a Familon in the mass range from 86 to 105 MeV/c$^2$, by observing stopped positive muons. This mass region is the search window blind spot of magnetic spectrometers. The search signal will be a mono-energetic positron peak on top of the standard model muon Michel decay spectrum. The decay positron spectrum will be measured in HPGe detectors surrounded by large volume NaI detectors and a charged particle tracking system used to help reduce false triggers. This short-term experiment requires a stopped positive muon rate of 200 cps with a trigger to stopped muon ratio of 10:1 or better. At this rate, in a period of 2-hours previous limits will be matched. With 1-year of data collection muon branching ratio limits will range between 10$^{-6}$ to 10$^{-7}$. This experiment takes advantage of Fermilab's higher energy muons to greatly suppress backgrounds for Familon masses near the muon mass compared to lower energy muon factories.