Two-loop unitarity constraints on the Higgs-boson coupling

• Published in: Physical review. D, Particles and fields Particles and fields, 1993-08, Vol.48 (3), p.1084-1096
• Main Authors: Durand, L, Maher, PN, Riesselmann, K
• Format: Article
• Language: English
• Subjects: 662130 - General Theory of Particles & Fields- S-Matrix Theory, Relativistic Scattering Theory- (1992-); 662210 - Specific Theories & Interaction Models; 662440 - Properties of Other Particles Including Hypothetical Particles- (1992-); 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; Particle Systematics- Unified Theories & Models- (1992-); PERTURBATION THEORY; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; POLARIZED BEAMS; POSTULATED PARTICLES; SCALE DIMENSION; SCATTERING AMPLITUDES; SCATTERPLOTS; UNIFIED GAUGE MODELS; UNITARITY
• ISSN: 0556-2821; 1089-4918
• DOI: 10.1103/PhysRevD.48.1084

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.