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