Two-loop unitarity constraints on the Higgs-boson coupling

Journal Article · Sun Aug 01 00:00:00 EDT 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.48.1084· OSTI ID:6437709

Durand, L; Maher, P N; Riesselmann, K ^[1]

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1. Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)

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.

• DOE Contract Number: AC02-76ER00881
• OSTI ID: 6437709
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 48:3; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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-)