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

TL;DR

The PSI MUSE experiment aims to precisely compare muon-proton and electron-proton scattering to resolve the proton radius puzzle, testing lepton universality and two-photon exchange effects with unprecedented accuracy.

Contribution

It introduces a simultaneous measurement of muon-proton and electron-proton scattering under identical conditions, reducing systematic uncertainties and improving the precision of lepton universality tests.

Findings

Enhanced precision in comparing muon and electron scattering data.

Potential to confirm or refute the proton radius discrepancy with high significance.

Improved constraints on two-photon exchange effects at low momentum transfer.

Abstract

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 exchange at the sub-percent level, about a factor of four improvement on uncertainties and over an order of magnitude more data points than previous low momentum transfer determinations, and similar to the current generation of higher momentum transfer electron experiments. The experiment has the potential to demonstrate whether the $\mu p$ and $ep$ interactions are consistent or different, and whether any difference results from novel physics or two-photon exchange. The uncertainties are such that if the discrepancy is real it should be confirmed with $\approx$5$\sigma$ significance, similar to that already established between the regular and muonic hydrogen Lamb shift.