The Shape of Covariantly Smeared Sources in Lattice QCD

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.