Exploring the Roper wave function in Lattice QCD

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.