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), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 48:3; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANOMALOUS DIMENSION
ARGAND DIAGRAMS
BEAMS
BOSONS
CONSTRAINTS
COUPLING CONSTANTS
DIAGRAMS
ELEMENTARY PARTICLES
ENERGY DEPENDENCE
HIGGS BOSONS
INTERMEDIATE BOSONS
INTERMEDIATE VECTOR BOSONS
MATHEMATICAL MODELS
PARTIAL WAVES
PARTICLE MODELS
PERTURBATION THEORY
POLARIZED BEAMS
POSTULATED PARTICLES
Pa
Particle Systematics-- Unified Theories & Models-- (1992-)
SCALE DIMENSION
SCATTERING AMPLITUDES
SCATTERPLOTS
UNIFIED GAUGE MODELS
UNITARITY