The permutation group S_N and large Nc excited baryons

TL;DR

This paper analyzes excited baryon states for any number of colors Nc using permutation group S_N, providing a general framework for understanding their spin-flavor structure and the effects of different quark-quark interactions.

Contribution

It introduces a group-theoretic approach to classify baryon states and operators under S_N, enabling a systematic analysis of their mass operators and interactions for arbitrary Nc.

Findings

Classified baryon states using permutation group S_N.

Derived the matching of quark-quark interactions onto the 1/Nc expansion.

Highlighted the importance of core and excited quark operators.

Abstract

We study the excited baryon states for an arbitrary number of colors Nc from the perspective of the permutation group S_N of N objects. Classifying the transformation properties of states and quark-quark interaction operators under S_N allows a general analysis of the spin-flavor structure of the mass operator of these states, in terms of a few unknown constants parameterizing the unknown spatial structure. We explain how to perform the matching calculation of a general two-body quark-quark interaction onto the operators of the 1/Nc expansion. The inclusion of core and excited quark operators is shown to be necessary. Considering the case of the negative parity L=1 states transforming in the MS of S_N, we discuss the matching of the one-gluon and the Goldstone-boson exchange interactions.