Polarized lepton-nucleon elastic scattering and a search for a light scalar boson

Lepton-nucleon elastic scattering, using the one-photon and one-scalar-boson exchange mechanisms considering all possible polarizations, is used to study searches for a new scalar boson and suggest new measurements of the nucleon form factors. A new light scalar boson, which feebly couples to leptons and nucleons, may account for the proton radius and muon g - 2 puzzles. We show that the scalar boson produces relatively large effects in a certain kinematic region when using sufficient control of lepton and nucleon spin polarization. We generalize current techniques to measure the ratio G(E) : G(M) and present a new method to separately measure G(M)(2) and G(E)(2) using polarized incoming and outgoing muons.