Wave Function of the Roper from Lattice QCD

TL;DR

This study successfully extracts the wave functions of the Roper and higher nucleon states using lattice QCD, confirming their structure aligns with constituent quark models and highlighting finite volume effects.

Contribution

It demonstrates a novel approach combining variational analysis and lattice QCD to determine nucleon excited state wave functions and compares them with quark model predictions.

Findings

Roper wave function shows a single node, consistent with a 2S state.

Higher state wave function shows two nodes, consistent with a 3S state.

Finite volume effects significantly influence excited state masses.

Abstract

We apply the eigenvectors from a variational analysis in lattice QCD to successfully extract the wave function of the Roper state, and a higher mass P_11 state of the nucleon. We use the 2+1 flavour 32^3x64 PACS-CS configurations at a near physical pion mass of 156 MeV. We find that both states exhibit a structure consistent with a constituent quark model. The Roper d-quark wave function contains a single node consistent with a 2S state, and the third state wave function contains two, consistent with a 3S state. A detailed comparison with constituent quark model wave functions is carried out, obtained from a Coulomb plus ramp potential. These results validate the approach of accessing these states by constructing a variational basis composed of different levels of fermion source and sink smearing. Furthermore, significant finite volume effects are apparent for these excited states which mix with multi-particle states, driving their masses away from physical values and enabling the extraction of resonance parameters from lattice QCD simulations.