The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges

Abstract

We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.

42 pages, 1 figure

References in corpus (57)

• Harmonic Polylogarithms
• Differential Equations for Two-Loop Four-Point Functions
• New features of FORM
• Differential Equations for Feynman Graph Amplitudes
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Numerical evaluation of multiple polylogarithms
• The analytical value of the electron (g-2) at order alpha^3 in QED
• Automatized analytic continuation of Mellin-Barnes integrals
• Two-loop light fermion contribution to Higgs production and decays
• HPL, a Mathematica implementation of the harmonic polylogarithms
• TESLA Technical Design Report Part III: Physics at an e+e- Linear Collider
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• One-loop leading logarithms in electroweak radiative corrections, I. Results
• Numerical Evaluation of Harmonic Polylogarithms
• Analytic treatment of the two loop equal mass sunrise graph
• Numerical evaluation of multi-loop integrals by sector decomposition
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms
• Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
• Numerical evaluation of phase space integrals by sector decomposition
• Sudakov Effects in Electroweak Corrections
• Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity
• Extension of HPL to complex arguments
• One-loop leading logarithms in electroweak radiative corrections: II. Factorization of collinear singularities
• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• All-Purpose Numerical Evaluation of One-Loop Multi-Leg Feynman Diagrams
• Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor - planar case
• Master Integrals for the 2-loop QCD virtual corrections to the Forward-Backward Asymmetry
• Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams
• An Approach Toward the Numerical Evaluation of Multi-Loop Feynman Diagrams
• Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
• A magic connection between massive and massless diagrams
• Two-loop self-energy master integrals on shell
• The strategy of regions for asymptotic expansion of two-loop vertex Feynman diagrams
• Two-Loop Electroweak Logarithms in Four-Fermion Processes at High Energy
• Master integrals with one massive propagator for the two-loop electroweak form factor
• Two-Loop Sudakov Form Factor in a Theory with Mass Gap
• Two-loop electroweak next-to-leading logarithmic corrections to massless fermionic processes
• Master Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs
• Master integrals for the two-loop light fermion contributions to $gg\to H$ and $H\to \gamma \gamma$
• Numerical evaluation of loop integrals
• Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case
• Rising Bosonic Electroweak Virtual Effects at High Energy e+e- Colliders
• Algebraic-Numerical Evaluation of Feynman Diagrams: Two-Loop Self-Energies
• Next-to-leading mass singularities in two-loop electroweak singlet form factors
• Two-Loop Electroweak Logarithms
• Zero-threshold expansion of two-loop self-energy diagrams
• Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations
• The two-loop vector form factor in the Sudakov limit
• Two-Loop Tensor Integrals in Quantum Field Theory
• Vertex diagrams for the QED form factors at the 2-loop level
• An algorithm for the high-energy expansion of multi-loop diagrams to next-to-leading logarithmic accuracy
• Fermionic and Scalar Corrections for the Abelian Form Factor at Two Loops
• Two-Loop Vertices in Quantum Field Theory: Infrared and Collinear Divergent Configurations
• Two Loop QFT in the Making
• Infrared Sensitive Physics in QCD and in Electroweak Theory

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