not been achieved so far because of the inherent defects in these quark actions: the explicit chiral symmetry breaking in the Wilson quark action causes the non-trivial operator mixing between different chiralities and for the KS quark it is hard to treat the heavy-light cases due to the flavor symmetry breaking.

The domain-wall quark formulation in lattice QCD, which is based on the introduction of many heavy regulator fields, was proposed by Shamir[@Shamir93; @Shamir95] anticipating superior features over other quark formulations: no need of the fine tuning to realize the chiral limit and no restriction for the number of flavors. Recent simulation results seem to support the former feature non-perturbatively[@Blum-Soni; @Wingate; @Blum]. It is also perturbatively shown that the massless mode at the tree level still remains stable against the quantum correction[@Aoki-Taniguchi]. These advantageous features fascinate us to the application of the domain-wall quark for calculation of the three- and four-quark hadron matrix elements.

In order to convert the matrix elements obtained by lattice simulations to those defined in some continuum renormalization scheme(${\it e.g.}, {{\overline {\rm MS}}}$), we must know the renormalization factors connecting the lattice operators to the continuum counterparts defined in some renormalization scheme. In this article we 