Comparison of the mixed-fermion-action Effects using different fermion and gauge actions with 2+1 and 2+1+1 flavors

TL;DR

This work quantifies the leading mixed-action discretization artifact $Δ_{ m mix}$ in lattice QCD by using $2+1+1$ HISQ sea ensembles with a tadpole-improved Symanzik gauge action across four lattice spacings and comparing to $2+1$ flavor ensembles with different gauge actions. By computing $Δ_{ m mix}$ with multiple valence actions (SC, HC, OV) and interpolating to common lattice spacings, the authors isolate the dominant influence of the sea fermion action, with secondary effects from the gauge action and negligible charm sea contributions. They demonstrate an $O(a^4)$ scaling of $Δ_{ m mix}$ when the sea action preserves chiral symmetry, and show consistency between $2+1$ and $2+1+1$ results at fixed $a$ with the same gauge action. These findings enable greater flexibility in choosing valence actions and inform ongoing optimization of mixed-action lattice QCD calculations.

Abstract

The leading-order low-energy constant $Δ_{\rm mix}$ in mixed-action chiral perturbation theory is calculated using $2+1+1$-flavor gauge ensembles with HISQ fermions and a tadpole-improved Symanzik gauge action at four lattice spacings $a \in [0.048, 0.111]$ fm. By comparing our results to those from different actions and a $2+1$-flavor case, We find that the fermion action has the dominant impact, the gauge action has a secondary but measurable effect, and the contribution from charm quark loops is negligible within our current uncertainties.

Figures (5)

• Figure 1: The normalized variance ratio $\sigma_n/\sigma_1$ of the averaged plaquette $\mathrm{ReTr}(P)$ (upper panel) and $m_{\eta_c}$ (lower panel), using the molecular-dynamics time $\tau=0.5$ (red), 1.0 (blue) and 2.0 (green) per trajectory.
• Figure 2: The ratio $\alpha^{\rm tad}_s/\alpha^{u_0}_s$ of two definitions of effective $\alpha_s$ using different fermion and gauge action combinations. they approach to 1 within a few percent deviations in the weak coupling limit $\alpha_s\rightarrow 0$.
• Figure 3: Mixed-action effects of the Stout link smeared Clover fermion (SC/HI, green triangles) and HYP smeared Clover fermion (HC/HI, yellow left triangles), overlap fermion (OV, blue right triangles, at a=0.108 and 0.073 fm only) on the 2+1+1 flavor HISQ ensembles at different lattice spacings.
• Figure 4: The mixed action effects $\Delta_{\rm mix}$ at $m_{\pi}\sim 0.30$ GeV for various valence fermion actions (OV, SC and HC) and $\bar{\Delta}_{\rm mix, uni}$ for different valence fermion actions (OV+HC, OV+SC and HC+HC) on the 2+1 flavor HI+I, HI+S$^{\rm tad}$, HI+S$^{(0)}$ ensembles, 2+1+1 flavor HI+S$^{\rm tad}$ ensembles, and also includes the values from Ref. Zhao:2022ooq (shown as histograms in the shaded region) for comparison
• Figure 5: Autocorrelation analysis across multiple lattice ensembles, depicting the bin-size dependence of variance for four fundamental quantities: the plaquette operator, topological charge, pion mass, and $\eta_c$ meson mass. The notation $\{\mathrm{Traj.\ }n_{\mathrm{min}},-n_{\mathrm{max}}, \mathrm{step\ }\Delta n\}$ accompanying each observable specifies the minimal and maximal trajectory indices, along with the stride parameter employed for configuration subsampling to ensure statistical independence in our analysis.