Exciting nucleon in Compton scattering and hydrogen-like atoms
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Abstract
This PhD thesis is devoted to the low-energy structure of the nucleon (proton and neutron) as seen through electromagnetic probes, e.g., electron and Compton scattering. The research presented here is based primarily on dispersion theory and chiral effective-field theory. The main motivation is the recent proton radius puzzle, which is the discrepancy between the classic proton charge radius determinations (based on electron-proton scattering and normal hydrogen spectroscopy) and the highly precise extraction based on first muonic-hydrogen experiments by the CREMA Collaboration. The precision of muonic-hydrogen experiments is presently limited by the knowledge of proton structure effects beyond the charge radius. A major part of this thesis is devoted to calculating these effects using everything we know about the nucleon electromagnetic structure from both theory and experiment.
The thesis consists of eight chapters. The first and last are, respectively, the introduction and conclusion. The remainder of this thesis can roughly be divided into the following three topics: finite-size effects in hydrogen-like atoms, real and virtual Compton scattering, and two-photon-exchange effects.
The first of these topics is of direct relevance to the proton charge radius extraction from hydrogen and muonic hydrogen. We derive the finite-size effects using a dispersive representation of the proton electromagnetic form factors. As result, we reveal some limitations in the usual accounting of finite-size effects in terms of the expansion in charge and magnetization radii. We can easily construct a model of nucleon form factors which exploits these limitations such as to resolve the proton radius puzzle.
The second topic - Compton scattering - is important for understanding the two-photon-exchange
effects. We review the concept of dispersion relations and Compton scattering sum rules, which are based on the general principles of unitarity, causality and analyticity. A new set of sum rules for the elastic-channel contribution to the quasi-static polarizabilities is derived and verified within quantum electrodynamics. We also perform the next-to-next-to-leading order calculation of Compton scattering using the SU(2) baryon chiral perturbation theory with Δ(1232)-isobar degrees of freedom.
In the last topic, we use the doubly-virtual Compton scattering off the nucleus to evaluate the two-photon-exchange effects in lepton-nucleus bound states. We focus on the leading and subleading, i.e., order (Z𝛂)^5 and (Z𝛂)^6, polarizability contributions to the spectra of muonic hydrogen, deuterium and helium. We present the next-to-leading order baryon chiral perturbation theory prediction for the proton-polarizability effect in the Lamb shift and hyperfine splitting of muonic hydrogen and a first model-independent prediction of the neutron-polarizability effect in light muonic atoms. Motivated by the large-Nc limit of quantum chromodynamics, we consider the effect of the Δ(1232)-excitation in the hyperfine splitting of muonic hydrogen. We study the neutral-pion exchange and an equivalent to the Coulomb-distortion contribution, both belonging to the class of off-forward two-photon-exchange effects. To allow for a detailed comparison with empirical information, we expand the contribution of non-Born two-photon exchange to the hyperfine splitting in terms of individual spin polarizabilities. We conclude by evaluating the impact of our model-independent predictions of polarizability effects on the extractions of proton charge and Zemach radii from muonic-hydrogen spectroscopy.