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

TL;DR

This paper systematically matches gauge invariant dimension-6 operators onto the B physics Hamiltonian for $b o s$ and $b o c$ transitions, including tree-level and one-loop effects, to understand potential new physics contributions.

Contribution

It provides a comprehensive gauge invariant matching framework for dimension-6 operators relevant to B physics, including both tree-level and one-loop effects.

Findings

Identified operators contributing at tree level to $b$ transitions.

Determined operators with relevant one-loop matching effects.

Established a basis for model-independent new physics analysis in B decays.

Abstract

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.