The $\Delta_{mix}$ parameter in the overlap on domain-wall mixed action

TL;DR

This paper directly calculates the mixed-action parameter $ ext{Δ}_{mix}$ using overlap fermions on a domain-wall sea, providing results that are consistent across different lattice spacings and smaller than previous estimates, enhancing understanding of mixed-action lattice QCD.

Contribution

The paper presents the first direct calculation of $ ext{Δ}_{mix}$ with valence overlap fermions on a domain-wall fermion sea, showing its independence from lattice spacing and its smaller magnitude compared to previous results.

Findings

$ ext{Δ}_{mix}$ is approximately 0.030 GeV^4 for pion masses near 300 MeV.

$ ext{Δ}_{mix}$ shows little dependence on lattice spacing.

The results are significantly smaller than previous estimates with different sea fermions.

Abstract

A direct calculation of the mixed-action parameter $\Delta_{mix}$ with valence overlap fermions on a domain-wall fermion sea is presented. The calculation is performed on four ensembles of the 2+1-flavor domain-wall gauge configurations: $24^3 \times 64$ ($a m_l= 0.005$, $a=0.114\fm$) and $32^3 \times 64$ ($a m_l = 0.004, 0.006, 0.008$, $a=0.085\fm$). For pion masses close to $300\MeV$ we find \hbox{$\Delta_{mix}=0.030(6)\GeV^4$} at $a=0.114\fm$ and $\Delta_{mix}=0.033(12)\GeV^4$ at $a=0.085\fm$. The results are quite independent of the lattice spacing and they are significantly smaller than the results for valence domain-wall fermions on Asqtad sea or those of valence overlap fermions on clover sea. Combining the results extracted from these two ensembles, we get $\Delta_{mix}=0.030(6)(5)\GeV^4$, where the first error is statistical and the second is the systematic error associated with the fitting method.