Low-lying positive-parity excited states of the nucleon

TL;DR

This paper reviews the CSSM Lattice Collaboration's correlation-matrix methods for isolating excited nucleon states, notably identifying a low-lying Roper resonance using advanced lattice QCD techniques.

Contribution

The paper demonstrates the first successful extraction of a low-lying Roper resonance using correlation matrix methods in lattice QCD, highlighting methodological robustness and the importance of smearing.

Findings

Identification of a low-lying Roper resonance contrasting earlier results.

Validation of correlation matrix methods for excited state extraction.

Demonstration of eigenstate energy independence from interpolator basis.

Abstract

We present an overview of the correlation-matrix methods developed recently by the CSSM Lattice Collaboration for the isolation of excited states of the nucleon. Of particular interest is the first positive-parity excited-state of the nucleon known as the Roper resonance. Using eigenvectors of the correlation matrix we construct parity and eigenstate projected correlation functions which are analysed using standardized methods. The robust nature of this approach for extracting the eigenstate energies is presented. We report the importance of using a variety of source and sink smearings in achieving this. Ultimately the independence of the eigenstate energies from the interpolator basis is demonstrated. In particular we consider $4\times 4$ correlation matrices built from a variety of interpolators and smearing levels. Using FLIC fermions to access the light quark mass regime, we explore the curvature encountered in the energy of the states as the chiral limit is approached. We report a low-lying Roper state contrasting earlier results using correlation matrices. To the best of our knowledge, this is the first time a low-lying Roper resonance has been found using correlation matrix methods. Finally, we present our results in the context of the Roper results reported by other groups.