RG-improvement of the effective action with multiple mass scales

TL;DR

This paper advances the renormalization group approach to the effective action in quantum field theories with multiple mass scales, applying it to Higgs-Yukawa and scalar models to incorporate threshold effects and field-dependent RGEs.

Contribution

It introduces an improved method for RG analysis with multiple mass scales, including wave-function renormalizations, and applies it to complex models with threshold effects and field-dependent mass matrices.

Findings

Effective RG improvement accounts for threshold effects in multi-scale models.

RGEs vary across field space due to field-dependent mass matrices.

Method successfully applies to Higgs-Yukawa and two-scalar models.

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.