2023/08/28 by Nicholas Miesch, Edward Shuryak, Miesch, Nicholas +3
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Particle physics theoretical and experimental studies #Nuclear physics research studies
paper · pdf · doi:10.48550/arxiv.2308.14694
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 S3. We extend the analysis for up to five ``spinors" with ρ,λ-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.