Before sailing on a domain-wall sea

TL;DR

The paper analyzes the impact of residual masses in domain-wall fermion simulations on systematic errors, emphasizing the need for optimized actions and specific residual mass thresholds to ensure accuracy.

Contribution

It highlights the different roles of valence and sea-quark residual masses and provides guidelines for controlling systematic errors in domain-wall fermion simulations.

Findings

Valence-quark residual mass can cause larger systematic errors.

Residual mass thresholds for 1% systematic error are estimated.

Mixed schemes and improved actions are recommended for better accuracy.

Abstract

We discuss the very different roles of the valence-quark and the sea-quark residual masses ($m_{res}^v$ and $m_{res}^s$) in dynamical domain-wall fermions simulations. Focusing on matrix elements of the effective weak hamiltonian containing a power divergence, we find that $m_{res}^v$ can be a source of a much bigger systematic error. To keep all systematic errors due to residual masses at the 1% level, we estimate that one needs $a m_{res}^s \le 10^{-3}$ and $a m_{res}^v \le 10^{-5}$, at a lattice spacing $a\sim 0.1$ fm. The practical implications are that (1) optimal use of computer resources calls for a mixed scheme with different domain-wall fermion actions for the valence and sea quarks; (2) better domain-wall fermion actions are needed for both the sea and the valence sectors.