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We calculate one-loop renormalization factors for heavy-light bilinears aswell as four-fermion operators relevant for $B^{0} - \bar{B}^{0}$ mixingcalculations on the lattice. We use the static approximation for heavy quarksand the domain-wall formulation for light quarks. We present results fordifferent choices of improved gauge action.Comment: 21 pages, 3 figures, 3 tables, revtex

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