New domain-wall fermion actions

In perturbation theory, the wave function of domain-wall quarks decreases exponentially with the fifth coordinate. We show that, regardless of the quark's own momentum, the fall-off rate of the one-loop wave function is equal to the slowest rate encountered at the tree level for any lattice four-momentum. We propose new domain-wall actions involving beyond-nearest-neighbor couplings in the four physical dimensions, for which the perturbative wave function decreases much faster. It is hoped that the new actions may preserve the good chiral properties of domain-wall fermions up to larger values of the lattice spacing.