Two-loop mixing of dimension-five flavor-changing operators

TL;DR

The paper addresses the two-loop QCD mixing of the dimension-five flavor-changing magnetic-moment operators O_gamma and O_g that arise after integrating out heavy SM fields. It employs a computerized, background-field calculation to obtain the full O(g^4) anomalous-dimension matrix for these operators, including a recalculation of the one-loop mixing and a thorough two-loop evaluation of the diagrams with an auxiliary-mass regulator. In the b -> s gamma basis, the authors translate the results into corrections to the Wilson coefficients C7_eff and C8_eff, revealing NNLL-like contributions that modestly reduce the predicted branching ratio for representative SM inputs. This work completes the remaining two-loop mixing for these operators and provides essential input for the complete next-to-leading calculation of B -> X_s gamma.

Abstract

We calculate the two-loop QCD mixing of the dimension-five flavor-changing operators that arise in the Standard Model after integrating out the $W$, $Z$ and Higgs bosons and the top-quark, i.e.~the mixing among gluonic and photonic magnetic moment operators. Our calculation completes the two-loop anomalous dimension matrix of operators that govern low energy flavor-changing processes. It is an important ingredient of the next-to-leading calculation of the $B \rightarrow X_s γ$ decay rate.

Figures (4)

• Figure 1: One-loop diagrams for the $q' \rightarrow q$, $q' \rightarrow q \gamma$ and $q' \rightarrow q Q$ transitions. The squares denote insertions of $O_{\gamma}$ or $O_g$.
• Figure 2: Convergent diagram for the $q' \rightarrow q \bar{\eta} \eta$ transition.
• Figure 3: Topologies of the Feynman diagrams for the two-loop self-mixing of $O_g$. The numbers in brackets are the numbers of diagrams corresponding to each topology.
• Figure 4: Examples of additional diagrams for flavor-conserving operators.