Construction of RG improved effective potential in a two real scalar system

Abstract

We study the improvement of effective potential by renormalization group (RG) equation in a two real scalar system. We clarify the logarithmic structure of the effective potential in this model. Based on the analysis of the logarithmic structure of it, we find that the RG improved effective potential up to $L$-th-to-leading log order can be calculated by the $L$-loop effective potential and $(L+1)$-loop $\beta$ and $\gamma$ functions. To obtain the RG improved effective potential, we choose the mass eigenvalue as a renormalization scale. If another logarithm at the renormalization scale is large, we decouple the heavy particle from the RG equation and we must modify the RG improved effective potential. In this paper we treat such a situation and evaluate the RG improved effective potential. Although this method was previously developed in a single scalar case, we implement the method in a two real scalar system. The feature of this method is that the choice of the renormalization scale does't change even in a calculation of higher leading log order. Following the our method one can derive the RG improved effective potential in a multiple scalar model.

arXiv comment21 pages, 8 figures

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Cited by in corpus (4)

• Weak scale from Planck scale -- Mass Scale Generation in Classically Conformal Two Scalar System --
• The hierarchy problem and fine-tuning in a decoupling approach to multi-scale effective potentials
• A model with light and heavy scalars in view of the effective theory
• Improved effective potential of Gildener-Weinberg models