Structure of the Nucleon and its Excitations

TL;DR

This paper investigates the nucleon's structure and excitations using three approaches: wave function analysis, parity-expanded variational analysis, and Hamiltonian effective field theory, revealing insights into gluonic roles, form factors, and resonance origins.

Contribution

It introduces new techniques for analyzing relativistic wave functions, isolates nucleon states at finite momentum, and connects lattice QCD results with effective field theory to understand nucleon excitations.

Findings

Node structure of nucleon wave functions illustrated.

Magnetic form factors of odd-parity nucleons examined.

Roper resonance linked to multi-particle interactions.

Abstract

The structure of the ground state nucleon and its finite-volume excitations are examined from three different perspectives. Using new techniques to extract the relativistic components of the nucleon wave function, the node structure of both the upper and lower components of the nucleon wave function are illustrated. A non-trivial role for gluonic components is manifest. In the second approach, the parity-expanded variational analysis (PEVA) technique is utilised to isolate states at finite momenta, enabling a novel examination of the electric and magnetic form factors of nucleon excitations. Here the magnetic form factors of low-lying odd-parity nucleons are particularly interesting. Finally, the structure of the nucleon spectrum is examined in a Hamiltonian effective field theory analysis incorporating recent lattice-QCD determinations of low-lying two-particle scattering-state energies in the finite volume. The Roper resonance of Nature is observed to originate from multi-particle coupled-channel interactions while the first radial excitation of the nucleon sits much higher at approximately 1.9 GeV.