Matrix elements of SU(6) generators for baryons with arbitrary $N_c$ quarks in mixed symmetric states $[N_c-1,1]$

TL;DR

This paper derives general formulas for SU(6) generator matrix elements in mixed symmetric baryon states with any number of quarks, aiding baryon spectroscopy and extending previous non-strange baryon work to include strange baryons.

Contribution

It provides new analytic expressions for SU(6) generator matrix elements applicable to arbitrary quark numbers in mixed symmetric states, enhancing baryon spectroscopy models.

Findings

Derived explicit formulas for SU(6) matrix elements.

Applicable to both non-strange and strange baryons.

Facilitates studies of excited baryon states.

Abstract

We derive general analytic formulae for the matrix elements of the SU(6) generators for mixed symmetric $[N_c-1,1]$ spin-flavor states with an arbitrary number $N_c$ of quarks. They are relevant for baryon spectroscopy in the $1/N_c$ expansion method applied to light baryons and can be used to study excited states. In this way previous work on non-strange baryons can be extended to both non-strange and strange baryons.