Calculating multiloop integrals using dimensional recurrence relation and D-analyticity

Abstract

We review the method of the calculation of multiloop integrals recently suggested in Ref.[Lee2010]. A simple method of derivation of the dimensional recurrence relation suitable for automatization is given. Some new analytic results are given.

Talk presented at 10th DESY Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Worlitz, Germany, 25-30 April 2010

References in corpus (5)

• Connection between Feynman integrals having different values of the space-time dimension
• Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• Explicit solutions of the multi-loop integral recurrence relations and its application
• High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles
• $(Z\alpha {)}^4$ order of the polarization operator in Coulomb field at low energy

Cited by in corpus (34)

• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Collider Physics at the Precision Frontier
• Critical points and number of master integrals
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• A quasi-finite basis for multi-loop Feynman integrals
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Inelastic Exponentiation and Classical Gravitational Scattering at One Loop
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Cuts from residues: the one-loop case
• The Three-loop Quark Jet Function
• Integration by parts: An introduction
• Extraction of Next-to-Next-to-Leading-Order PDFs from Lattice QCD Calculations
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Baikov representations, intersection theory, and canonical Feynman integrals
• The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
• Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
• Two-Loop Radiative Jet Function for Exclusive $B$-Meson and Higgs Decays
• Differential equations for loop integrals in Baikov representation
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT
• Application of the DRA method to the calculation of the four-loop QED-type tadpoles
• On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams
• Constructing multi-loop scattering amplitudes with manifest singularity structure
• The recursive structure of Baikov representations I: generics and application to symbology
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Cuts and Isogenies
• DRA method: Powerful tool for the calculation of the loop integrals
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals
• Three-loop jet function for boosted heavy quarks
• CALICO: Computing Annihilators from Linear Identities Constraining (differential) Operators
• Tensor structure from scalar Feynman matroids
• Massive Two-Loop Heavy Particle Diagrams