Precision nucleon structure and fundamental physics: from the proton radius puzzle to leptonic CP violation

The discrepancy between the measured Lamb shift in muonic hydrogen and expectations from electron-proton scattering and hydrogen spectroscopy has become known as the proton radius puzzle, whose most "mundane" resolution requires a ∼5σ shift in the value of the Rydberg constant. I review the status of spectroscopic and scattering measurements, recent theoretical developments, and implications for particle physics. Lessons learned from the proton radius puzzle have important implications for neutrino-nucleus cross sections at long baseline neutrino experiments exploring fundamental neutrino properties. I discuss the application of soft-collinear effective theory to radiative corrections in lepton-nucleus scattering, the potential impact of lattice QCD for neutrino physics, and the interplay with other processes such as muon capture and pion electroproduction.