A new algorithm for the generation of unitarity-compatible integration by parts relations

Journal of High Energy Physics

Volumn 2012, Issue 1, 2012, Pages

  Schabinger, Robert M ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

NLO Computations; QCD

Indexed keywords

EID: 84857314269     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP01(2012)077     Document Type: Article

References (18)

1. K. Chetyrkin and F. Tkachov, Integration by parts: the algorithm to calculate ß-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
2. V.A. Smirnov, Evaluating Feynman integrals, Springer Tracts Mod. Phys. 211 (2004) 1.
3. S. Gorishnii, S. Larin, L. Surguladze and F. Tkachov, MINCER: program for multiloop calculations in quantum field theory for the Schoonschip system, Comput. Phys. Commun. 55 (1989) 381 [INSPIRE].
4. S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
5. C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations, JHEP 07 (2004) 046 [hep-ph/0404258] [INSPIRE].
6. A. Smirnov, Algorithm FIRE \- Feynman integral reduction, JHEP 10 (2008) 107 [arXiv: 0807. 3243] [INSPIRE] .
7. C. Studerus, Reduze-Feynman integral reduction in C++,Comput. Phys. Commun. 181 (2010) 1293 [arXiv:0912.2546] [INSPIRE].
8. D.A. Kosower and K.J. Larsen, Maximal unitarity at two loops, arXiv:1108.1180 [INSPIRE].
9. P. Mastrolia and G. Ossola, On the integrand-reduction method for two-loop scattering amplitudes, JHEP 11 (2011) 014 [arXiv:1107.6041] [INSPIRE].
10. J. Gluza, K. Kajda and D.A. Kosower, Towards a basis forplanar two-loop integrals, Phys. Rev. D 83 (2011) 045012 [arXiv:1009.0472] [INSPIRE].
11. D. Bayer and D. Mumford, What can be computed in algebraic geometry?, math.AG/9304003.
12. W. Adams and P. Loustaunau, An introduction to Gr̈obner bases, Graduate Studies in Mathematics 3, American Mathematical Society, Providence U.S.A (1994).
13. D. Cabarcas and J. Ding, Linear algebra to compute syzygies and Gr̈obner bases, in ISSAC '11: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation (2011).
14. B. Buchberger, Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, Ph.D. Thesis, Universiẗat Innsbruck, Innsbruck Austria (1965) [http://www.risc.jku.at/ Groebner-Bases-Bibliography/details.php?details-id=706].
15. C. Eder, J. Gash and J. Perry, Modifying Faug̀ere's F5 algorithm to ensure termination arXiv:1006.0318 .
16. J.C. Faug̀ere, A new efficient algorithm for computing Gr̈obner bases without reduction to zero (i), in ISSAC '02: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation (2002).
17. G. Ars and A. Hashemi, Computing syzygies by Faug̀ere's it algorithm, Results in Mathematics 59 (2011) 35.
18. R. Stanley Enumerative combinatorics, volume I, Cambridge University Press, Cambridge U.K. (1997).