On the position of a heavy Higgs pole

Higher loop calculations in the Higgs sector of the standard model at the Higgs mass scale have shown that perturbation theory diverges very badly at about 1 TeV in the on-shell renormalization scheme. The prediction of the position of the Higgs pole in the complex s-plane becomes unreliable. We show that in the pole renormalization scheme this appears to have much better convergence properties, while showing good agreement with the on-shell scheme over the validity range of the latter. This suggests that the pole scheme should be preferable for phenomenological studies of heavy Higgs bosons. We discuss whether this behaviour can be the result of a certain relation between the on-shell mass and the pole mass at the nonperturbative level.Comment: replaced by the published version, 12 pages LaTex, 3 eps figures include

Loops and legs beyond perturbation theory

Within the non-perturbative 1/N expansion, we discuss numerical methods for calculating multi-loop Feynman graph needed to derive physical scattering amplitudes. We apply higher order 1/N methods to the scalar sector of the standard model, and show the existence of a mass saturation effect. The mass saturation has direct implications for future searches at the LHC and at possible muon colliders.Comment: Talk presented at the Loops and Legs in Quantum Field Theory 2000 meetin

Nonperturbative three-point functions of the O(N) sigma model in the 1/N expansion at NLO

We present a calculation of the three-point functions of the O(N)-symmetric sigma model. The calculation is done nonperturbatively by means of a higher-order 1/N expansion combined with a tachyonic regularization which we proposed in previous publications. We use the results for calculating the standard model process ff -> H -> WW nonperturbatively in the quartic coupling of the scalar sector

Reduction and evaluation of two-loop graphs with arbitrary masses

We describe a general analytic-numerical reduction scheme for evaluating any 2-loop diagrams with general kinematics and general renormalizable interactions, whereby ten special functions form a complete set after tensor reduction. We discuss the symmetrical analytic structure of these special functions in their integral representation, which allows for optimized numerical integration. The process Z -> bb is used for illustration, for which we evaluate all the 3-point, non-factorizable g^2*alpha_s mixed electroweak-QCD graphs, which depend on the top quark mass. The isolation of infrared singularities is detailed, and numerical results are given for all two-loop three-point graphs involved in this process

Mass and Width of a Heavy Higgs Boson

The gauge dependence of the Higgs-boson mass and width in the on-shell scheme of renormalization is studied in the heavy-Higgs-boson approximation. The corresponding expansions in the pole scheme are analyzed adopting three frequently employed parametrizations. The convergence properties and other theoretical features of the on-shell and pole expansions, as well as their relative merits, are discussed.Comment: 8 pages (Latex), 1 figure (Postscript

Analytic evaluation of two-loop renormalization constants of enhanced electroweak strength in the Higgs sector of the Standard Model

We calculate renormalization constants Z_H, Z_w, the Higgs and W-boson mass and tadpole counterterms in the on-mass-shell renormalization scheme to two loops in the heavy-Higgs-boson limit m_H >> M_W. Explicit analytic formulae are presented for the two-loop integrals with masses, which are not known in the literature. As an application, the analytic expression for the two-loop leading correction to the fermionic Higgs boson width is obtained.Comment: 8 pages, 3 Postscript figures, uses epsfig.st

Muon colliders and the non-perturbative dynamics of the Higgs boson

A muon collider operating in the TeV energy range can be an ideal s-channel Higgs boson factory. This is especially true for a heavy Higgs boson. The non-perturbative dynamical aspects of such a Higgs boson were recently investigated with large N expansion methods at next to leading order, and reveal the existence of a mass saturation effect. Even at strong coupling, the Higgs resonance remains always below 1 TeV. However, if the coupling is strong enough, the resonance becomes impossible to be detected.Comment: Contributed to the International Conference on Physics Potential and Development of mumu Colliders, December 15-17, 1999, San Francisco, C