Numerical evaluation of multi-loop integrals by sector decomposition
By Thomas Binoth, Gudrun Heinrich. 2003
203 citations recorded by the source corpus.
Abstract In a recent paper [Nucl. Phys. B 585 (2000) 741] we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines. Here we show how to extend this algorithm to Feynman diagrams with massive propagators and arbitrary propagator powers. As applications, we present numerical results for the master 2-loop 4-point topologies with massive internal lines occurring in Bhabha scattering at two loops, and for the master integrals of planar and non-planar massless double box graphs with two off-shell legs. We also evaluate numerically some two-point functions up to 5 loops relevant for beta-function calculations, and a 3-loop 4-point function, the massless on-shell planar triple box. Whereas the 4-point functions are evaluated in non-physical kinematic regions, the results for the propagator functions are valid for arbitrary kinematics.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/987a0c69fe746e4be3667373cf69a19e4b62e41c
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In Nuclear and High Energy Physics
- Erik Panzer
- Hjalte Frellesvig
- Costas G. Papadopoulos
- Gudrun Heinrich
- Ansgar Denner
- Stefan Dittmaier
- Stefan Kallweit
- Thomas Gehrmann
Citations in the corpus
- Collider physics at the precision frontier (2020, unknown): “merically by several groups [776{783]. Methods to calculate one-loop integrals in a parameter representation numerically also have been worked out [784{792], partially with extensions beyond one loop [793, 794, 786, 743, 45, 795{798], see also Sections 3.3.4 and 3.4 for more details. A four-dimensio”
- Cuts of Feynman Integrals in Baikov representation (2017, methodology): “The introduction of the sector decomposition [39, 40, 41, 42, 43] method resulted in a powerful computational framework for the numerical evaluation of FI, see for instance SecDec [7].”
- Sector Decomposition (2008, methodology): “Subsequently, sector decomposition was used to check a considerable number of analytical results for two-loop [27, 34, 35, 48–52], three-loop [53–55] and four-loop [36, 51] diagrams(3).”
- Feynman integrals and hyperlogarithms (2015, methodology): “Comparison with sector decomposition Available programs [33, 37, 155] for numeric evaluation of Feynman integrals are based on sector decomposition [20, 21], which is a very general method for desingularization of polynomials [34] and therefore applicable in most cases of practical interest (at leas”