Twoloop unitarity constraints on the Higgsboson coupling
Abstract
We use the results of Maher [ital et] [ital al]. (preceding paper) to construct the matrix of [ital j]=0 partialwave twobody and 2[r arrow]3 scattering amplitudes for the scattering of longitudinally polarized gauge bosons [ital W][sub [ital L]][sup +],[ital Z][sub [ital L]] and Higgs bosons [ital H] correct to two loops in the highenergy, heavyHiggsboson limit [radical][ital s] [much gt][ital M][sub [ital H]][much gt][ital M][sub [ital W]]. We show explicitly that the energy dependence of the 2[r arrow]2 amplitudes can be completely adsorbed into a running quartic Higgs boson coupling [lambda][sub [ital s]]=[lambda][sub [ital s]]([ital s],[ital M][sub [ital H]][sup 2]) and factors which involve small anomalous dimensions and remain near unity. After diagonalizing the matrix of partialwave amplitudes we use an Arganddiagram analysis to show that the elastic scattering amplitudes are approximately unitary and weakly interacting for [lambda][sub [ital s]][approx lt]2.3, but that threeloop corrections are necessary to restore unitarity for larger values of [lambda][sub [ital s]]. That is, the interactions in the Higgs sector of the standard model are effectively strong with respect to the perturbative expansion for [lambda][sub [ital s]][approx gt]2.3. The bound [lambda][sub [ital s]][approx lt]2.3 for a weakly interacting theory translates to a physical Higgs bosonmore »
 Authors:

 Department of Physics, University of WisconsinMadison, Madison, Wisconsin 53706 (United States)
 Publication Date:
 OSTI Identifier:
 6437709
 DOE Contract Number:
 AC0276ER00881
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review, D (Particles Fields); (United States)
 Additional Journal Information:
 Journal Volume: 48:3; Journal ID: ISSN 05562821
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Pa; HIGGS BOSONS; COUPLING CONSTANTS; INTERMEDIATE VECTOR BOSONS; UNITARITY; CONSTRAINTS; ANOMALOUS DIMENSION; ARGAND DIAGRAMS; ENERGY DEPENDENCE; PARTIAL WAVES; PERTURBATION THEORY; POLARIZED BEAMS; SCATTERING AMPLITUDES; UNIFIED GAUGE MODELS; AMPLITUDES; BEAMS; BOSONS; DIAGRAMS; ELEMENTARY PARTICLES; INTERMEDIATE BOSONS; MATHEMATICAL MODELS; PARTICLE MODELS; POSTULATED PARTICLES; SCALE DIMENSION; SCATTERPLOTS; 662440*  Properties of Other Particles Including Hypothetical Particles (1992); 662130  General Theory of Particles & Fields SMatrix Theory, Relativistic Scattering Theory (1992); 662210  Specific Theories & Interaction Models; Particle Systematics Unified Theories & Models (1992)
Citation Formats
Durand, L, Maher, P N, and Riesselmann, K. Twoloop unitarity constraints on the Higgsboson coupling. United States: N. p., 1993.
Web. doi:10.1103/PhysRevD.48.1084.
Durand, L, Maher, P N, & Riesselmann, K. Twoloop unitarity constraints on the Higgsboson coupling. United States. doi:10.1103/PhysRevD.48.1084.
Durand, L, Maher, P N, and Riesselmann, K. Sun .
"Twoloop unitarity constraints on the Higgsboson coupling". United States. doi:10.1103/PhysRevD.48.1084.
@article{osti_6437709,
title = {Twoloop unitarity constraints on the Higgsboson coupling},
author = {Durand, L and Maher, P N and Riesselmann, K},
abstractNote = {We use the results of Maher [ital et] [ital al]. (preceding paper) to construct the matrix of [ital j]=0 partialwave twobody and 2[r arrow]3 scattering amplitudes for the scattering of longitudinally polarized gauge bosons [ital W][sub [ital L]][sup +],[ital Z][sub [ital L]] and Higgs bosons [ital H] correct to two loops in the highenergy, heavyHiggsboson limit [radical][ital s] [much gt][ital M][sub [ital H]][much gt][ital M][sub [ital W]]. We show explicitly that the energy dependence of the 2[r arrow]2 amplitudes can be completely adsorbed into a running quartic Higgs boson coupling [lambda][sub [ital s]]=[lambda][sub [ital s]]([ital s],[ital M][sub [ital H]][sup 2]) and factors which involve small anomalous dimensions and remain near unity. After diagonalizing the matrix of partialwave amplitudes we use an Arganddiagram analysis to show that the elastic scattering amplitudes are approximately unitary and weakly interacting for [lambda][sub [ital s]][approx lt]2.3, but that threeloop corrections are necessary to restore unitarity for larger values of [lambda][sub [ital s]]. That is, the interactions in the Higgs sector of the standard model are effectively strong with respect to the perturbative expansion for [lambda][sub [ital s]][approx gt]2.3. The bound [lambda][sub [ital s]][approx lt]2.3 for a weakly interacting theory translates to a physical Higgs boson mass [ital M][sub [ital H]][approx lt]380 GeV if the bound is to hold for energies up to a few TeV, or [ital M][sub [ital H]][le]155 GeV in perturbatively unified theories with mass scales of order 10[sup 16] GeV.},
doi = {10.1103/PhysRevD.48.1084},
journal = {Physical Review, D (Particles Fields); (United States)},
issn = {05562821},
number = ,
volume = 48:3,
place = {United States},
year = {1993},
month = {8}
}