Improving the Chiral Properties of Lattice Fermions

Abstract

The chiral properties of lattice fermions can be improved by altering either their fermion-gauge coupling or the pure gauge part of the action (or both). Using both perturbation theory and nonperturbative simulation, we compare a simple alteration of the gauge action (which encompasses the Wilson, Symanzik, Iwasaki, and DBW2 actions), and HYP-blocked links in the fermion action. Perturbative tests include calculations of the potential, flavor-changing quark scattering amplitudes, and matching factors for currents. Non-perturbative tests include the potential, measurements of flavor symmetry breaking for staggered fermions, the behavior of topological objects, and properties of overlap actions. Our results display the bad properties of these actions as well as their good ones.

Figures (11)

• Figure 1: The scaled static potential $4\pi rV(r)$ for several lattice actions: (a) Wilson ($c_{1}=0$), (b) tree level Symanzik ($c_{1}=-1/12$), (c) Iwasaki ($c_{1}=-0.331$)(d) DWB2 ($c_{1}=-1.4088$).
• Figure 2: The scaled static "smeared potential" $4\pi rV(r)$ for two lattice actions and two smearing functions: (a) Wilson ($c_{1}=0$) gauge action with HYP blocking, (b) tree level Symanzik ($c_{1}=-1/12$) gauge action with HYP blocking, (c) Wilson ($c_{1}=0$) gauge action with Asqtad blocking, (d) tree level Symanzik ($c_{1}=-1/12$) gauge action with Asqtad blocking,
• Figure 3: $k^{2}G_{\mu \mu }(k)$ for several lattice actions: (a) Wilson ($c_{1}=0$), (b) tree level Symanzik ($c_{1}=-1/12$), (c) Iwasaki ($c_{1}=-0.331$)(d) DWB2 ($c_{1}=-1.4088$).
• Figure 4: $k^{2}{\cal G}_{\mu \mu }(k)$ for two lattice actions and two smearing functions: (a) Wilson ($c_{1}=0$) gauge action with HYP blocking, (b) tree level Symanzik ($c_{1}=-1/12$) gauge action with HYP blocking, (c) Wilson ($c_{1}=0$) gauge action with Asqtad blocking, (d) tree level Symanzik ($c_{1}=-1/12$) gauge action with Asqtad blocking,
• Figure 5: The static potential measured with a) Wilson gauge action, b) 1-loop Symanzik gauge action and c) DBW2 gauge action. In all cases both the thin link (diamonds) and HYP smeared (octagons) potentials are plotted, shifted to agree at $r/a=\sqrt{7}$. The dotted and dashed lines are the fitted continuum potentials as described in the text.