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

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

The rare decay B --> X_s l^+ l^- to NNLL precision for arbitrary dilepton invariant mass

We present a new phenomenological analysis of the inclusive rare decay $B \to X_s \ell^+\ell^-$. In particular, we present the first calculation of the NNLL contributions due to the leading two-loop matrix elements, evaluated for arbitrary dilepton invariant mass. This allows to obtain the first NNLL estimates of the dilepton mass spectrum and the lepton forward-backward asymmetry in the high $M^2_{\ell^+ \ell^-}$ region, and to provide an independent check of previously published results in the low $M^2_{\ell^+ \ell^-}$ region. The numerical impact of these NNLL corrections in the high-mass region ($M^2_{\ell^+ \ell^-} > 14.4 GeV^2$) amounts to -13% in the integrated rate, and leads to a reduction of the scale uncertainty to $\pm 3$. The impact of non-perturbative contributions in this region is also discussed in detail.Comment: 40 pages, 12 figures. v2: extended phenomenological discussion; results unchanged; published versio

NLO correction to Higgs boson parameters in the 1/N expansion

We present the result of a calculation of the next-to-leading correction to the Higgs propagator in the 1/N expansion, where the Higgs sector is treated as an O(N) symmetric sigma-model. The results are compared with two-loop perturbation theory. The existing discrepancy between the lowest order of the 1/N expansion and perturbation theory is dramatically reduced by including the NLO in 1/N. We find a maximum effective Higgs mass of 930-980 GeV. We give an approximate relation between Higgs width and mass, which can be used for phenomenological purposes.Comment: 5 pages LaTex, 1 eps figure included. To appear in Phys.Lett.

Perturbative and nonperturbative Higgs signals

We discuss the current picture of the standard Higgs sector at strong coupling and the phenomenological implications for direct searches at the LHC.Comment: Invited talk presented by A. Ghinculov at the Theory of LHC Processes meeting, 9--13 February 1998, CERN, Genev