A model with light and heavy scalars in view of the effective theory

TL;DR

This paper derives an effective potential for a model with both light and heavy scalars, incorporating renormalization group improvements to sum large logarithmic corrections and analyze vacuum expectation values.

Contribution

It introduces a method to derive and improve the effective potential for models with light and heavy scalars, including one-loop and leading logarithmic corrections.

Findings

Effective potential independent of renormalization scale approximately

Large logarithms summed via RG improvement

Vacuum expectation value corrections depend on heavy scalar mass

Abstract

The low energy effective potential for the model with a light scalar and a heavy scalar is derived. We perform the path integration for both heavy and light scalars and derive the low energy effective potential in terms of only the light scalar. The effective potential is independent of the renormalization scale approximately. By setting the renormalization scale equal to the mass of the heavy scalar, one finds the corrections with the logarithm of the ratio of the two scalar masses. The large logarithm is summed with the renormalization group (RG) and the RG improved effective potential is derived. The improved effective potential includes the one-loop correction of the heavy scalar and the leading logarithmic corrections due to the light scalar. We study the correction to the vacuum expectation value of the light scalar and the dependence on the mass of the heavy scalar.