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Recent measurements of the proton radius using the Lamb shift in muonichydrogen are troublingly discrepant with values extracted from hydrogenspectroscopy and electron-proton scattering experiments. This discrepancy,which differs by more than five standard deviations, may be a signal of newphysics caused by a violation of lepton universality. Another candidate for anew physics signal is the muon anomalous magnetic moment. The measurement atBNL differs from the standard model prediction by at least three standarddeviations. Motivated by these two puzzles, first we use polarizedlepton-nucleon elastic scattering to search for a new scalar boson, andfurthermore we suggest new measurements of the nucleon form factors. Next, wedisplay a method to analyze the beam dump experiments without usingapproximation on phase space, and we use it to constrain all possible newspin-0 and spin-1 particles, and a variety of other measurements to study thepossibility of the new physics. Finally, assuming a new scalar boson can solvethe two puzzles simultaneously, we present a general model-independent analysisand constrain the existence of the new physics.

Possible Beyond the Standard Model Physics Motivated by Muonic Puzzles