FIESTA 2: parallelizeable multiloop numerical calculations

Abstract

The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin-Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators and Speer sectors as a strategy, the possibility to evaluate more general parametric integrals.

31 pages, 5 figures

References in corpus (30)

• Quark and gluon form factors to three loops
• Three-loop static potential
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Sector Decomposition
• Resolution of singularities for multi-loop integrals
• Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Two-loop divergences of scattering amplitudes with massive partons
• Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log
• Fermionic contributions to the three-loop static potential
• Single Scale Tadpoles and O(GF mt^2 as^3) Corrections to the rho Parameter
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Fermionic Corrections to the Heavy-Quark Pair Production in the Quark-Antiquark Channel
• NNLO corrections to inclusive semileptonic B decays in the shape-function region
• Two-loop electroweak next-to-leading logarithmic corrections to massless fermionic processes
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• A geometric method of sector decomposition
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• Matching QCD and HQET heavy-light currents at three loops
• Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
• Completely automated computation of the heavy-fermion corrections to the three-loop matching coefficient of the vector current
• Blowing up Feynman integrals
• Radiative-nonrecoil corrections of order alpha^2 (Z alpha)^5 to the Lamb shift
• $\mathcal{O}(\alpha {\alpha }_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold
• The sector decomposition approach to real radiation at NNLO
• Semi-numerical power expansion of Feynman integrals
• Threshold corrections to the gamma t anti-t vertex at O(alpha alpha(s))

Cited by in corpus (92)

• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• FIESTA 4: optimized Feynman integral calculations with GPU support
• Quark mass relations to four-loop order
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• Expansion by regions: revealing potential and Glauber regions automatically
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• SecDec: A general program for sector decomposition
• FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions
• Geometric approach to asymptotic expansion of Feynman integrals
• Leading singularities and off-shell conformal integrals
• Collider Physics at the Precision Frontier
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
• $\overline{\mathrm{MS}}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
• A quasi-finite basis for multi-loop Feynman integrals
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• Evaluating single-scale and/or non-planar diagrams by differential equations
• Three-mass triangle integrals and single-valued polylogarithms
• Single soft gluon emission at two loops
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• FIESTA5: numerical high-performance Feynman integral evaluation
• Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
• The three-loop form factor in N=4 super Yang-Mills
• Automated Solution of First Order Factorizable Systems of Differential Equations in One Variable
• The quark and gluon form factors to three loops in QCD through to O(eps^2)
• Analytic results for two-loop master integrals for Bhabha scattering I
• Numerical Evaluation of Tensor Feynman Integrals in Euclidean Kinematics
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• Determine Arbitrary Feynman Integrals by Vacuum Integrals
• Five-loop Konishi in N=4 SYM
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Next-to-Leading Order QCD Corrections to the Decay Width $H\to Z\gamma$
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Removing infrared divergences from two-loop integrals
• Three-loop matching of the vector current
• Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment
• Numerical Scattering Amplitudes with pySecDec
• The three-loop equal-mass banana integral in $\epsilon$-factorised form with meromorphic modular forms
• Master integrals for the four-loop Sudakov form factor
• Electroweak pseudo-observables and Z-boson form factors at two-loop accuracy
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• NNLO QCD$\times$EW corrections to Z production in the $q\bar{q}$ channel
• Heavy Quark Form Factors at Three Loops in the Planar Limit
• The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
• Semi-analytical calculation of gluon fragmentation into ${}^1{S}_0^{[1,8]}$ quarkonia at next-to-leading order
• Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
• Four-loop wave function renormalization in QCD and QED
• The on-shell expansion: from Landau equations to the Newton polytope
• Analytic results for planar three-loop integrals for massive form factors
• Numerical multi-loop integrals and applications
• Application of the DRA method to the calculation of the four-loop QED-type tadpoles
• CosmoFlow: Python Package for Cosmological Correlators
• Pseudoscalar Quarkonium Exclusive Decays to Vector Meson Pair
• Two-loop splitting in double parton distributions
• TVID 2: Evaluation of planar-type three-loop self-energy integrals with arbitrary masses
• On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams
• Identifying regions in wide-angle scattering via graph-theoretical approaches
• Dissecting polytopes: Landau singularities and asymptotic expansions in $2\to 2$ scattering
• HepLib: A C++ Library for High Energy Physics
• FaRe: a Mathematica package for tensor reduction of Feynman integrals
• DRA method: Powerful tool for the calculation of the loop integrals
• A $QQ\to QQ$ planar doublebox in canonical form
• Systematic approximation of multi-scale Feynman integrals
• The static quark potential to three loops in perturbation theory
• Learning Feynman integrals from differential equations with neural networks
• Machine Learning Post-Minkowskian Integrals
• Full result for the three-loop static quark potential
• Sector decomposition via computational geometry
• Non-relativistic high-energy physics: top production and dark matter annihilation
• ftint: Calculating gradient-flow integrals with pySecDec
• Antenna Operator Product Expansion of ABJ(M) Lightlike Polygon Wilson Loop
• Numerical multi-loop calculations with SecDec
• Critical properties of three-dimensional many-flavour QEDs
• Evaluation of Multi-Box Diagrams in Six Dimensions
• NNLO mixed EW-QCD corrections to single vector boson production
• An off-shell I.R. regularization strategy in the analysis of collinear divergences
• Applications of the Perturbative Gradient Flow
• Three loop QCD corrections to heavy quark form factors
• Numerical evaluation of multi-loop integrals
• Evaluating master integrals in non-factorizable corrections to $t$-channel single-top production at NNLO QCD
• Three-loop vertex corrections
• Two-loop corrections to the Lamb shift
• A strategy for the off-shell analysis of collinear singularities in Feynman diagrams