|Delta F| = 1 Nonleptonic Effective Hamiltonian in a Simpler Scheme

Abstract

We consider |ΔF| = 1 (F = S,C or B) nonleptonic effective hamiltonian in a renormalization scheme which allows to consistently use fully anticommuting gamma_5 at any number of loops, but at the leading order in the Fermi coupling G_F. We calculate two-loop anomalous dimensions and one-loop matching conditions for the effective operators in this scheme. Finally, we transform our results to one of the previously used renormalization schemes, and find agreement with the original calculations.

Figures (7)

• Figure 1: Tree-level matching condition.
• Figure 2: One-loop current-current diagrams.
• Figure 3: One-loop penguin diagrams with no Dirac trace.
• Figure 4: One-loop SM current-current diagrams.
• Figure 5: One-loop matching for $C_4$. Dots stand for ${\cal O}(1/M_W^4)$, a counterterm, and for a diagram with insertion of the chromomagnetic moment operator given in eqn. (\ref{['magn.mom']}).