  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 $SU(3)_C \times SU(2)_L \times U(1)_Y$ gauge
invariant dim-6 operators on the standard $B$ physics Hamiltonian relevant for
$b \to s$ and $b\to c$ 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 dim-6 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 $b \to s$ transitions already at tree level, but can give relevant
one-loop matching effects.
