Baryon properties and glueballs from Poincare-covariant bound-state equations

TL;DR

This thesis uses the covariant Bethe-Salpeter formalism with Rainbow-Ladder truncation to study baryon properties and proposes a framework for glueball equations, demonstrating model independence and ~10% accuracy in results.

Contribution

It evaluates the model dependence in Bethe-Salpeter calculations of baryons and introduces a Bethe-Salpeter approach for glueballs, extending the application of covariant bound-state equations.

Findings

Rainbow-Ladder truncation reproduces physical results within ~10% accuracy.

Model dependence is qualitatively small across different models.

Proposes a Bethe-Salpeter equation framework for glueballs.

Abstract

In this thesis the covariant Bethe-Salpeter equation formalism is used to study some properties of ground-state baryons. This formalism relies on the knowledge of the interaction kernel among quarks and of the full quark propagator. For the interaction kernel, which is in principle a sum of infinitely many diagrams, I use the Ladder truncation. It amounts to reduce the interaction to a flavor-blind quark-mass independent vector-vector interaction between two quarks, mediated by a dressed gluon. The irreducible three-body interactions are neglected. The full quark propagator is obtained as a solution of the quark Dyson-Schwinger equation which is truncated such that, together with the truncation in the interaction kernel, chiral symmetry is correctly implemented. It is called Rainbow truncation, and together with the truncated kernel equation it constitutes the Rainbow-Ladder truncation of the Bethe-Salpeter equation. Any truncation induces the introduction of a model to account for the properties of the full system. The main goal of this thesis is to evaluate the model dependence of corrsponding results and, as a consequence, to isolate the features related to the truncation itself. To this end two non-related models are used to calculate the baryon spectra, from light to heavy quarks, and the electromagnetic properties of the Delta(1232). From these results one concludes a qualitative model independence, and that a Rainbow-Ladder truncated bound-state calculation reproduces the physical results with an accuracy of ~10%. Covariant bound-state equations are not limited to the study of hadronic bound states. As an example, in a further chapter of this thesis a Bethe-Salpeter equation for glueballs is proposed, and the main steps for a consistent resolution of the equation are described. However, to obtain this solution is beyond the scope of this work.