A Feynman-Hellmann approach to the spin structure of hadrons

TL;DR

This paper introduces a Feynman-Hellmann approach in lattice QCD to determine quark spin fractions of hadrons, offering a potentially more precise and less contaminated method compared to traditional techniques.

Contribution

The study applies the Feynman-Hellmann theorem to lattice QCD for calculating quark spin contributions, demonstrating its effectiveness and advantages over standard methods.

Findings

Feynman-Hellmann method achieves statistical precision comparable to three-point functions.

The method reduces excited state contamination in measurements.

Connected quark spin fractions range from 55% to 70% at SU(3) symmetry.

Abstract

We perform a Nf = 2 + 1 lattice QCD simulation to determine the quark spin fractions of hadrons using the Feynman-Hellmann theorem. By introducing an external spin operator to the fermion action, the matrix elements relevant for quark spin fractions are extracted from the linear response of the hadron energies. Simulations indicate that the Feynman-Hellmann method offers statistical precision that is comparable to the standard three-point function approach, with the added benefit that it is less susceptible to excited state contamination. This suggests that the Feynman-Hellmann technique offers a promising alternative for calculations of quark line disconnected contributions to hadronic matrix elements. At the SU(3)-flavour symmetry 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.