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

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

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

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

New developments in the 1/N expansion and nonperturbative Higgs physics

We show in this paper that the 1/N expansion is a reliable tool to calculate the properties of a heavy Higgs boson. The 1/N expansion sums up all orders in perturbation theory, and therefore avoids the renormalization scheme dependence of the conventional perturbative approach. It is explained how effects due to the Landau pole of the Higgs sector are isolated and subtracted, and how to perform actual calculations, by computing the Higgs line shape for the processes f\bar f\to H \to ZZ,f'\bar f' at next-to-leading order in the 1/N expansion. The results are compared to the perturbative results to show the agreement between the perturbative and the nonperturbative approach for Higgs masses up to 1 TeV. We conclude that the theoretical predictions for Higgs observables are well under control for the entire kinematical region of the LHC.Comment: 23 pages, latex, eps-figures include

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

Exact O(g^2 alpha_s) top decay width from general massive two-loop integrals

We calculate the b-dependent self-energy of the top quark at O(g^2 \alpha_s) by using a general massive two-loop algorithm proposed in a previous article. From this we derive by unitarity the O(\alpha_s) radiative corrections to the decay width of the top quark, where all effects associated with the $b$ quark mass are included without resorting to a mass expansion. Our results agree with the analytical results available for the O(\alpha_s) correction to the top quark width