Can the renormalization group improved effective potential be used to estimate the Higgs mass in the conformal limit of the standard model?

Journal Article · Sun May 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.105009· OSTI ID:21502632

Chishtie, F A; Jia, J ^[1]; Hanif, T ^[2]; Mann, R B ^[3]; McKeon, D G. C. ^[1]; Sherry, T N ^[4]; Steele, T G ^[5]

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1. Department of Applied Mathematics, University of Western Ontario, London, ON N6A 5B7 (Canada)
2. Department of Physics and Astronomy, University of Western Ontario, London, ON N6A 5B7 (Canada)
3. Department of Physics, University of Waterloo, Waterloo, ON N2L 3G1 (Canada)
4. School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway (Ireland)
5. Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SK S7N 5E2 (Canada)

We consider the effective potential V in the standard model with a single Higgs doublet in the limit that the only mass scale {mu} present is radiatively generated. Using a technique that has been shown to determine V completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg renormalization scheme, we first sum leading-log (LL) contributions to V using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling x, the quartic coupling of the Higgs field y, the SU(3) gauge coupling z, and the SU(2)xU(1) couplings r and s). We then employ the two loop RG functions with the three couplings x, y, z to sum the next-to-leading-log (NLL) contributions to V and then the three to five loop RG functions with one coupling y to sum all the N{sup 2}LL...N{sup 4}LL contributions to V. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction scheme to their form in the Coleman-Weinberg scheme. The Higgs mass can then be determined from the effective potential: the LL result is m{sub H}=219 GeV/c{sup 2} and decreases to m{sub H}=188 GeV/c{sup 2} at N{sup 2}LL order and m{sub H}=163 GeV/c{sup 2} at N{sup 4}LL order. No reasonable estimate of m{sub H} can be made at orders V{sub NLL} or V{sub N}{sup 3}{sub LL} since the method employed gives either negative or imaginary values for the quartic scalar coupling. The fact that we get reasonable values for m{sub H} from the LL, N{sup 2}LL, and N{sup 4}LL approximations is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of m{sub H}. The mass 163 GeV/c{sup 2} is argued to be an upper bound on m{sub H}.

• OSTI ID: 21502632
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 10; Other Information: DOI: 10.1103/PhysRevD.83.105009; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
CONVERGENCE
COUPLING
HIGGS BOSONS
HIGGS MODEL
MASS
RENORMALIZATION
STANDARD MODEL
SU-2 GROUPS
SU-3 GROUPS
SYMMETRY BREAKING
T QUARKS
U-1 GROUPS
YUKAWA POTENTIAL
BOSONS
CALCULATION METHODS
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
GRAND UNIFIED THEORY
LIE GROUPS
MATHEMATICAL MODELS
NUCLEAR POTENTIAL
PARTICLE MODELS
POSTULATED PARTICLES
POTENTIALS
QUANTUM FIELD THEORY
QUARKS
SU GROUPS
SYMMETRY GROUPS
TOP PARTICLES
U GROUPS
UNIFIED GAUGE MODELS