Nuclear Muon Capture on the Proton and 3He within the Standard Model and Beyond

Nuclear muon capture on the proton and $^3$He is considered both within and beyond the Standard Model in terms as general as is possible. Explicit and precise analytic expressions for all possible observables are given, assuming only a Dirac neutrino in the limit of vanishing mass. These results allow both for precision tests of the Standard Model and new physics, as well as for the assessment of the potential physics reach of experiments designed to measure specific observables. Using these expressions, stringent constraints can already be inferred from a recent precision measurement of the statistical capture rate on $^3$He. Likewise, similar constraints should follow the completion of a precision measurement in progress of the singlet capture rate on the proton.