Matching of gauge invariant dimension-six operators for b -> s and b -> c transitions

New physics realized above the electroweak scale can be encoded in a model independent way in the Wilson coefficients of higher dimensional operators which are invariant under the Standard Model gauge group. In this article, we study the matching of the SU(3)(C) x SU(2)(L) x U(1)(Y) gauge invariant dimension-six operators on the standard B physics H(a)miltonian relevant for b -> s and b -> c transitions. The matching is performed at the electroweak scale (after spontaneous symmetry breaking) by integrating out the top quark, W, Z and the Higgs particle. We first carry out the matching of the dimension-six operators that give a contribution at tree level to the low energy Hamiltonian. In a second step, we identify those gauge invariant operators that do not enter b -> s transitions already at tree level, but can give relevant one-loop matching effects.