Novel approaches to the study of the heavy meson spectrum at finite temperature

Abstract

This thesis is structured in three broad sections. The first presents a brief intro-duction to the field of quantum chromodynamics (QCD) and regularisation methods, which precedes a more thorough description of the lattice field theoretic approach to QCD and its non-relativistic formalism, NRQCD, which is used in the analysis contained within this document. The second section introduces the first problem of interest, spectral reconstruction in the case of bottomonium mesons. We focus in particular on the Laplacian nature of the problem and present the Backus-Gilbert method as a means of pro-ducing regularised solutions. The resolving power of the method is discussed and the overall approach is then extended with the inclusion of a novel technique known as Laplace shifting, which takes advantage of the structure of the problem to pro-vide a controlled resolution improvement to the method. A study of this technique is presented and applied to results obtained from Fastsum’s anisotropic NRQCD ensembles from which connections with a known phenomenon in Monte-Carlo based physics called Parisi-Lepage statistical scaling are elucidated. The third and final section focuses on probing the temperature dependence of the gluon propagator again calculated using the Fastsum Gen-2L ensembles. We begin by showing results for the propagator in the Coulomb gauge, before extending to the Landau gauge where we discuss the necessary modifications to support the lattice anisotropy.