The Shape of Covariantly Smeared Sources in Lattice QCD

TL;DR

This paper studies how covariantly smeared sources in lattice QCD are affected by magnetic field concentrations, revealing distortions at small lattice spacings, and introduces a new 'free-form smearing' method to create arbitrarily shaped sources.

Contribution

The paper identifies distortions in covariant smearing due to magnetic fields and proposes a novel 'free-form smearing' technique for flexible source shaping in lattice QCD.

Findings

Magnetic field concentrations cause distortions in smeared sources.

Iterative smearing requires many iterations at small lattice spacings.

'Free-form smearing' enables arbitrary source shapes, including Gaussian profiles.

Abstract

Covariantly smeared sources are commonly used in lattice QCD to enhance the projection onto the ground state. Here we investigate the dependence of their shape on the gauge field background and find that the presence of localized concentrations of magnetic field can lead to strong distortions which reduce the smearing radii achievable by iterative smearing prescriptions. In particular, as $a\to 0$, iterative procedures like Jacobi smearing require increasingly large iteration counts in order to reach physically-sized smearing radii $r_{sm}\sim$ 0.5 fm, and the resulting sources are strongly distorted. To bypass this issue, we propose a covariant smearing procedure (``free-form smearing'') that allows us to create arbitrarily shaped sources, including in particular Gaussians of arbitrary radius.