Lin Li

Date of Award

Summer 2022

Document Type

Open Access Dissertation


Physics and Astronomy

First Advisor

Steffen Strauch


The root-mean-square (rms) radius of the proton charge is a fundamental quantity. In 2010, the studies of muonic hydrogen with high precision found a notably smaller value than the one from earlier non-muonic measurements. This discrepancy has led to theoretical and experimental investigations. A missing measurement in determining the proton radius is muon scattering, a measurement that the MUon Scattering Experiment (MUSE) collaboration proposed at Paul Scherrer Institute (PSI). MUSE will measure elastic electron-proton and muon-proton scattering data with positively and negatively charged beams in a four-momentum-transfer square range from Q2 = 0.002 to 0.08 GeV2 . Each of the four sets of data will allow the extraction of the proton charge radius. In combination, the data test possible differences between the electron and muon interactions and additionally two-photon exchange effects.

MUSE uses a large acceptance detector system without a magnetic spectrometer. As the final-state lepton momentum remains unmeasured, the MUSE acceptance is integrated over a range of final-state lepton momenta to obtain the cross section. To extract the Born cross section, which contains the form factors, the radiative corrections in MUSE need to be determined. An event generator (ESEPP) is used in the target position to simulate the $\ell^\pm p \to \ell^\pm p$ and $\ell^\pm p \to \ell^\pm p \gamma$ processes and to study the radiative corrections for both electrons and muons. A dedicated downstream photon detector is introduced to suppress initial-state radiation effects by detecting the events with a hit in the detector that has a photon energy above the photon detector threshold.

The results show that, with the help of the photon calorimeter, the radiative corrections to the Born cross section are below 0.1 for electrons and 0.01 for muons under MUSE conditions. The radiative corrections for electrons are reduced by a factor of 3 using the photon calorimeter. The total uncertainties of the radiative corrections due to the knowledge of the setup in the experiment for electron scattering are smaller than 0.5%, while angular-dependent uncertainties related to the proton radius extraction for electrons are smaller than 0.38%. The total uncertainties of the radiative corrections from the uncertainties in the experimental input for muons are less than 0.05%. Due to this work, the relative systematic cross-section uncertainties of MUSE are enabled to be of tolerable size.

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