Electromagnetic form factors and radii of the nucleon from Lattice QCD and the proton radius puzzles
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Abstract
In this thesis, we investigate the electromagnetic form factors of the proton and neutron in the framework of Quantum Chromodynamics (QCD). To perform a calculation of such low-energy quantities based on first principles, we employ the lattice regularization of QCD. In Lattice-QCD simulations of nucleon-structure observables, systematic errors are inherent due to the finite lattice spacing and volume as well as due to contamination by excited states. These can be controlled and removed in a systematic fashion: for the removal of excited-state contributions, a variety of dedicated methods exists, while discretization and finite-volume effects also need to be taken into account by performing a continuum and infinite-volume extrapolation. However, all previous lattice studies of the electromagnetic form factors of the nucleon have either neglected the numerically challenging quark-disconnected contributions or were not extrapolated to the continuum and infinite-volume limit.
We present results for the electromagnetic form factors of the proton and neutron computed on the (2 + 1)-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions while, at the same time, controlling all sources of systematic uncertainties. For the excited-state analysis, we explore three complementary methods based on two-state fits to the effective form factors and on two different truncations of the summation method, respectively. The Q^2-, pion-mass, lattice-spacing and finite-volume dependence of our form factor data is fitted simultaneously to the expressions resulting from covariant baryon chiral perturbation theory including vector mesons amended by models for lattice artefacts. From these fits, we determine the electric, magnetic, Zemach and Friar radii as well as the magnetic moments of the proton and neutron. To assess the influence of systematic effects, we average over various cuts in the pion mass and the momentum transfer, as well as over different models for the lattice-spacing and finite-volume dependence, using weights derived from the Akaike Information Criterion (AIC).
Our ab-initio QCD results for the electromagnetic radii of the proton are of particular relevance in light of the so-called proton radius puzzle, i.e., the observation of a large tension between different experimental measurements of the proton's electric radius, which is after more than a decade of vigorous research still not completely explained. Also for the magnetic radius, analyses based on different data sets find discrepant results. In this situation, a firm theoretical prediction of the proton radii can contribute towards the clarification of the origins of the discrepancies.
Our results for the magnetic moments of the proton and neutron are in good agreement with the experimentally very precisely known values. For the radii of the proton, we achieve, including all systematic errors, a precision which enables a meaningful comparison to the various experiments and data-driven evaluations. On the one hand, our result for the electric radius of the proton clearly points towards a small value, as favored by muonic hydrogen spectroscopy, the recent ep-scattering experiment by PRad and data-driven dispersive analyses. Our estimate for the magnetic radius, on the other hand, is well compatible with that inferred from the A1 ep-scattering experiment by a z-expansion analysis and in tension with z-expansion on the remaining world data as well as with dispersive approaches.