arXiv subjects

Maximilian Ammer

Publications and source records attributed to Maximilian Ammer.

7 recordsLinked to original sources

arXiv2026

One-loop $c_\mathrm{SW}$ for Wilson and Brillouin fermions with stout smearing or Wilson flow

We present results for the one-loop value of the improvement coefficient $c_\mathrm{SW}$ for Wilson and Brillouin fermions subject to stout smearing or Wilson flow, in combination with Wilson or Symanzik glue. To this end we use a recently developed method that allows one to modify an existing perturbative calculation, like the one for $c_\mathrm{SW}^{(1)}$, to include stout smearing or Wilson flow at arbitrary stout parameters ($\varrho$, $n_\mathrm{stout}$) or flow times $t/a^2$, respectively. Our results indicate that already a small amount of smoothing makes the perturbative series well behaved, suggesting that a non-perturbatively determined $c_\mathrm{SW}$ might be close to its one-loop value for couplings $g_0^2\simeq 1$.

hep-lat↗

arXiv2024

Stout smearing and Wilson flow in lattice perturbation theory

We present the expansion of stout smearing and the Wilson flow in lattice perturbation theory to order $g_0^3$, which is suitable for one-loop calculations. As the Wilson flow is generated by infinitesimal stout smearing steps, the results are related to each other by taking the appropriate limits. We show how to apply perturbative stout smearing or Wilson flow to the Feynman rules of any lattice fermion action and and illustrate them by calculating the self-energy of the clover-improved Wilson fermion.

hep-lat↗

arXiv2024

Eigenvalue based taste breaking of staggered, Karsten-Wilczek and Borici-Creutz fermions with stout smearing in the Schwinger model

In two spacetime dimensions staggered fermions are minimally doubled, like Karsten-Wilczek and Borici-Creutz fermions. A continuum eigenvalue is thus represented by a pair of near-degenerate eigenvalues, with the splitting $δ$ quantifying the cut-off induced taste symmetry breaking. We use the quenched Schwinger model to determine the low-lying fermionic eigenvalues (with 0, 1 or 3 steps of stout smearing), and analyze them in view of the global topological charge $q\in\mathbb{Z}$ of the gauge background. For taste splittings pertinent to would-be zero modes, we find asymptotic Symanzik scaling of the form $δ_\mathrm{wzm} \propto a^2$ with link smearing, and $δ_\mathrm{wzm} \propto a$ without, for each action. For taste splittings pertinent to non-topological modes, staggered splittings scale as $δ_\mathrm{ntm} \propto a^p$ (where $p\simeq2$ with smearing and $p=1$ without), while Karsten-Wilczek and Boriçi-Creutz fermions scale as $δ_\mathrm{ntm} \propto a$ (regardless of the smearing level). Large logarithmic corrections are seen with smearing.

hep-lat↗

arXiv2024

Stout-smearing, gradient flow and $c_{\text{SW}}$ at one loop order

The one-loop determination of the coefficient $c_\text{SW}$ of the Wilson quark action has been useful to push the leading cut-off effects for on-shell quantities to $\mathcal{O}(α^2 a)$ and, in conjunction with non-perturbative determinations of $c_\text{SW}$, to $\mathcal{O}(a^2)$, as long as no link-smearing is employed. These days it is common practice to include some overall link-smearing into the definition of the fermion action. Unfortunately, in this situation only the tree-level value $c_\text{SW}^{(0)}=1$ is known, and cut-off effects start at $\mathcal{O}(αa)$. We present some general techniques for calculating one loop quantities in lattice perturbation theory which continue to be useful for smeared-link fermion actions. Specifically, we discuss the application to the 1-loop improvement coefficient $c_\text{SW}^{(1)}$ for overall stout-smeared Wilson fermions.

hep-lat↗

arXiv2024

Calculation of $c_\mathrm{SW}$ at one-loop order for Brillouin fermions

The Brillouin action is a Wilson-like lattice fermion action with a 81-point stencil, which was found to ameliorate the Wilson action in many respects. The Sheikholeslami-Wohlert coefficient $c_\mathrm{SW}$ of the clover improvement term has a perturbative expansion $c_\mathrm{SW}=c_\mathrm{SW}^{(0)}+g_0^2c_\mathrm{SW}^{(1)}+\mathcal{O}(g_0^4)$. At tree-level $c_\mathrm{SW}^{(0)}=r$ holds for Wilson and Brillouin fermions alike. We present the Feynman rules for the Brillouin action in lattice perturbation theory, and employ them to calculate the one-loop coefficient $c_\mathrm{SW}^{(1)}$ with plaquette or Lüscher-Weisz gluons. Numerically its value is found to be about half that of the Wilson action.

hep-lat↗

arXiv2022

$\mathbf{c_\textbf{SW}}$ at One-Loop Order for Brillouin Fermions

Wilson-like Dirac operators can be written in the form $D=γ_μ\nabla_μ-\frac {ar}{2} Δ$. For Wilson fermions the standard two-point derivative $\nabla_μ^{(\mathrm{std})}$ and 9-point Laplacian $Δ^{(\mathrm{std})}$ are used. For Brillouin fermions these are replaced by improved discretizations $\nabla_μ^{(\mathrm{iso})}$ and $Δ^{(\mathrm{bri})}$ which have 54- and 81-point stencils respectively. We derive the Feynman rules in lattice perturbation theory for the Brillouin action and apply them to the calculation of the improvement coefficient ${c_\mathrm{SW}}$, which, similar to the Wilson case, has a perturbative expansion of the form ${c_\mathrm{SW}}=1+{c_\mathrm{SW}}^{(1)}g_0^2+\mathcal{O}(g_0^4)$. For $N_c=3$ we find ${c_\mathrm{SW}}^{(1)}_\mathrm{Brillouin} =0.12362580(1) $, compared to ${c_\mathrm{SW}}^{(1)}_\mathrm{Wilson} = 0.26858825(1)$, both for $r=1$.

hep-lat↗

arXiv2019

Details of a staggered fermion data analysis

We present technical details of an analysis of pseudo-scalar data from a QCD simulation with staggered fermions. The data were obtained close to the physical point with an inverse lattice spacing of about 3 GeV, and $N_f=2+1+1$. We compare different methods of extracting effective masses and decay constants in lattice units. The results of several correlated and uncorrelated fitting methods are compared, both on the simulated data set, and on a synthetically generated data set.

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