Positive-parity Excited-states of the Nucleon in Quenched Lattice QCD

TL;DR

This paper investigates positive-parity excited states of the nucleon in quenched lattice QCD using the variational method with large correlation matrices and operator basis improvements to reliably extract multiple excited states.

Contribution

It demonstrates how expanding the operator basis and using large correlation matrices enhances the extraction of nucleon excited states in quenched lattice QCD.

Findings

Improved basis splitting of states into multiple eigenstates

Large correlation matrices improve excited state extraction

Methodology emphasizes the utility of the variational approach

Abstract

Positive-parity spin-1/2 excitations of the nucleon are explored in lattice QCD. The variational method is used in this investigation and several correlation matrices are employed. As our focus is on the utility and methodology of the variational approach, we work in the quenched approximation to QCD. Various sweeps of Gaussian fermion-field smearing is applied at the source and at the sink of $\chi_{1}\bar\chi_{1}$ and $\chi_{1}\chi_{2}$ correlation functions to obtain a large basis of operators. Using several different approaches for constructing basis interpolators, we demonstrate how improving the basis can split what otherwise might be interpreted as a single state into multiple eigenstates. Consistency of the extracted excited energy states are explored over various dimensions of the correlation matrices. The use of large correlation matrices is emphasized for the reliable extraction of the excited eigenstates of QCD.