Flavor Twisted Boundary Conditions and the Nucleon Vector Current

TL;DR

This paper develops a theoretical framework using flavor twisted boundary conditions to improve the extraction of nucleon vector current matrix elements from lattice QCD simulations, accounting for finite volume effects.

Contribution

It introduces a method to analyze finite volume corrections for nucleon matrix elements with twisted boundary conditions using partially twisted, partially quenched heavy baryon chiral perturbation theory for the SU(7|5) group.

Findings

Finite volume corrections are exponentially small but significant at small twist angles.

Using the Breit frame does not reduce volume corrections.

The formalism applies broadly to nucleon matrix elements and improves extraction of physical observables.

Abstract

Using flavor twisted boundary conditions, we study nucleon matrix elements of the vector current. We twist only the active quarks that couple to the current. Finite volume corrections due to twisted boundary conditions are determined using partially twisted, partially quenched, heavy baryon chiral perturbation theory, which we develop for the graded group SU(7|5). Asymptotically these corrections are exponentially small in the volume, but can become pronounced for small twist angles. Utilizing the Breit frame does not mitigate volume corrections to nucleon vector current matrix elements. The derived expressions will allow for better controlled extractions of the isovector magnetic moment and the electromagnetic radii from simulations at zero lattice momentum. Our formalism, moreover, can be applied to any nucleon matrix elements.