RG-improvement of the effective action with multiple mass scales

Abstract

Improving the effective action by the renormalization group (RG) with several mass scales is an important problem in quantum field theories. A method based on the decoupling theorem was proposed in \cite{Bando:1992wy} and systematically improved \cite{Casas:1998cf} to take threshold effects into account. In this paper, we apply the method to the Higgs-Yukawa model, including wave-function renormalizations, and to a model with two real scalar fields $(\varphi, h)$. In the Higgs-Yukawa model, even at one-loop level, Feynman diagrams contain propagators with different mass scales and decoupling scales must be chosen appropriately to absorb threshold corrections. On the other hand, in the two-scalar model, the mass matrix of the scalar fields is a function of their field values $(\varphi, h)$ and the resultant running couplings obey different RGEs on a different point of the field space. By solving the RGEs, we can obtain the RG improved effective action in the whole region of the scalar fields.