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Item New insights into the sign problem of QCD and heavy tetraquarks(2020) Cai, Yiming; Cohen, Thomas; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum Chromodynamics (QCD) describes strong interactions among the fundamental particles known as quarks and gluons. In principle, QCD can be used to explain complicated phenomena in the strong sector. However, at the energy scale of hadronic physics, the strong coupling constant is so large that the traditional perturbative method is not applicable. There are two powerful alternative approaches utilized in the non-pertubative regime: (1) lattice QCD, which discretizes space-time and utilizes Monte Carlo computer simulations, and (2) finding new systematic expansion regimes to obtain physical insights in certain limits. In this dissertation, three problems are studied in the context of these two approaches. In Chapter 2, a notorious numeric problem in lattice QCD known as the sign problem is explored. A subtle phenomenon caused by the interplay between the sign problem and the infinite volume limit is discussed and explained using the saddle point approximation. This work provides insight into the sign problem and the physics of the QCD theta-vacuum. Chapter 3 and Chapter 4 focus on tetraquarks, which are unconventional hadrons containing four valence quarks. Despite numerous tetraquark candidates seen in experiments, there is no unified and well-accepted theoretical descriptions of the tetraquark state yet. This dissertation examines the existence of tetraquarks in the heavy quark mass limit. A powerful systematic expansion regime can be built when the heavy quark mass is extremely large. In Chapter 3, a framework is established to analyze tetraquarks in the heavy quark mass limit. It is shown in a model-independent way that multiple parametrically narrow doubly heavy tetraquarks must exist in this limit. Many of these states will be parametrically close to the threshold of decaying into two heavy mesons. In Chapter 4, based on a modification of the framework in Chapter 3, it is shown that tetraquarks containing a heavy quark and a heavy antiquark with appropriate large angular momentum must exist in the heavy quark mass limit. This may provide insights into the experimentally-observed narrow near-threshold tetraquarks which contain a heavy quark and a heavy antiquark.Item Partonic Contributions to the Proton Spin in Lattice QCD(2015) Zhao, Yong; Ji, Xiangdong; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In Feynman's parton picture, the proton spin can be understood as sum of the contributions from the spin and orbital angular momentum of the quark and gluon partons. However, in gauge theories, there is no local gauge-invariant notion of the spin or orbital angular momentum of the gauge particles. It is shown that in the infinite momentum frame of the proton, the gluons can be equivalent to free radiation, which is analogous to the Weizsaecker-Williams approximation in electrodynamics, and therefore one can talk about gluon helicity and longitudinal orbital angular momentum. We will justify the physical meaning of the Jaffe-Manohar sum rule for the longitudinal proton spin which uses the free-field expression of the QCD angular momentum operator in the light-cone gauge. Furthermore, it is discovered that each term in the Jaffe-Manohar sum rule can be related to the matrix element of a gauge-invariant, but frame-dependent operator through a factorization formula in large-momentum effective field theory. This provides a new approach for the nonperturbative calculation of the proton spin content in lattice QCD, and can be applied to the other parton observables as well. We present all the matching coefficients for the proton spin sum rule and non-singlet quark distributions at one-loop order in perturbation theory. These results will be useful for a first direct lattice calculation of the corresponding parton properties, especially the gluon helicity and parton orbital angular momentum.Item Topics in Lattice QCD and Effective Field Theory(2010) Buchoff, Michael Ireland; Bedaque, Paulo F; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The only method for performing these calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice in order to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. Developing analytic formulae describing the systematic errors due to the discrete lattice spacings is the main focus of this work. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. Effective field theory (EFT) provides a formalism for categorizing low-energy effects of a high-energy fundamental theory as long as there is a significant separation in scales. An example of this is in chiral perturbation theory (χPT ), where the low-energy effects of QCD are contained in a mesonic theory whose applicability is a result of a pion mass smaller than the chiral breaking scale. In a similar way, lattice χPT accounts for the low-energy effects of lattice QCD, where a small lattice spacing acts the same way as the quark mass. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 ππ scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a combination of effective field theory and an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.Item Lattice QCD Simulations of Baryon Spectra and Development of Improved Interpolating Field Operators(2005-08-03) Sato, Ikuro; Wallace, Stephen J; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Because of the cubical discretization of space, the continuum rotational group is broken down to a finite point group. Operators are classified according to the irreducible representations of the double octahedral group. At first, three-quark quasi-local operators are constructed for each isospin and strangeness with suitable symmetry of Dirac indices. Nonlocal baryon operators are formulated in a second step as direct products of the quasi-local spinor structures together with lattice displacements. Appropriate Clebsch-Gordan coefficients of the octahedral group are used to form linear combinations of such direct products. The construction maintains maximal overlap with the continuum SU(2) group in order to provide a physically interpretable basis. Nonlocal operators provide direct couplings to states that have nonzero orbital angular momentum. Monte Carlo simulations of nucleon and delta baryon spectra are carried out with anisotropic lattices of anisotropy 3.0 with $\beta=6.1$. Gauge configurations are generated by the Wilson gauge action in quenched approximation with space-time volumes $(1.6\,\mbox{fm})^3\times 2.1\,\mbox{fm}$ and $(2.4\,\mbox{fm})^3\times 2.1\,\mbox{fm}$. The Wilson fermion action is used with pion mass $\simeq 500\,\mbox{MeV}$. The variational method is applied to matrices of correlation functions constructed using improved operators in order to extract mass eigenstates including excited states. Stability of the obtained masses is confirmed by varying the dimensions of the matrices. The pattern of masses for the low-lying states that we compute is consistent with the pattern that is observed in nature. Ordering of masses is consistent for positive-parity excited states, but mass splittings are considerably larger than the physical values. Baryon masses for spin $S \ge 5/2$ states are obtained in these simulations. Hyperfine mass splittings are studied for both parities. No significant finite volume effect is seen at the quark mass that is used.