Two-Loop Tensor Integrals in Quantum Field Theory

Abstract

A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of smoothness algorithms already employed for the numerical evaluation of ordinary scalar functions, are introduced for each family of diagrams.

95 pages, Latex. Presentation improved, substantial typographical restyling. To be published in Nuclear Physics B

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• Differential Equations for Two-Loop Four-Point Functions
• Differential Equations for Feynman Graph Amplitudes
• Dimensionally Regulated Pentagon Integrals
• Connection between Feynman integrals having different values of the space-time dimension
• Generalized Recurrence Relations for Two-loop Propagator Integrals with Arbitrary Masses
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• Two-Loop QCD Helicity Amplitudes for $e^{+}{e}^{-}\to 3$~Jets
• Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
• Two-Loop Amplitudes for Gluon Fusion into Two Photons
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• The Nielsen Identities of the SM and the definition of mass
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• Two-loop QCD corrections to massless quark-gluon scattering
• Reduction of general two-loop self-energies to standard scalar integrals
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• Algebraic reduction of one-loop Feynman graph amplitudes
• Reduction formalism for dimensionally regulated one-loop N-point integrals
• Two-loop QCD corrections to massless identical quark scattering
• Two-loop QED and QCD corrections to massless fermion-boson scattering
• TARCER - A Mathematica program for the reduction of two-loop propagator integrals
• The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
• Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
• Complete Two Loop Bosonic Contributions to the Muon Lifetime in the Standard Model
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• A Feynman Diagram Analyser DIANA
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• An Approach Toward the Numerical Evaluation of Multi-Loop Feynman Diagrams
• Bosonic Corrections to $\Delta r$ at the Two Loop Level
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• The two-loop scalar and tensor pentabox graph with light-like legs
• The strategy of regions for asymptotic expansion of two-loop vertex Feynman diagrams
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• Two-loop corrections to Light-by-Light scattering in Supersymmetric QED
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• Width and Partial Widths of Unstable Particles in the Light of the Nielsen Identities
• Two Loop QCD Vertices and Three Loop MOM $\beta$ functions
• Algebraic algorithms for multiloop calculations. The first 15 years. What's next?
• Two-Loop Form Factors in QED
• Algebraic-Numerical Evaluation of Feynman Diagrams: Two-Loop Self-Energies
• Solving Recurrence Relations for Multi-Loop Feynman Integrals
• Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations
• Tensor reduction of two-loop vacuum diagrams and projectors for expanding three-point functions
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• Probing negative dimensional integration: two-loop covariant vertex and one-loop light-cone integrals
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• New representation of the two-loop crossed vertex function
• Project "CalcPHEP: Calculus for Precision High Energy Physics"
• NDIM achievements: Massive, Arbitrary tensor rank and N-loop insertions in Feynman integrals
• Project {\tt SANC} (former {\tt CalcPHEP}): Support of Analytic and Numeric calculations for experiments at Colliders
• Advanced method of solving recurrence relations for multi-loop Feynman integrals
• Methods to calculate scalar two-loop vertex diagrams
• New representation of two-loop propagator and vertex functions
• Introduction to XLOOPS

Cited by in corpus (31)

• NNLO Computational Techniques: the Cases H -> gamma gamma and H -> g g
• Feynman Diagrams and Differential Equations
• The Standard Model Prediction of the Muon Anomalous Magnetic Moment
• Collider Physics at the Precision Frontier
• Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges
• Numerical evaluation of loop integrals
• Two-Loop Renormalization in the Standard Model Part III: Renormalization Equations and their Solutions
• Gauge-independent $\overline{MS}$ renormalization in the 2HDM
• The effective electroweak mixing angle ${\sin }^2{\theta }_{eff}$ with two-loop fermionic contributions
• Complete Two-Loop Corrections to H -> gamma gamma
• Two-Loop Renormalization in the Standard Model Part I: Prolegomena
• Two-Loop Threshold Singularities, Unstable Particles and Complex Masses
• Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations
• 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
• An algorithm for the high-energy expansion of multi-loop diagrams to next-to-leading logarithmic accuracy
• Two-Loop Renormalization in the Standard Model Part II: Renormalization Procedures and Computational Techniques
• Numerical multi-loop integrals and applications
• Two-Loop Vertices in Quantum Field Theory: Infrared and Collinear Divergent Configurations
• Status of the Standard Model Prediction of the Muon g-2
• Higgs-mass dependence of the effective electroweak mixing angle ${\sin }^2{\theta }_{eff}$ at the two-loop level
• On the two-loop contributions to the pion mass
• 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
• Electroweak corrections in the 2HDM for neutral scalar Higgs-boson production through gluon fusion
• Reduction of Feynman Integrals in the Parametric Representation
• 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