Blowing up Feynman integrals
arXiv:0806.4307 · doi:10.1016/j.nuclphysbps.2008.09.113
Abstract
In this talk we discuss sector decomposition. This is a method to disentangle overlapping singularities through a sequence of blow-ups. We report on an open-source implementation of this algorithm to compute numerically the Laurent expansion of divergent multi-loop integrals. We also show how this method can be used to prove a theorem which relates the coefficients of the Laurent series of dimensionally regulated multi-loop integrals to periods.
6 pages, talk given at the conference "Loops and Legs in Quantum Field Theory", Sondershausen, April 2008
References in corpus (8)
- An automatized algorithm to compute infrared divergent multi-loop integrals
- Connection between Feynman integrals having different values of the space-time dimension
- Generalized Recurrence Relations for Two-loop Propagator Integrals with Arbitrary Masses
- Numerical evaluation of multi-loop integrals by sector decomposition
- Sector Decomposition
- Resolution of singularities for multi-loop integrals
- On Motives Associated to Graph Polynomials
- High-Energy Approximation of One-Loop Feynman Integrals
Cited by in corpus (20)
- FIESTA 4: optimized Feynman integral calculations with GPU support
- FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions
- FIESTA 2: parallelizeable multiloop numerical calculations
- Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
- Analytic Results for Massless Three-Loop Form Factors
- FIESTA5: numerical high-performance Feynman integral evaluation
- A geometric method of sector decomposition
- Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
- Three-loop on-shell Feynman integrals with two masses
- Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
- Hepp and Speer Sectors within Modern Strategies of Sector Decomposition
- Massive kite diagrams with elliptics
- On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams
- Meromorphic Continuation of Koba-Nielsen String Amplitudes
- Non-planar elliptic vertex
- Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium
- Master integrals for bipartite cuts of three-loop photon self energy
- Analytic and numerical approaches for depictive 3-loop integrals using sector decomposition
- Massive Two-Loop Heavy Particle Diagrams
- Integral representation for three-loop banana graph