Technical Design Report for the Paul Scherrer Institute Experiment R-12-01.1: Studying the Proton "Radius" Puzzle with $\mu p$ Elastic Scattering

The difference in proton radii measured with $\mu p$ atoms and with $ep$ atoms and scattering remains an unexplained puzzle. The PSI MUSE proposal is to measure $\mu p$ and $e p$ scattering in the same experiment at the same time. The experiment will determine cross sections, two-photon effects, form factors, and radii independently for the two reactions, and will allow $\mu p$ and $ep$ results to be compared with reduced systematic uncertainties. These data should provide the best test of lepton universality in a scattering experiment to date, about an order of magnitude improvement over previous tests. Measuring scattering with both particle polarities will allow a test of two-photon exch…