Exploring the Roper wave function in Lattice QCD

TL;DR

This paper uses lattice QCD techniques to analyze the Roper resonance, revealing its structure and dominant components, and compares it with constituent quark model predictions.

Contribution

It demonstrates the successful isolation of the Roper state on the lattice and provides detailed insights into its wave function and structure, validating the variational basis approach.

Findings

Roper state is dominated by the $ ext{chi}_1$ nucleon interpolator.

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

The lattice wave function matches constituent quark model predictions.

Abstract

Using a correlation matrix analysis consisting of a variety of smearings, the CSSM Lattice collaboration has successfully isolated states associated with the Roper resonance and other "exotic" excited states such as the $\Lambda(1405)$ on the lattice at near-physical pion masses. We explore the nature of the Roper by examining the eigenvectors that arise from the variational analysis, demonstrating that the Roper state is dominated by the $\chi_1$ nucleon interpolator and only poorly couples to $\chi_2.$ By examining the probability distribution of the Roper on the lattice, we find a structure consistent with a constituent quark model. In particular, the Roper $d$-quark wave function contains a single node consistent with a $2S$ state. A detailed comparison with constituent quark model wave functions is carried out, validating the approach of accessing these states by constructing a variational basis composed of different levels of fermion source and sink smearing.