Studies in hadron structure using lattice QCD with quark masses that almost reach the physical point

Abstract

Lattice QCD allows us to study the structure of hadrons from first-principles calculations of quantum chromodynamics. We present calculations that shed light on the behavior of quarks inside hadrons in both qualitative and quantitative ways. The first is a study of diquarks. We bind two quarks in a baryon with a static quark and compute the simultaneous two-quark density, including corrections for periodic boundary conditions. Defining a correlation function to isolate the intrinsic correlations of the diquark, we find that away from the immediate vicinity of the static quark, the diquark has a consistent shape, with much stronger correlations seen in the scalar diquark than in the axial-vector diquark. We present results at pion masses 293 and 940 MeV and discuss the dependence on the pion mass. The second set of calculations is a more quantitative study that covers a wide range of (mainly isovector) nucleon observables, including the Dirac and Pauli radii, the magnetic moment, the axial charge, and the average quark momentum fraction. Two major advances over previous calculations are the use of a near-physical pion mass, which nearly eliminates the uncertainty associated with extrapolation to the physical point, and the control over systematic errors caused by excited states, which is a significant focus of this thesis. Using pion masses as low as 149 MeV and spatial box sizes as large as 5.6 fm, we show the importance of good control over excited states for obtaining successful postdictions -- which we achieve for several quantities -- and we identify a remaining source of systematic error that is likely responsible for disagreement with experiment in the axial sector. We then use this understanding of systematics to make predictions for observables that have not been measured experimentally.