Baryon resonances in large N_c QCD

TL;DR

This thesis develops a systematic, predictive approach to baryon spectra in large N_c QCD using the $1/N_c$ expansion, improving upon traditional models by providing a rigorous group theoretical framework for excited states.

Contribution

It introduces a new group theoretical method for analyzing baryon states in large N_c QCD, avoiding approximations of the decoupling approach and offering more accurate mass predictions.

Findings

The $1/N_c$ expansion is effective for low momentum transfer baryon studies.

A new group theoretical approach yields leading corrections of order 1/N_c.

Dependence of spin-dependent mass terms on excitation energy is established.

Abstract

This thesis deals with the study of baryon spectra in the context of the $1/N_c$ expansion. The standard tool to study baryon properties is the constituent quark model. The results are naturally model dependent. The $1/N_c$ expansion generates a new perturbative approach to QCD, convenient for low momentum transfer. It provides a new theoretical method that is quantitative, systematic and predictive. In the first part of the thesis, the $1/N_c$ expansion is introduced as well as the baryon structure at large $N_c$. A summary of important results for ground-state baryons is provided. The second part of the thesis is devoted to excited baryon states. The symmetric orbital states are treated by analogy to the ground state. For mixed symmetric states, two approaches are presented. The traditional one starts from the decoupling of the wave function into an excited quark and a symmetric core. To make the problem tractable the wave function is treated approximately, justified by a Hartree scheme. This approach is applied to the study of the $[{\bf 70},\ell^+] (\ell=0,2)$ multiplets (nonstrange and strange cases) and of the $[{\bf 56},4^+]$ multiplet. An important physical result is the dependence of the spin dependent terms of the mass operator on the excitation energy. Recently we suggested a new approach based on a rigorous group theoretical treatment of the matrix elements of SU(4). No decoupling and no approximations are necessary. When applied to the $[{\bf 70},1^-]$ nonstrange multiplet, it is found that the leading corrections to the mass operator are of order $1/N_c$ instead of $N_c^0$, as predicted by the decoupling procedure.