Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations

Abstract

A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different topologies, and comparisons with analytical results, whenever available, are performed. An internal cross-check, based on alternative procedures, is also applied. The analysis of infrared divergent configurations, as well as the treatment of tensor integrals, will be discussed in two forthcoming papers.

65 pages

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• Two-Loop Renormalization in the Standard Model Part I: Prolegomena
• Two-Loop Threshold Singularities, Unstable Particles and Complex Masses
• Two-loop electroweak fermionic corrections to sin^2 theta_{eff}^{b anti-b}
• The effective electroweak mixing angle ${\sin }^2{\theta }_{eff}$ with two-loop bosonic contributions
• Two-Loop Tensor Integrals in Quantum Field Theory
• Numerical Computation of Two-loop Box Diagrams with Masses
• Two-Loop Renormalization in the Standard Model Part II: Renormalization Procedures and Computational Techniques
• An algorithm for the high-energy expansion of multi-loop diagrams to next-to-leading logarithmic accuracy
• Numerical multi-loop integrals and applications
• Two-Loop Vertices in Quantum Field Theory: Infrared and Collinear Divergent Configurations
• Laurent series expansion of a class of massive scalar one-loop integrals to ${\cal O}(\ep^2)
• Higgs-mass dependence of the effective electroweak mixing angle ${\sin }^2{\theta }_{eff}$ at the two-loop level
• PV-Reduction of Sunset Topology with Auxiliary Vector
• Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking
• SecDec: A tool for numerical multi-loop calculations
• Electroweak corrections in the 2HDM for neutral scalar Higgs-boson production through gluon fusion
• Peaks and cusps: anomalous thresholds and LHC physics
• Supersymmetric QCD corrections to $e^{+}{e}^{-}\to t\bar{b}{H}^{-}$ and the Bernstein-Tkachov method of loop integration
• Numerical evaluation of non-infrared two-loop vertices
• Evaluating massive planar two-loop tensor vertex integrals
• Electroweak corrections to $g+g\to H_{l,h}$ and $H_{l,h}\to \gamma +\gamma$ in the Higgs-singlet extension of the Standard model