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

RG-improvement of the effective action with multiple mass scales