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Register a new userStudying the Proton Radius Puzzle with mu p Elastic Scattering
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The Proton Radius Puzzle is the inconsistency between the proton radius determined from muonic hydrogen and the proton radius determined from atomic hydrogen level transitions and ep elastic scattering. No generally accepted resolution to the Puzzle has been found. Possible solutions generally fall into one of three categories: the two radii are different due to novel beyond-standard-model physics, the two radii are different due to novel aspects of nucleon structure, and the two radii are the same, but there are underestimated uncertainties or other issues in the ep experiments. The MUon proton Scattering Experiment (MUSE) at the Paul Scherrer Institut is a simultaneous measurement of mu^+ p and e^+ p elastic scattering, as well as mu^- p and e^- p elastic scattering, which will allow a determination of the consistency of the mu p and the ep interactions. The differences between + and - charge scattering are sensitive to two-photon exchange effects, higher-order corrections to the scattering process. The slopes of the cross sections as Q^2 -> 0 determine the proton radius. We plan to measure relative cross sections at a typical level of a few tenths of a percent, which should allow the proton radius to be determined at the level of ~0.01 fm, similar to previous ep measurements. The measurements will test several possible explanations of the proton radius puzzle, including some models of beyond-standard-model physics, some models of novel hadronic physics, and some issues in the radius extraction from scattering data.
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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.
It is suggested that proton elastic scattering on atomic electrons allows a precise measurement of the proton charge radius. Very small values of transferred momenta (up to four order of magnitude smaller than the ones presently available) can be reached with high probability.
In two recent papers it is argued that the proton radius puzzle can be explained by truncating the electron scattering data to low momentum transfer and fit the rms radius in the low momentum expansion of the form factor. It is shown that this procedure is inconsistent and violates the Fourier theorem. The puzzle cannot be explained in this way.
In 2010 the proton charge radius was extracted for the first time from muonic hydrogen, a bound state of a muon and a proton. The value obtained was five standard deviations away from the regular hydrogen extraction. Taken at face value, this might be an indication of a new force in nature coupling to muons, but not to electrons. It also forces us to reexamine our understanding of the structure of the proton. Here I describe an ongoing theoretical research effort that seeks to address this proton radius puzzle. In particular, I will present the development of new effective field theoretical tools that seek to directly connect muonic hydrogen and muon-proton scattering.
The proton size, specifically its charge radius, was thought known to about 1% accuracy. Now a new method probing the proton with muons instead of electrons finds a radius about 4% smaller, and to boot gives an uncertainty limit of about 0.1%. We review the different measurements, some of the calculations that underlie them, some of the suggestions that have been made to resolve the conflict, and give a brief overview new related experimental initiatives. At present, however, the resolution to the problem remains unknown.
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