Hadron structure is an important field in particle physics because hadrons make up most of the matter in nature. The theory of the strong nuclear force, via which the partons of hadrons interact, is Quantum Chromodynamics (QCD) and cannot be solved analytically. Lattice QCD (LQCD) is an ideal formulation of QCD and is the only formulation starting from first principles. In this thesis, we use LQCD for two primary topics of study: 1) nucleon structure and 2) pion and kaon structure. In the first study, we calculate the quark momentum fraction, helicity, and transversity for the nucleon. The calculations are performed on three ensembles at the physical point of the pion mass allowing us to study finite volume, discretization, strange and charm quark quenching, and excited-state systematic effects. Our calculations of the helicity and transversity are first predictions at the physical point. In the second study, we investigate pion and kaon structure. We calculate the first three non-trivial Mellin moments of the meson parton distribution functions (PDFs). For the kaon, this is the first direct calculation of the second and third moments. We carefully choose which matrix elements we implement so that there is no mixing with lower derivative operators, avoiding systematic uncertainties which are not well understood. We also perform an extensive study of the excited-state contamination. In a pioneering study, we show that the full x-dependence of the PDFs can be calculated from the first three Mellin moments. Such a calculation was previously thought to be unfeasible using moments calculated from LQCD. Our reconstruction of the PDFs allow us to comment on SU(3) flavor symmetry breaking and the high-x behavior of the pion PDF which are both interesting topics in hadron structure.

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.

Straddling the traditional disciplines of nuclear and particle physics, hadron physics is a vital and extremely active research area, as evidenced by a 2004 Nobel prize and new research facilities, such as that scheduled to open at CERN. Scientifically it is of vital importance in extrapolating our knowledge of quark-gluon physics at the sub-nucleon level to provide a wider perspective of strongly interacting hadrons, which make up the vast bulk of known matter in the Universe. Through detailed, pedagogical chapters contributed by key international experts, Hadron Physics maps out our contemporary knowledge of the subject. It covers both the theoretical and experimental aspects of hadron structure and properties along with a wide range of specific research topics, results, and applications. Providing a full picture of activity in the field, the book highlights three particular areas of current research: computational lattice hadron physics, the structure and dynamics of hadrons, and generalized parton distributions. It provides a solid introduction, includes background theory, and presents the current state of understanding of the subject.

This introduction to quantum chromodynamics presents the basic concepts and calculations in a clear and didactic style accessible to those new to the field. Readers will find useful methods for obtaining numerical results, including pure gauge theory and quenched spectroscopy.

This is the conference proceedings for the 18th International Conference on Hadron Spectroscopy and Structure (HADRON2019), held in Guilin, China. It is among the most important conference series in the field of hadron spectroscopy and structure. Collecting more than 130 contributions from this conference, the book spans over the topics of meson and baryon spectroscopy, exotic hadrons, hadron production and interactions, analysis tools, QCD and hadron structure, hadrons in nuclear environment and hypernuclei. Summaries of the recent discoveries from Belle, BESIII, LHCb and other high-energy experiments, as well as recent theoretical developments in the above mentioned topics, are contained in this volume, rendering it as a valuable resource for researchers working on hadron spectroscopy and structure.