Hadronic structure on the light-front IX . Orbital-spin-isospin wave functions of baryons

TL;DR

This paper develops detailed baryon wavefunctions in both the center-of-mass and light-front frameworks, clarifying permutation symmetries, and introduces a new basis for longitudinal wavefunctions, advancing the understanding of baryon structure.

Contribution

It provides explicit symmetric and antisymmetric wavefunctions for baryons, extends analysis to five-quark spinors, and introduces a novel basis for light-front longitudinal wavefunctions.

Findings

Explicit symmetric wavefunctions for excited nucleons derived.

New basis set for light-front longitudinal wavefunctions introduced.

Permutation symmetries and spin-mixing effects analyzed.

Abstract

This paper which is part of a series, is devoted to several technical issues. In the first part of the paper, we discuss the usual wavefunctions in the CM frame for baryons, by clarifying the representations of the three-quark permutation group $S_3$. We extend the analysis for up to five ``spinors" with $\rho,\lambda$-symmetry, and derive explicitly the totally symmetric wavefunctions modulo color. They are explicitly used to describe the excited nucleons $N^*$ states, in the P- and D-shell. We also show how to use symbolic operations in Mathematica, in spin-tensor notations to make explicit these states. For the S- and P-shells, the totally antisymmetric wavefunctions are given, and the pertinent matrix elements for the spin-dependent operators calculated, including the mixing between states with different total spin $S$. In the second part of the paper we turn to the light front wavefunctions, with an emphasis on the longitudinal wavefunctions, with a novel basis set. We also discuss their symmetries under permutations, and select the proper combinations for the transverse and longitudinal excitations for $N^*$ on the light front.