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We apply effective field theory (EFT) methods to compute the renormalizationgroup improved effective potential for theories with a large mass hierarchy.Our method allows one to compute the effective potential in a systematicexpansion in powers of the mass ratio, as well as to sum large logarithms ofmass ratios using renormalization group evolution. The effective potential isthe sum of one-particle irreducible diagrams (1PI) but information about whichdiagrams are 1PI is lost after matching to the EFT, since heavy lines getshrunk to a point. We therefore introduce a tadpole condition in place of the1PI condition, and use the renormalization group improved value of the tadpolein computing the effective potential. We explain why the effective potentialcomputed using an EFT is not the same as the effective potential of the EFT. Weillustrate our method using the $O(N)$ model, a theory of two scalars in theunbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result,obtained by integrating the one-loop $\beta$-functions, correctly reproducesthe log-squared term in explicit two-loop calculations. Our method does nothave a Goldstone boson infrared divergence problem.

Renormalization Group Improvement of the Effective Potential: an EFT Approach