Negative parity baryons in the $1/N_c$ expansion: the three towers of states revisited

TL;DR

This paper revisits the classification of negative parity baryons in large N_c QCD, demonstrating that a new Hamiltonian approach without system separation reproduces the three degenerate state towers and aligns with scattering picture predictions.

Contribution

The paper introduces a new Hamiltonian approach for negative parity baryons that does not require system separation, confirming the three towers of states and their degeneracies.

Findings

Three degenerate state towers are obtained with the new approach.

Eigenvalues depend linearly on three dynamical coefficients.

The new method aligns with the meson-nucleon scattering picture.

Abstract

We discuss the compatibility between the quark-shell picture and the meson-nucleon scattering picture in large $N_c$ QCD for mixed symmetric $\ell$ = 1 states previously analyzed by using a simple Hamiltonian including operators up to order $\mathcal{O}(N^0_c)$ defined in the standard ground state symmetric core + excited quark procedure. Here we introduce a Hamiltonian of order $\mathcal{O}(N^0_c)$ defined in a new approach where the separation of the system into two parts is not required. Three degenerate sets of states (towers) with the same quantum numbers as in the scattering picture and in the standard procedure are obtained. Thus the 0 is equally achieved. The eigenvalues of the presently chosen Hamiltonian also have simple analytic expressions, depending linearly on the three dynamical coefficients entering the Hamiltonian. This reinforces the validity of the new approach which had already 0 described excited negative parity baryons in a large energy range.