New implementation of the sector decomposition on FORM

Abstract

Nowadays the sector decomposition technique, which can isolate divergences from parametric representations of integrals, becomes a quite useful tool for numerical evaluations of the Feynman loop integrals. It is used to verify the analytical results of multi-loop integrals in the Euclidean region, or in some cases practically used in the physical region by combining with other methods handling the threshold. In an intermediate stage of the sector decomposition for the multi-loop integrals, one often has to handle enormously large expressions containing tons of terms. The symbolic manipulation system FORM is originally designed to treat such huge expressions and has a strong advantage for it. In this talk, the implementation of the sector decomposition algorithm on FORM is discussed. A number of concrete examples including cases of multi-loop diagrams are also shown.

5 pages, uses PoS.cls, proceedings of ACAT 2008, Erice, Italy, Nov. 3-7, 2008

Cited by in corpus (11)

• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• SecDec: A general program for sector decomposition
• FIESTA 2: parallelizeable multiloop numerical calculations
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
• A geometric method of sector decomposition
• Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
• Numerical Computation of Two-loop Box Diagrams with Masses
• Sector decomposition via computational geometry
• Multi-loop calculations: numerical methods and applications
• Numerical evaluation of two-loop integrals with pySecDec