Access Type

Open Access Dissertation

Date of Award

January 2018

Degree Type


Degree Name



Physics and Astronomy

First Advisor

Gil Paz


In 2010 the first extraction of the proton charge radius from muonic hydrogen was found to be five standard deviations away from the regular hydrogen value. Seven years later, this proton radius puzzle still persists, and challenges our understanding of the structure of the proton. An effective field theory analysis using Non-Relativistic Quantum Electrody- namics (NRQED) indicates that the muonic hydrogen result can be interpreted as a large, compared to some model estimates, muon-proton spin-independent contact interaction. The muonic hydrogen result can be tested by a muon-proton scattering experiment, MUSE, that is planned at the Paul Scherrer Institute in Switzerland. The typical momentum of the muons in this experiment is of the order of the muon mass. In this energy regime the muons are relativistic but the protons are still non-relativistic. The interaction between the muons and protons can be described by a new effective field theory QED-NRQED. This document will present elements of this effective field theory, which will include the reproduction of Rosenbluth scattering up to the second power in the inverse proton mass, relativistic scattering off of a static potential, scattering amplitudes up to the inverse proton mass squared, and the determination of the four-fermion contact interactions.

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