Perturbative renormalization for static and domain-wall bilinears and four-fermion operators with improved gauge actions

We calculate one-loop renormalization factors for heavy-light bilinears as well as four-fermion operators relevant for $B^0-{\bar{B}}^0$ mixing calculations on the lattice. We use the static approximation for heavy quarks and the domain-wall formulation for light quarks. We present results for different choices of improved gauge action.