  A new scalar boson which couples to the muon and proton can simultaneously
solve the proton radius puzzle and the muon anomalous magnetic moment
discrepancy. Using a variety of measurements, we constrain the mass of this
scalar and its couplings to the electron, muon, neutron, and proton. Making no
assumptions about the underlying model, these constraints and the requirement
that it solve both problems limit the mass of the scalar to between about 100
keV and 100 MeV. We identify two unexplored regions in the coupling
constant-mass plane. Potential future experiments and their implications for
theories with mass-weighted lepton couplings are discussed.
