An Analysis of the Hadronic Spectrum from Lattice QCD

TL;DR

This paper reviews lattice QCD methods and presents lattice predictions for the hadronic mass spectrum using chiral perturbation theory extrapolations, highlighting the connection between numerical simulations and theoretical physics.

Contribution

The paper introduces lattice QCD techniques for predicting the hadronic spectrum and applies chiral perturbation theory for extrapolation, providing new insights into non-perturbative QCD calculations.

Findings

Lattice QCD can predict hadronic masses with chiral extrapolation.

Numerical techniques effectively reproduce continuum physics.

Symmetry breaking and chiral perturbation theory are crucial for spectrum analysis.

Abstract

I begin by discussing the basic ideas of quantum field theory (QFT). I provide a review of symmetries in physics and then move on to discuss the quark model. I then review lattice gauge theory with particular attention paid to lattice QCD and some of the associated problems. I discuss gauge fields on the lattice along with free lattice fermions. I follow this with a definition of the lattice QCD action and discuss how to reproduce the correct continuum physics. I include a discussion of the basic numerical techniques employed in lattice simulations. I review methods for putting particles onto the lattice and describe how to fit the resulting data. The symmetries of the QCD Lagrangian are reviewed along with various forms of symmetry breaking in physics, the PCAC relation, the Goldberger-Treiman relation and the spontaneous breakdown of the axial symmetry. I move on to discuss sigma models and finally arrive at a basic chiral perturbation theory. I present research completed with my supervisor C. Allton and collaborators A.W. Thomas, D.B. Leinweber and R. Young in the final three chapters. This work involves making lattice predictions for the Hadronic mass spectrum using extrapolation techniques based on the predictions of chiral perturbation theory which have been developed by the Adelaide group.