Ordering of Spin-$\frac{1}{2}$ Excitations of the Nucleon in Lattice QCD

TL;DR

This study investigates the ordering of nucleon excitations using lattice QCD, finding evidence that the physical level ordering emerges at light quark masses through a comprehensive variational analysis.

Contribution

It provides the first detailed lattice QCD analysis of the level ordering between the Roper and negative parity nucleon states using a variational method with smeared correlation functions.

Findings

Evidence of physical level ordering at light quark masses.

Successful isolation of the negative parity nucleon state.

Use of comprehensive correlation matrix analysis.

Abstract

We present results for the negative parity low-lying state of the nucleon, $N{\frac{1}{2}}^{-}$ (1535 MeV) ${\rm S}_{11}$, from a variational analysis method. The analysis is performed in quenched QCD with the FLIC fermion action. The principal focus of this paper is to explore the level ordering between the Roper (${\rm{P}}_{11}$) and the negative parity ground (${\rm{S}}_{11}$) states of the nucleon. Evidence of the physical level ordering is observed at light quark masses. A wide variety of smeared-smeared correlation functions are used to construct correlation matrices. A comprehensive correlation matrix analysis is performed to ensure an accurate isolation of the $N{\frac{1}{2}}^{-}$ state.