Pion in a uniform background magnetic field with clover fermions

TL;DR

This paper investigates how clover fermions can mitigate unphysical mass renormalization effects caused by background magnetic fields in lattice QCD, improving the accuracy of hadronic property calculations.

Contribution

It demonstrates that nonperturbative improvement of clover fermions effectively suppresses field-dependent mass renormalization artifacts in background field calculations.

Findings

Clover fermions reduce unphysical mass shifts in magnetic fields.

Proper nonperturbative improvement is essential for accurate results.

The method is effective over a broad range of magnetic field strengths.

Abstract

Background field methods provide an important nonperturbative formalism for the determination of hadronic properties which are complementary to matrix-element calculations. However, new challenges are encountered when utilising a fermion action exposed to additive mass renormalisations. In this case, the background field can induce an undesired field-dependent additive mass renormalisation that acts to change the quark mass as the background field is changed. For example, in a calculation utilising Wilson fermions in a uniform background magnetic field, the Wilson term introduced a field-dependent renormalisation to the quark mass which manifests itself in an unphysical increase of the neutral-pion mass for large magnetic fields. Herein, the clover fermion action is studied to determine the extent to which the removal of $\mathcal{O}(a)$ discretisation errors suppresses the field-dependent changes to the quark mass. We illustrate how a careful treatment of nonperturbative improvement is necessary to resolve this artefact of the Wilson term. Using the $32^3 \times 64$ dynamical-fermion lattices provided by the PACS-CS Collaboration we demonstrate how our technique suppresses the unphysical mass renormalisation over a broad range of magnetic field strengths.