Distance between various discretized fermion actions

Abstract

We present the leading order mixed-action effect ${\Delta }_{\mathrm{mix}}\equiv m_{\pi ,\mathrm{vs}}^2-\frac{m_{\pi ,\mathrm{vv}}^2+m_{\pi ,\mathrm{ss}}^2}{2}$ using HISQ, clover or overlap valence fermion actions on gauge ensembles using various sea fermion actions across a widely-used lattice spacing range $a\in [0.04,0.19]$~fm. The results suggest that ${\Delta }_{\mathrm{mix}}$ decreases as the fourth order of the lattice spacing on the gauge ensembles with dynamical chiral sea fermions, such as Domain wall or HISQ fermions. When a clover sea fermion action which has explicit chiral symmetry breaking is used in the ensemble, ${\Delta }_{\mathrm{mix}}$ can be much larger regardless of the valence fermion action used.

Comments: 12 pages, 9 figures, add a new figure to illustrate the mix action effect