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Title: Two-loop unitarity constraints on the Higgs-boson coupling

Abstract

We use the results of Maher [ital et] [ital al]. (preceding paper) to construct the matrix of [ital j]=0 partial-wave two-body 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 high-energy, heavy-Higgs-boson 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 partial-wave amplitudes we use an Argand-diagram 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 three-loop 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 » 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.« less

Authors:
; ;  [1]
  1. Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)
Publication Date:
OSTI Identifier:
6437709
DOE Contract Number:  
AC02-76ER00881
Resource Type:
Journal Article
Journal Name:
Physical Review, D (Particles Fields); (United States)
Additional Journal Information:
Journal Volume: 48:3; Journal ID: ISSN 0556-2821
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- S-Matrix 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. Two-loop unitarity constraints on the Higgs-boson coupling. United States: N. p., 1993. Web. doi:10.1103/PhysRevD.48.1084.
Durand, L, Maher, P N, & Riesselmann, K. Two-loop unitarity constraints on the Higgs-boson coupling. United States. doi:10.1103/PhysRevD.48.1084.
Durand, L, Maher, P N, and Riesselmann, K. Sun . "Two-loop unitarity constraints on the Higgs-boson coupling". United States. doi:10.1103/PhysRevD.48.1084.
@article{osti_6437709,
title = {Two-loop unitarity constraints on the Higgs-boson 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 partial-wave two-body 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 high-energy, heavy-Higgs-boson 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 partial-wave amplitudes we use an Argand-diagram 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 three-loop 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 = {0556-2821},
number = ,
volume = 48:3,
place = {United States},
year = {1993},
month = {8}
}