{
  "id": "1409.3489",
  "version": "v1",
  "published": "2014-09-11T16:15:17.000Z",
  "updated": "2014-09-11T16:15:17.000Z",
  "title": "Multi-scale Renormalization Group Methods for Effective Potentials with Multiple Scalar Fields",
  "authors": [
    "T. G. Steele",
    "Zhi-Wei Wang",
    "D. G. C. McKeon"
  ],
  "comment": "13 pages, 3 figures",
  "categories": [
    "hep-ph"
  ],
  "abstract": "Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method beyond the weak coupling limit. A model containing two interacting real scalar fields is used to illustrate multi-scale RG methods and the multi-scale RG functions of this model are calculated to one-loop order for the $\\beta$ function and two-loop order for the anomalous mass dimension. The introduction of an extra renormalization scale allows the mapping of the effective potential in this model onto an RG-equivalent form with an O(2) symmetric structure along a particular trajectory in the multiple renormalization-scale space, leading to a simplified form of the effective potential. It is demonstrated that the physical content of the effective potential in the original model, referenced to a single conventional renormalization scale, can be extracted from a particular RG-trajectory that connects to this multi-scale O(2)-symmetric form of the effective potential. Extensions of these multi-scale methods for effective potentials in models containing multiple scalars with $O(M)\\times O(N)$ symmetry are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-11T16:15:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11.30.Qc",
      "11.10.Hi",
      "12.60.-i",
      "12.60.Fr"
    ],
    "keywords": [
      "effective potential",
      "multi-scale renormalization group methods",
      "multiple scalar fields",
      "illustrate multi-scale rg methods",
      "single conventional renormalization scale"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevD.90.105012",
      "journal": "Physical Review D",
      "year": 2014,
      "month": "Nov",
      "volume": 90,
      "number": 10,
      "pages": 105012
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1315967,
      "adsabs": "2014PhRvD..90j5012S"
    }
  }
}