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

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

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

Recent Progress in the Golem Project

We report on the current status of the Golem project which aims at the construction of a general one-loop evaluator for matrix elements. We construct the one-loop matrix elements from Feynman diagrams in a highly automated way and provide a library for the reduction and numerically stable evaluation of the tensor integrals involved in this approach. Furthermore, we present applications to physics processes relevant for the LHC.Comment: 7 pages, 4 figures, contrib. to proceedings of "Loops and Legs in Quantum Field Theory", 10th DESY Workshop on Elementary Particle Theory, 25-30 April 2010, Woerlitz, German

Gluon-induced W-boson pair production at the LHC

Pair production of W bosons constitutes an important background to Higgs boson and new physics searches at the Large Hadron Collider LHC. We have calculated the loop-induced gluon-fusion process gg -> W*W* -> leptons, including intermediate light and heavy quarks and allowing for arbitrary invariant masses of the W bosons. While formally of next-to-next-to-leading order, the gg -> W*W* -> leptons process is enhanced by the large gluon flux at the LHC and by experimental Higgs search cuts, and increases the next-to-leading order WW background estimate for Higgs searches by about 30%. We have extended our previous calculation to include the contribution from the intermediate top-bottom massive quark loop and the Higgs signal process. We provide updated results for cross sections and differential distributions and study the interference between the different gluon scattering contributions. We describe important analytical and numerical aspects of our calculation and present the public GG2WW event generator.Comment: 20 pages, 4 figure

NLO Cross Sections for the LHC using GOLEM: Status and Prospects

In this talk we review the GOLEM approach to one-loop calculations and present an automated implementation of this technique. This method is based on Feynman diagrams and an advanced reduction of one-loop tensor integrals which avoids numerical instabilities. We have extended our one-loop integral library golem95 with an automated one-loop matrix element generator to compute the virtual corrections of the process $q\bar{q}\to b\bar{b}b\bar{b}$. The implementation of the virtual matrix element has been interfaced with tree-level Monte Carlo programs to provide the full result for the above process.Comment: 8 pages, 1 figure, contribution to the proceedings of the 9th International Symposium on Radiative Corrections (RADCOR 2009), October 25-30 2009, Ascona, Switzerlan

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

An algebraic/numerical formalism for one-loop multi-leg amplitudes

We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which naturally isolates infrared divergences by construction. We prove that for N>4, higher dimensional integrals can be avoided. We derive many useful relations which allow for algebraic simplifications of one-loop amplitudes. We introduce a form factor representation of tensor integrals which contains no inverse Gram determinants by choosing a convenient set of basis integrals. For the evaluation of these basis integrals we propose two methods: An evaluation based on the analytical representation, which is fast and accurate away from exceptional kinematical configurations, and a robust numerical one, based on multi-dimensional contour deformation. The formalism can be implemented straightforwardly into a computer program to calculate next-to-leading order corrections to multi-particle processes in a largely automated way.Comment: 71 pages, 7 figures, formulas for rank 6 pentagons added in Appendix

Testing nonperturbative techniques in the scalar sector of the standard model

We discuss the current picture of the standard model's scalar sector at strong coupling. We compare the pattern observed in the scalar sector in perturbation theory up to two-loop with the nonperturbative solution obtained by a next-to-leading order 1/N expansion. In particular, we analyze two resonant Higgs scattering processes, ff -> H -> f'f' and ff -> H -> ZZ, WW. We describe the ingredients of the nonperturbative calculation, such as the tachyonic regularization, the higher order 1/N intermediate renormalization, and the numerical methods for evaluating the graphs. We discuss briefly the perspectives and usefulness of extending these nonperturbative methods to other theories

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