Renormalization Group Improvement of the Effective Potential: an EFT Approach

TL;DR

This paper introduces a systematic EFT-based method to compute the renormalization group improved effective potential for theories with large mass hierarchies, summing large logs and avoiding infrared issues.

Contribution

It develops a novel approach using EFT and tadpole conditions to accurately compute the effective potential, including leading-log corrections, in theories with mass hierarchies.

Findings

Successfully reproduces two-loop log-squared terms

Avoids Goldstone boson infrared divergence

Provides a systematic expansion in mass ratios

Abstract

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the $O(N)$ model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop $\beta$-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.