Two-loop Renormalization Group Equations in the Standard Model

TL;DR

Two-loop renormalization group equations in the standard model are recalculated and a new coefficient is found in the beta function of the quartic coupling and a class of gauge invariants is found to be absent in the Beta functions of hadronic Yukawa couplings.

Abstract

Two-loop renormalization group equations in the standard model are re-calculated. A new coefficient is found in the beta-function of the quartic coupling and a class of gauge invariants are found to be absent in the beta-functions of hadronic Yukawa couplings. The two-loop beta-function of the Higgs mass parameter is presented in complete form.

Figures (3)

• Figure 1: Two-loop diagrams which affect hadronic Yukawa couplings. $(a)$ and $(b)$ ($(c)$ and $(d)$) cancel with each other, thus resulting in a null contribution to $\beta_H^{(2)}$ ($\beta_{F_D}^{(2)}$).
• Figure 2: (a) and (b): part of hadronic Yukawa coupling contribution to Higgs boson propagators, which in turn affect $\beta_\lambda$; (c) and (d): relevant proper scalar quartic vertex diagrams.
• Figure 3: Part of $SU(2) \times U(1)$ contributions to the Higgs boson propagators.