A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop

Abstract

We present an evaluation of the two master integrals for the crossed vertex diagram with a closed loop of top quarks that allows for an easy numerical implementation. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular points. The different series are then matched numerically with high accuracy in intermediate points. The expansions allow a fast and precise numerical calculation of the two master integrals in all the regions of the phase space. A numerical routine that implements these expansions is presented.

arXiv comment23 pages, 2 figures, numerical routine available with submission

References in corpus (74)

• Harmonic Polylogarithms
• Differential Equations for Two-Loop Four-Point Functions
• Differential Equations for Feynman Graph Amplitudes
• Higgs boson gluon-fusion production in N3LO QCD
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Algorithm FIRE -- Feynman Integral REduction
• Numerical evaluation of multiple polylogarithms
• FIRE5: a C++ implementation of Feynman Integral REduction
• Two-loop light fermion contribution to Higgs production and decays
• Kira - A Feynman Integral Reduction Program
• Reduze - Feynman Integral Reduction in C++
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• Multiple polylogarithms and mixed Tate motives
• Lectures on differential equations for Feynman integrals
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• Reduze 2 - Distributed Feynman Integral Reduction
• The elliptic dilogarithm for the sunset graph
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Three-Loop Results for Quark and Gluon Form Factors
• Analytic treatment of the two loop equal mass sunrise graph
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Feynman Diagrams and Differential Equations
• High-precision calculation of multi-loop Feynman integrals by difference equations
• FIRE4, LiteRed and accompanying tools to solve integration by parts relations
• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
• A Feynman integral via higher normal functions
• Elliptic Feynman integrals and pure functions
• Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: the Quark-Antiquark Channel
• The two-loop sunrise graph with arbitrary masses
• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• Analytic Results for Massless Three-Loop Form Factors
• An Elliptic Generalization of Multiple Polylogarithms
• On the Generalized Harmonic Polylogarithms of One Complex Variable
• Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor - planar case
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• A non-planar two-loop three-point function beyond multiple polylogarithms
• The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
• Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• An Analytical Method for the NLO QCD Corrections to Double-Higgs Production
• The iterated structure of the all-order result for the two-loop sunrise integral
• Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral
• Master Integrals for the 2-loop QCD virtual corrections to the Forward-Backward Asymmetry
• Solving differential equations for Feynman integrals by expansions near singular points
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the non-planar graphs
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the planar graphs
• Master integrals with one massive propagator for the two-loop electroweak form factor
• Two-Loop Leading Color Corrections to Heavy-Quark Pair Production in the Gluon Fusion Channel
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges
• Master integrals for the two-loop light fermion contributions to $gg\to H$ and $H\to \gamma \gamma$
• Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case
• Two-Loop Formfactors in Theories with Mass Gap and Z-Boson Production
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• The $n_f^2$ contributions to fermionic four-loop form factors
• Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel
• Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions
• BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams
• Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production
• Evaluating `elliptic' master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points
• Massive three-loop form factor in the planar limit
• Massive planar and non-planar double box integrals for light Nf contributions to gg->tt
• Vertex diagrams for the QED form factors at the 2-loop level
• Analytic results for planar three-loop integrals for massive form factors
• Three-loop massive form factors: complete light-fermion and large-$N_c$ corrections for vector, axial-vector, scalar and pseudo-scalar currents
• Three-loop massive form factors: complete light-fermion corrections for the vector current
• Three-loop planar master integrals for heavy-to-light form factors

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