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Title: Non-relativistic QCD on the lattice
Author: Lidsey, Andrew John
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 1995
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Traditional perturbative techniques for solving QCD are unable to successfully describe the properties of hadrons, where non-perturbative effects are likely to be present. One way to solve QCD non-perturbatively is to use Lattice QCD which offers a solution of QCD from first principles. This thesis describes the solution of bound states of heavy quarks using a Non-Relativistic formulation of QCD (NRQCD) together with Lattice techniques. Chapter 1 is an introduction to QCD as well as Lattice QCD, introducing the discretized action for relativistic fermions and the gauge field action. Chapter 2 describes potential models which to some extent can successfully predict the spectrum of Quarkonium states composed of Charm or Bottom quarks. NRQCD is then defined as an effective field theory in the continuum and relativistic corrections are derived as a power series of the typical quark velocity inside the Quarkonium. In Chapter 3 NRQCD is derived on the Lattice and the evolution of the quark Greens function given. The importance of tadpole- improved perturbation theory is stressed and its effect on spin-splittings is noted. Operators for various spin and orbital angular momentum states are derived and smearing of these operators are done to increase the signal to noise ratio. Chapter 4 describes the calculation in detail of the spectrum of Charmonium. To extract ground state masses to high precision and also excited states, fits of multiple correlation functions to multi-exponential terms are done. The spectrum for Upsilon is calculated on a coarser lattice than has previously been done to try to quantify any remaining lattice spacing errors. The spectrum for Be mesons is also calculated. These exotic heavy mesons have not been observed experimentally yet and the low lying states calculated can act as a prediction. In chapter 5 the two most important systematic errors remaining in the simulation are estimated using a simple Schrodinger equation. These errors are quenching and O (a)2 corrections in the gluonic action. Adjusting for corrections it is possible to observe scaling of mass-independent splittings on going from a finer to coarser lattice. This indicates there is no significant error left from lattice spacing errors. Chapter 6 is the conclusion.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral