Renormalization Group Determination of the FiveLoop Effective Potential for Massless Scala.pdfVIP

Renormalization Group Determination of the Five-Loop Effective Potential for Massless Scalar Field Theory ∗ † ‡ F.A. Chishtie, D.G.C. McKeon, T.G. Steele February 20, 2008 8 0 0 Abstract 2 The five-loop effective potential and the associated summation of subleading logarithms for O(4) globally- b 4 ˛ ˛ symmetric massless λφ4 field theory in the Coleman-Weinberg renormalization scheme d V = λ (where µ is ˛ e dφ4 F φ=µ the renormalization scale) is calculated via renormalization-group methods. An important aspect of this analysis 0 is conversion of the known five-loop renormalization-group functions in the minimal-subtraction (MS) scheme to 2 the Coleman-Weinberg scheme. ] Conventional electroweak (EW) symmetry-breaking requires a quadratic term for the Higgs field, which is not h natural from a grand-unification perspective because of the hierarchy problem. The most familiar aspect of the p- hierarchy problem is the fine-tuning necessary to control unification-scale perturbative corrections generated by this p m