Matching of gauge invariant dimension 6 operators for $b\to s$ and $b\to c$ transitions

Understand

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.