$[{\bf 70, \ell^+}]$ baryons in large $N_c$ QCD revisited: The effect on Regge trajectories

TL;DR

This paper revisits the structure of $70, \, \ell^+$ baryons in large $N_c$ QCD, demonstrating the importance of spin and isospin operators in mass formulas and exploring implications for Regge trajectories across different multiplets.

Contribution

It applies a unified $1/N_c$ expansion approach to positive parity baryons, highlighting the dominant role of spin and isospin operators and analyzing their impact on Regge trajectories.

Findings

Both spin and isospin operators are crucial in describing baryon masses.

The leading spin-isospin singlet term varies with band number, indicating different Regge trajectories.

The approach successfully describes mixed symmetric positive parity baryon states.

Abstract

A simple procedure within the $1/N_c$ expansion method where all the $N_c$ quarks are treated on the same footing has been found successful in describing mixed symmetric negative parity baryon states belonging to the $[{\bf 70},\ell^-]$ multiplets %with $\ell$ = 1, 2 or 3. of the $N$ = 1 and 3 bands. Presently it is applied to mixed symmetric positive parity $[{\bf 70},0^+]$ and $[{\bf 70},2^+]$ multiplets of the $N$ = 2 band. We search for the most dominant terms in the mass formula. The results are compared to those obtained in the procedure where the system is separated into a core and an excited quark. We find that both the spin and isospin operators of the entire system of $N_c$ quarks play dominant roles in describing the data, like for negative parity states. As a by-product we present the contribution of the leading spin-isospin singlet term as a function of the band number, which hints at distinct Regge trajectories for the symmetric and mixed symmetric states.