Studies In Hadron Structure Using Lattice Qcd With Quark Masses That Almost Reach The Physical Point

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.

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.

Particle and nuclear physicists frequently take results from Lattice QCD at their face value without probing into their reliability or sophistication. This attitude usually stems from a lack of knowledge of the field. The aim of the present volume is to rectify this by introducing in an elementary way several topics, which we believe are appropriate for, and of possible interest to, both particle and nuclear physicists who are non-experts in the field.

Novel forms of matter, such as states made of gluons (glueballs), multiquark mesons or baryons and hybrid mesons are predicted by low energy QCD, for which several candidates have recently been identified. Searching for such exotic states of matter and studying their production and decay properties in detail has become a flourishing field at the experimental facilities now available or being built - e.g. BESIII in Beijing, BELLE II at SuperKEKB, GlueX at Jefferson Lab, PANDA at FAIR, J-PARC and in the upgraded LHC experiments, in particular LHCb. A modern primer in the field is required so as to both revive and update the teaching of a new generation of researchers in the field of QCD. These lectures on hadron spectroscopy are intended for Master and PhD students and have been originally developed for a course delivered at the Stefan Meyer Institute of the Austrian Academy of Sciences. They are phenomenologically oriented and intended as complementary material for basic courses in particle and nuclear physics. The book describes the spectra of light and heavy mesons and baryons, and introduces the fundamental properties based on symmetries. Further, it derives multiplet structures, mixing angle, decay coupling constants, magnetic moments of baryons, and predictions for multiquark states and compares these with suitable experimental data. Basic methods of calculating decay angular distributions and determining masses and widths of resonances are also presented. The appendices provide students and newcomers to the field with the necessary background information, and include a set of problems and solutions.

Quantum chromodynamics is generally accepted to be the quantum field theory which describes the strong interactions in elementary particle physics. However, the question of the mechanism responsible for the “confinement” of the color degrees of freedom of quarks and gluons into hadrons still ranks as one of the most interesting open problems in physics.This proceedings volume summarizes the state of the art in this area of research. Mathematically inclined readers will find the articles based on monopoles, vortices, and topology most interesting. Meanwhile, lattice calculations can be performed for many important physical quantities. Their results can be used as guidelines for developing models of quark confinement. These models are indispensable for theoretical physicists performing calculations with the Bethe-Salpeter equation, Dyson-Schwinger equations, effective Hamiltonians, and potential models. The cross-fertilization of all these subfields of research becomes evident from the articles in this book. A few experimental papers are also included.

The confinement mechanism of the quarks in QCD is one of the most challenging and open problems in physics. Confinement is a nonperturbative phenomenon, and a definite way to handle it has not yet been found in field theory. There are lattice calculations that can produce the low-lying states of the spectrum and ?measure? many important physical quantities, but nevertheless the development of analytical techniques is of extreme importance for understanding the physics involved in confinement. In this respect it is important to test the results obtained directly from the theory (Bethe-Salpeter kernel, effective Hamiltonians, quark potential, etc.) on the spectrum, form factors and decays of bound states of quarks and gluons, and to relate them to the results of lattice theory.In this book, the question of the confinement mechanism is addressed; explanations in terms of monopoles, instantons and dyons are reviewed and the connection with duality is discussed.

This is probably the only textbook available that gathers QCD, many-body theory and phase transitions in one volume. The presentation is pedagogical and readable. It provides materials interesting to both students and researchers of astrophysics, nuclear physics and high energy physics.

Filling the gap in the literature on low-energy quark models, The Quark Confinement Model of Hadrons investigates confinement effects in the low-energy regions of particle physics using the methods of nonlocal quantum field theory. It also elucidates their role in describing microscopic quantities that characterize hadron-hadron interactions. The authors present a quark confinement model to describe the low-energy physics of light hadrons. Hadrons are treated as collective colorless excitations of quark-gluon interactions while the quark confinement is to be provided by averaging over gluon backgrounds. The model is shown to reproduce the low-energy relations of chiral theory in the case of null momenta and, in addition, allow the researcher to obtain more sophisticated hadron characteristics, such as slope parameters and form factors. Presenting a unified view on a number of low-energy phenomena, The Quark Confinement Model of Hadrons enables an understanding of problems related to the treatment of large distances within quantum chromodynamics.

The structure of neutrons, protons, and other strongly interacting particles in terms of their quark and gluon constituents can be calculated from first principles by solving QCD on a discrete space-time lattice. With the advent of SciDAC software and prototype clusters and of DOE supported dedicated lattice QCD computers, it is now possible to calculate physical observables using full QCD in the regime of large lattice volumes and light quark masses that can be compared with experiment. This talk will describe selected examples, including the nucleon axial charge, structure functions, electromagnetic form factors, the origin of the nucleon spin, the transverse structure of the nucleon, and the nucleon to Delta transition form factor.

The 20-year-old problem of the confinement and the resulting spectrum of the bound states is central to quantum chromodynamics (QCD). Many approaches have been tried starting from different points of view: the potential theory, the Bethe-Salpeter equation, string and flux tube models, bag models, vacuum structure, current algebra, lattice theory, and numerical simulations. Phenomenological assumptions and first-principle theoretical results or indications have been combined. Many partial successes have been attained, but a unified and comprehensive treatment is still lacking.In recent years, new attention has been given to the problem, both in terms of theoretical developments and for the purpose of evaluating the spectrum and other properties of the particles. In particular, attention has been focussed on areas like numerical simulations, the derivation of the potential, the use of the Bethe-Salpeter equation, the connection between the potential and the chiral symmetry approach.This workshop was an opportunity for a synthesis and a comparison of the different points of view.