Domain-Wall Fermion with $R_5$ Symmetry

We present the domain-wall fermion operator which is reflection symmetric in the fifth dimension, with the approximate sign function $S(H)$ of the effective 4-dimensional Dirac operator satisfying the bound $ |1-S(\lambda)| \le 2 d_Z $for$ \lambda^2 \in [\lambda_{min}^2, \lambda_{max}^2] $,where$ d_Z $isthemaximumdeviation$ | 1- \sqrt{x} R_Z(x) |{\rm max} $ of the Zolotarev optimal rational polynomial $R_Z(x)$ of $1\mathrm{/}\sqrt{x}$ for $ x \in [1, \lambda{max}^2/\lambda_{min}^2] $,withdegrees$ (n-1,n) $for$ N_s = 2n $,and$ (n,n) $for$ N_s = 2 n + 1 $.