Updated $1/N_c$ expansion analysis of $[{\bf 56, 2^+}]$ and $[{\bf 70, \ell^+}]$ baryon multiplets

TL;DR

This paper updates the $1/N_c$ expansion analysis of certain baryon multiplets using 2014 data, focusing on mass formulas, SU(3) symmetry breaking, and hyperon assignments, revealing different Regge trajectories for symmetric and mixed states.

Contribution

It provides a unified mass formula framework for both multiplets and examines the role of SU(3) breaking operators, with implications for hyperon classification and baryon trajectory distinctions.

Findings

Mass formulas include corrections up to 1/N_c and first order SU(3) breaking.

Distinct Regge trajectories are suggested for symmetric and mixed symmetric states.

Tentative hyperon assignments are proposed for the multiplets.

Abstract

The mass spectra of the $[{\bf 56, 2^+}]$ and $[{\bf 70, \ell+}]$ multiplets, both belonging to the $N$ = 2 band, is reviewed in the $1/N_c$ expansion method. Previous studies, separately made for each multiplet, are presently updated to the 2014 Particle Data Group. The mass formula including corrections up to $\mathcal{O}(1/N_c)$ and first order in SU(3) flavor symmetry breaking, has the same independent operator basis in both cases. A special emphasis is made on the role of the SU(3) symmetry breaking operators $B_i$ $(i = 1,2,3)$. This can allow for multiplet assignment of $\Lambda$ and $\Sigma$ hyperons, which generally is quite difficult to make. Tentative assignments of hyperons with two- and one-star resonances are made to the $[{\bf 70, \ell+}]$ multiplet. Another important aim is to find out whether or not a common value of the coefficient $c_1$ of the dominant operator in the mass formula, can well fit the present data in both multiplets. A negative answer, which is here the case, implies distinct Regge trajectories for symmetric and mixed symmetric states.