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 in-variant under the Standard Model gauge group. In this article, we study the matching of the SU(3) C × SU(2) L × U(1) Y gauge invariant dimension-six operators on the standard B physics Hamiltonian 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.