Do Quarks Really Form Diquark Clusters in the Nucleon?

A gauge invariant method for the investigation of scalar diquark clustering in the nucleon ground state is presented. The method focuses on a comparison of quark distributions in the nucleon with those in the $\Delta$ baryon resonance. Recent lattice QCD calculations of these quark distribution radii are analyzed in a search for evidence of scalar diquark clustering. The analysis indicates the lattice results describe the negative squared charge radius of the neutron with little resort to hyperfine clustering between $u$-$d$-quark pairs. This result contrasts both quark-diquark and nonrelativistic quark models where hyperfine attraction between $u$ and $d$ quarks in the nucleon is argued to play a significant role. Comparison of light quark distributions in $\Lambda^0$ and $\Sigma^{*0}$ indicate only a small reduction of the scalar diquark distribution radius relative to the vector diquark distribution. Current lattice QCD determinations of baryon charge distributions do not support the concept of substantial $u$-$d$ scalar diquark clustering as an appropriate description of the internal structure of the nucleon.