Understand
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.
Built on
R. Piessens, E. de Doncker, C. W. Ubelhuber and D. K. Kahaner, QUADPACK, A Subroutine Package for Automatic Integration , Springer Series in Computational Mathematics. Springer-Verlag, 1983
1983
Earlier work this paper cites.
J. Berntsen, T. O. Espelid and A. Genz, DCUHRE: an adaptive multidemensional integration routine for a vector of integrals , ACM Trans. Math. Softw. (1991) 452
1991
Earlier work this paper cites.
T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multi-loop integrals , Nucl. Phys. B585
2000
Earlier work this paper cites.
T. Binoth and G. Heinrich, Numerical evaluation of multi-loop integrals by sector decomposition , Nucl. Phys. B680
2004
Earlier work this paper cites.
Similar
E. de Doncker, Y. Shimizu, J. Fujimoto and F. Yuasa, Computation Of Loop Integrals Using Extrapolation , Comput. Phys. Commun. 159
2004
Cited alongside, same era.
Z. Nagy and D. E. Soper, Numerical integration of one-loop Feynman diagrams for N-photon amplitudes , Phys. Rev. D74
2006
Cited alongside, same era.
A. Lazopoulos, K. Melnikov and F. Petriello, QCD corrections to tri-boson production , Phys. Rev. D76
2007
Cited alongside, same era.
A. V. Smirnov and M. N. Tentyukov, Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA) , [ 0807.4129 [hep-ph]
Cited in the paper.
J. A. M. Vermaseren, New features of FORM , [ math-ph/0010025
Cited in the paper.
Then
C. Anastasiou, S. Beerli and A. Daleo, Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically , JHEP 0705
2007
Later among the works it cites.
G. Heinrich, Sector Decomposition , Int. J. Mod. Phys. A23
2008
Later among the works it cites.
C. Bogner and S. Weinzierl, Resolution of singularities for multi-loop integrals , Comput. Phys. Commun. 178
2008
Later among the works it cites.
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