Isolating Excited States of the Nucleon in Lattice QCD

TL;DR

The paper introduces a robust projection method for extracting nucleon excited-state masses from lattice QCD correlation functions, demonstrating its effectiveness through quenched QCD simulations and highlighting limitations of standard interpolators.

Contribution

A new projection technique using eigenvectors from the variational method improves excited-state extraction in lattice QCD, revealing limitations of standard nucleon interpolators.

Findings

Systematic dependence of excited-state masses on smearing levels.

Correlation matrix of standard interpolators is insufficient to isolate eigenstates.

The method enhances the analysis of nucleon excited states in lattice QCD.

Abstract

We discuss a robust projection method for the extraction of excited-state masses of the nucleon from a matrix of correlation functions. To illustrate the algorithm in practice, we present results for the positive parity excited states of the nucleon in quenched QCD. Using eigenvectors obtained via the variational method, we construct an eigenstate-projected correlation function amenable to standard analysis techniques. The method displays its utility when comparing results from the fit of the projected correlation function with those obtained from the eigenvalues of the variational method. Standard nucleon interpolators are considered, with $2\times 2$ and $3\times 3$ correlation matrix analyses presented using various combinations of source-smeared, sink-smeared and smeared-smeared correlation functions. Using these new robust methods, we observe a systematic dependency of the nucleon excited-state masses on source- and sink-smearing levels. To the best of our knowledge, this is the first clear indication that a correlation matrix of standard nucleon interpolators is insufficient to isolate the eigenstates of QCD.