Flavour singlet physics in lattice QCD with background fields

TL;DR

This paper introduces a background field method in lattice QCD that enables the calculation of flavor-singlet hadronic matrix elements without disconnected diagrams, improving the study of nucleon spin and nuclear properties.

Contribution

The authors develop a background field approach that simplifies the computation of flavor-singlet matrix elements in lattice QCD, avoiding disconnected diagrams and enabling new calculations.

Findings

Facilitates calculation of quark spin contributions to the proton.

Allows direct lattice QCD study of the EMC effect.

Enables computation of deuteron magnetic and quadrupole moments.

Abstract

We show that hadronic matrix elements can be extracted from lattice simulations with background fields that arise from operator exponentiation. Importantly, flavour-singlet matrix elements can be evaluated without requiring the computation of disconnected diagrams, thus facilitating a calculation of the quark contribution to the spin of the proton and the singlet axial coupling, $g_A^0$. In the two nucleon sector, a background field approach will allow calculation of the magnetic and quadrupole moments of the deuteron and an investigation of the EMC effect directly from lattice QCD. Matrix elements between states of differing momenta are also analysed in the presence of background fields.