Sector Decomposition

Abstract

Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multi-loop Feynman parameter integrals as well as infrared divergent phase-space integrals over real radiation matrix elements.

Replaced by published version, references updated

References in corpus (55)

• Electroweak gauge boson production at hadron colliders through O(alpha_s^2)
• Antenna Subtraction at NNLO
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Connection between Feynman integrals having different values of the space-time dimension
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order
• Higgs boson production at hadron colliders: differential cross sections through next-to-next-to-leading order
• A new method for real radiation at NNLO
• Numerical evaluation of multi-loop integrals by sector decomposition
• Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop
• An algebraic/numerical formalism for one-loop multi-leg amplitudes
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Infrared Structure of $e^{+}{e}^{-}\to 2$ jets at NNLO
• Resolution of singularities for multi-loop integrals
• The W boson production cross section at the LHC through O(alpha_s^2)
• The Two-Loop QCD Matrix Element for $e^{+}{e}^{-}\to 3$ Jets
• Numerical evaluation of phase space integrals by sector decomposition
• Second-order QCD corrections to the thrust distribution
• Four-Particle Phase Space Integrals in Massless QCD
• Jet rates in electron-positron annihilation at O(α_s^3) in QCD
• Electroweak two-loop corrections to the effective weak mixing angle
• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• High-Energy Approximation of One-Loop Feynman Integrals
• Techniques for QCD calculations by numerical integration
• QCD corrections to tri-boson production
• Single Scale Tadpoles and O(GF mt^2 as^3) Corrections to the rho Parameter
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• All-Purpose Numerical Evaluation of One-Loop Multi-Leg Feynman Diagrams
• Master integrals for massive two-loop Bhabha scattering in QED
• Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
• Real radiation at NNLO: e^+e^- to 2 jets through O(alpha_s^2)
• Analytical Evaluation of Dimensionally Regularized Massive On-Shell Double Boxes
• The electron energy spectrum in muon decay through O(alpha^2)
• QCD Calculations by Numerical Integration
• Two-loop electroweak next-to-leading logarithmic corrections to massless fermionic processes
• A numerical method for NNLO calculations
• A numerical evaluation of the scalar hexagon integral in the physical region
• Hopf algebra approach to Feynman diagram calculations
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box
• Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions
• Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell
• The planar four-point master integrals for massive two-loop Bhabha scattering
• A new approach to the momentum expansion of multiloop Feynman diagrams
• Bosonic Corrections to The Effective Weak Mixing Angle at O(alpha^2)
• NLO QCD corrections to the production of t-tbar-Z in gluon fusion
• An algorithm for the high-energy expansion of multi-loop diagrams to next-to-leading logarithmic accuracy
• Towards e+e- --> 3 jets at NNLO by sector decomposition
• A numerical approach to infrared divergent multi-parton phase space integrals
• Landau equations and asymptotic operation
• Analytical evaluation of certain on-shell two-loop three-point diagrams
• A Simple Proof of the BPH Theorem

Cited by in corpus (123)

• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• FIESTA 4: optimized Feynman integral calculations with GPU support
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• Towards a Basis for Planar Two-Loop Integrals
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Two-Loop QCD Corrections to the Helicity Amplitudes for $H\to$ 3 partons
• Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• The two-loop hemisphere soft function
• SecDec: A general program for sector decomposition
• FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions
• FIESTA 2: parallelizeable multiloop numerical calculations
• 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
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours
• FeynCalc 10: Do multiloop integrals dream of computer codes?
• Analytic Results for Massless Three-Loop Form Factors
• FIESTA5: numerical high-performance Feynman integral evaluation
• Multiloop corrections for collider processes using auxiliary mass flow
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Loop Tree Duality for multi-loop numerical integration
• Antenna subtraction for gluon scattering at NNLO
• Two-loop QCD helicity amplitudes for $q\bar{q}\to W^{\pm }\gamma$ and $q\bar{q}\to Z^0\gamma$
• Momentum-dependent two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM
• Determining Feynman integrals with only input from linear algebra
• Numerical Evaluation of Tensor Feynman Integrals in Euclidean Kinematics
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Two-Loop Leading Color Corrections to Heavy-Quark Pair Production in the Gluon Fusion Channel
• A geometric method of sector decomposition
• Determine Arbitrary Feynman Integrals by Vacuum Integrals
• A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms
• Tropical Monte Carlo quadrature for Feynman integrals
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• The Pentabox Master Integrals with the Simplified Differential Equations approach
• Targeting Multi-Loop Integrals with Neural Networks
• Analytic integration of real-virtual counterterms in NNLO jet cross sections II
• Numerical Scattering Amplitudes with pySecDec
• On the status of expansion by regions
• Real-Virtual corrections for gluon scattering at NNLO
• Efficient Numerical Evaluation of Feynman Integral
• The FORM project
• Computing one-loop corrections to effective vertices with two scales in the EFT for Multi-Regge processes in QCD
• 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
• Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
• Two-loop Master Integrals with the Simplified Differential Equations approach
• Double real radiation corrections to $t\bar{t}$ production at the LHC: the all-fermion processes
• Two-Loop Master Integrals for Leading-Color $pp\to t\bar{t}H$ Amplitudes with a Light-Quark Loop
• Causal representation of multi-loop Feynman integrands within the loop-tree duality
• Introduction to QCD
• Massive non-planar two-loop four-point integrals with SecDec 2.1
• Two-Loop QCD Corrections to Higgs $\to b+\bar{b}+g$ Amplitude
• Integration of collinear-type doubly unresolved counterterms in NNLO jet cross sections
• Numerical multi-loop integrals and applications
• Automatic computation of Feynman integrals containing linear propagators via auxiliary mass flow
• Next-to-leading order corrections for $gg\to ZH$ with top quark mass dependence
• Efficient computation of two-loop amplitudes for Higgs boson pair production
• Direct reduction of multiloop multiscale scattering amplitudes
• Numerical integration of loop integrals through local cancellation of threshold singularities
• Double real radiation corrections to $t\bar{t}$ production at the LHC: the $gg\to t\bar{t}q\bar{q}$ channel
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• Blowing up Feynman integrals
• Hepp and Speer Sectors within Modern Strategies of Sector Decomposition
• IBP methods at finite temperature
• Radiative-nonrecoil corrections of order alpha^2 (Z alpha)^5 to the Lamb shift
• Analytic integration of soft and collinear radiation in factorised QCD cross sections at NNLO
• Intersection theory rules symbology
• A new method for taming tensor sum-integrals
• Massive kite diagrams with elliptics
• On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams
• Two-loop amplitudes for ttH production: the quark-initiated Nf-part
• HepLib: A C++ Library for High Energy Physics
• A fresh look on three-loop sum-integrals
• QCD Static Force in Gradient Flow
• Reduction of Feynman Integrals in the Parametric Representation II: Reduction of Tensor Integrals
• The Asymptotic Structure of Cosmological Integrals
• SecDec: A tool for numerical multi-loop calculations
• Systematic approximation of multi-scale Feynman integrals
• Non-planar elliptic vertex
• Master integrals for bipartite cuts of three-loop photon self energy
• Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium
• Expansion by regions with pySecDec
• News on Ambre and CSectors
• Machine Learning Post-Minkowskian Integrals
• Toric geometry and regularization of Feynman integrals
• Cosmological Infrared Subtractions & Infrared-Safe Computables
• Classical gravitational scattering from a gauge-invariant double copy
• Algebraic Interplay between Renormalization and Monodromy
• NNLO jet cross sections by subtraction
• Numerical Evaluation of Two-Loop Integrals in FDR
• Schwinger, ltd: Loop-tree duality in the parametric representation
• Three-loop jet function for boosted heavy quarks
• ftint: Calculating gradient-flow integrals with pySecDec
• Research on the Phase space of three- and four-body final states process
• On the two-loop amplitude for $gg\to ZZ$ production with full top-mass dependence
• NNLO QED contribution to the $\mu e\to \mu e$ elastic scattering
• Critical exponent $\eta$ in 2D $O(N)$-symmetric ${\phi }^4$-model up to 6~loops
• Numerical multi-loop calculations with SecDec
• Analytic and numerical approaches for depictive 3-loop integrals using sector decomposition
• Two-loop master integrals for a planar and a non-planar topology relevant for single top production
• Multi-loop calculations: numerical methods and applications
• $\text{history}$: A tool for fully-differential cross sections at next-to-next-to-leading order
• Quantum-field multiloop calculations in critical dynamics
• Numerical evaluation of multi-loop integrals
• QCD static force in gradient flow
• Massive Two-Loop Heavy Particle Diagrams
• Numerical multi-loop calculations: tools and applications
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics
• CoLoRFulNNLO for hadron collisions: integrating the iterated single unresolved subtraction terms
• Reduction of planar double-box diagram for single-top production via auxiliary mass flow
• Laplace method for the simplest diagrams of elastic scattering of scalar particles
• Numerical calculation of 3-pion Coulomb scattering using scalar QED
• Subtraction method of computing QCD jet cross sections at NNLO accuracy
• Scalar one-loop four-point Feynman integrals with complex internal masses
• Integral representation for three-loop banana graph
• Mixed QCD-EW corrections to $W$-pair production at electron-positron colliders
• IR subtraction schemes: integrating the counterterms at NNLO in QCD