{
  "id": "2010.15806",
  "version": "v1",
  "published": "2020-10-29T17:43:22.000Z",
  "updated": "2020-10-29T17:43:22.000Z",
  "title": "Renormalization Group Improvement of the Effective Potential: an EFT Approach",
  "authors": [
    "Aneesh V. Manohar",
    "Emily Nardoni"
  ],
  "comment": "63 pages, 16 figures",
  "categories": [
    "hep-ph",
    "hep-th"
  ],
  "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 answer in a systematic expansion in powers of the mass ratio, as well as to sum the logarithms 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. We also 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-29T17:43:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "effective potential",
      "renormalization group improvement",
      "eft approach",
      "large mass hierarchy",
      "renormalization group evolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}