Rationale for UV-filtered clover fermions

TL;DR

The paper addresses chiral symmetry breaking in Wilson-type lattice QCD by examining UV-filtered (fat-link) Wilson and clover fermions. It combines 1-loop perturbative calculations of the additive mass shift $m_{crit}$ and renormalization factors $Z_S$, $Z_P$, $Z_V$, $Z_A$ across APE, HYP, EXP, and HEX smearings with and without a clover term, and pairs these with non-perturbative quenched tests. The main finding is that applying UV-filtering together with clover improvement substantially suppresses chiral-symmetry breaking, reducing residual masses to $m_{res} = O(10^{-2})$ in lattice units and to tens of MeV in physical units in the tested regimes. While 1-loop perturbation theory with tree-level improvement does not perfectly match non-perturbative data, the combined approach brings perturbative predictions much closer to reality, suggesting that filtered clover fermions are promising for large-scale dynamical simulations; future work includes determining 1-loop $c_{SW}$ for expanded smearing schemes to achieve near-continuum behavior at accessible couplings.

Abstract

We study the contributions Sigma_0 and Sigma_1, proportional to a^0 and a^1, to the fermion self-energy in Wilson's formulation of lattice QCD with UV-filtering in the fermion action. We derive results for m_{crit} and the renormalization factors Z_S, Z_P, Z_V, Z_A to 1-loop order in perturbation theory for several filtering recipes (APE, HYP, EXP, HEX), both with and without a clover term. The perturbative series is much better behaved with filtering, in particular tadpole resummation proves irrelevant. Our non-perturbative data for m_{crit} and Z_A/(Z_m*Z_P) show that the combination of filtering and clover improvement efficiently reduces the amount of chiral symmetry breaking -- we find residual masses am_{res}=O(10^{-2}).

Figures (4)

• Figure 1: Finite pieces $z_{S,P,V,A}$ of the $Z_X$ for 1 APE and 1 HYP fermions as a function of $c_\mathrm{SW}$.
• Figure 2: Our data for $2m^\mathrm{PCAC}$ vs. $m_0$ with $c_\mathrm{SW}\!=\!0$ (left) and $c_\mathrm{SW}\!=\!1$ (right) at three couplings.
• Figure 3: $-am_\mathrm{crit}$ vs. $g_0^2$ for Wilson ($c_\mathrm{SW}\!=\!0$, left) and clover ($c_\mathrm{SW}\!=\!1$, right) fermions with 8 filterings. The curves indicate 3-parameter rational fits.
• Figure 4: $Z_A/(Z_mZ_P)$ vs. $g_0^2$ for Wilson ($c_\mathrm{SW}\!=\!0$, left) and clover ($c_\mathrm{SW}\!=\!1$, right) fermions with 8 filterings. The curves indicate 3-parameter rational fits.