Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)

Abstract

Up to the moment there are two known algorithms of sector decomposition: an original private algorithm of Binoth and Heinrich and an algorithm made public lastyear by Bogner and Weinzierl. We present a new program performing the sector decomposition and integrating the expression afterwards. The program takes a set of propagators and a set of indices as input and returns the epsilon-expansion of the corresponding integral.

References in corpus (10)

• An automatized algorithm to compute infrared divergent multi-loop integrals
• Numerical evaluation of multi-loop integrals by sector decomposition
• Sector Decomposition
• Resolution of singularities for multi-loop integrals
• Numerical evaluation of phase space integrals by sector decomposition
• Single Scale Tadpoles and O(GF mt^2 as^3) Corrections to the rho Parameter
• 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
• Evaluating the three-loop static quark potential

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