Understanding the structure of nucleon excitations from their wavefunctions

TL;DR

This study analyzes relativistic wavefunctions of nucleon excitations from lattice QCD to understand their node structures and the role of local interpolating fields in shaping the nucleon spectrum.

Contribution

It reveals two types of wavefunction nodes—superposition and built-in nodes—and explores their origins using visualizations and radial wavefunction calculations.

Findings

Identified two distinct node types in nucleon wavefunctions.

Visualized wavefunctions through volume and surface renderings.

Connected wavefunction properties to fundamental lattice operators.

Abstract

Relativistic wavefunctions of nucleon excitations are scrutinised to understand their node structure and the underlying role of local interpolating fields in generating the nucleon spectrum. In addressing quark model perspectives, approximately 4000 propagators are employed on the heaviest PACS-CS ensemble at $m_\pi \simeq$ 702 MeV. We examine the ground and four lowest-lying excited states at zero momentum for both positive- and negative-parity spectra, where the proton's d-quark wavefunction is calculated about the two u quarks at the origin. This is achieved using two local interpolating fields that each carry the quantum numbers of the nucleon but with differing spin-flavour structures, one of which vanishes in the nonrelativistic limit. We find that two distinct types of wavefunction nodes are manifest: "superposition nodes" formed through a linear combination of interpolating fields, and novel "built-in nodes" that are fundamentally built in to the s-wave Dirac components of an individual interpolating field. These are investigated qualitatively through visualisations in the form of both volume and surface renderings, and quantitatively by the calculation of radial wavefunctions. Combined, these findings build a comprehensive picture of the single-particle nucleon spectrum and how its properties derive from fundamental lattice operators.