Connected and disconnected quark contributions to hadron spin

TL;DR

This paper uses the Feynman-Hellmann theorem to determine quark spin contributions to hadrons, revealing significant connected contributions and initial insights into disconnected contributions, with sensitivity to SU(3) symmetry breaking.

Contribution

It introduces a novel application of the Feynman-Hellmann theorem to compute both connected and disconnected quark contributions to hadron spin in lattice QCD.

Findings

Connected quark spin fractions are 55-70% for various hadrons.

Disconnected contributions to nucleon spin are small and negative.

Tensor matrix elements from disconnected diagrams are consistent with zero.

Abstract

By introducing an external spin operator to the fermion action, the quark spin fractions of hadrons are determined from the linear response of the hadron energies using the Feynman-Hellmann (FH) theorem. At our SU(3)-flavour symmetric point, we find that the connected quark spin fractions are universally in the range 55-70\% for vector mesons and octet and decuplet baryons. There is an indication that the amount of spin suppression is quite sensitive to the strength of SU(3) breaking. We also present first preliminary results applying the FH technique to calculations of quark-line disconnected contributions to hadronic matrix elements of axial and tensor operators. At the SU(3)-flavour symmetric point we find a small negative contribution to the nucleon spin from disconnected quark diagrams, while the corresponding tensor matrix elements are consistent with zero.