Before sailing on a domain-wall sea

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.

Comments: latex, 25 pages. Improved discussion in appendix, including correction of some technical mistakes; ref. added