Numerical contour integration for loop integrals

Computer Physics Communications

Volumn 174, Issue 7, 2006, Pages 530-539

  Kurihara, Y ^a   Kaneko, T ^a  

^a HIGH ENERGY ACCELERATOR RESEARCH ORGANIZATION KEK   (Japan)

Author keywords

Loop integral; Numerical integration; Radiative correction

Indexed keywords

FUNCTION EVALUATION; GEOMETRY; INTEGRAL EQUATIONS; INTEGRATION; MATHEMATICAL MODELS; TENSORS;

LOOP INTEGRAL; NUMERICAL INTEGRATION; RADIATIVE CORRECTION;

NUMERICAL METHODS;

EID: 33644769145     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2005.05.009     Document Type: Article

References (36)

1. Y. Oyanagi, T. Kaneko, T. Sasaki, S. Kawabata, and Y. Shimizu How to calculate one-loop diagram S. Matsuda Perspective of Particle Physics 1988 World Scientific 369 KEK-Preprint 88-6
2. J. Fujimoto, Y. Shimizu, K. Kato, and Y. Oyanagi Numerical approach to one-loop integrals Y. Watase F. Abe Proc. of Internat. Conf. on Computing in High Energy Physics '91 1991 Universal Academy Press, Inc. 407
3. J. Fujimoto, Y. Shimizu, K. Kato, and Y. Oyanagi Prog. Theor. Phys. 87 1992 1233
4. J. Fujimoto, Y. Shimizu, K. Kato, and Y. Oyanagi Numerical Approach to loop Integrals D. Perret-Gallix New Computing Techniques in Physics Research II 1992 World Scientific 625
5. J. Fujimoto, Y. Shimizu, K. Kato, Y. Oyanagi Numerical Approach to Two-loop Integrals, KEK-Preprint 92-213.
6. J. Fujimoto, Y. Shimizu, K. Kato, and T. Kaneko Internat. J. Modern Phys. C 6 1995 525
7. M. Sato Theory of prehomogeneous vector spaces (Algebraic part) Nagoya Math. J. 120 1990 1 (The English translation of Sato's lecture from Shintani's Note (1970))
8. M. Sato, and T. Shintani On zeta functions associated with prehomogeneous vector space Proc. Natl. Acad. Sci. USA 69 1972 1081
9. L.N. Bernstein Funct. Anal. Appl. 6 1972 66
10. F.V. Tkachov Nucl. Instrum. Methods A 389 1997 309
11. G. Passarino Nucl. Phys. B 629 2001 257
12. A. Ferroglia, M. Passera, G. Passarino, and S. Uccirati Nucl. Phys. B 650 2003 162
13. Nucl. Phys. B 680 2004 199
14. G. Passarino, and S. Uccirati Nucl. Phys. B 629 2002 97
15. M.M. Weber Acta Phys. Polonica B 55 2004 2655
16. S. Uccirati Acta Phys. Polonica B 55 2004 2573
17. E. de Doncker, Y. Shimizu, J. Fujimoto, F. Yuasa, K. Kaugars, L. Cucos, and J. Van Voorst Nucl. Instrum. Methods A 534 2004 269
18. E. de Doncker, Y. Shimizu, J. Fujimoto, and F. Yuasa Comput. Phys. Comm. 159 2004 145
19. F. del Aguila, and R. Pittau J. High Energy Phys. (JHEP) 0407 2004 017
20. A. van Hameren, J. Vollinga, and S. Weinzierl hep-ph/0502165
21. W.T. Giele, and E.W.N. Glover J. High Energy Phys. (JHEP) 0404 2004 029
22. T. Binoth, J.Ph. Guillet, and G. Heinrich Nucl. Phys. B 572 2000 361
23. G. Duplanžić, and B. Nižić Eur. Phys. J. C 35 2004 105
24. T. Binoth, G. Heinrich, and N. Kauer Nucl. Phys. B 654 2003 277
25. G. Bélanger, F. Boudjema, J. Fujimoto, T. Ishikawa, T. Kaneko, K. Kato, and Y. Shimizu hep-ph/0308080 (Section 5)
26. For example, see I.H. Sloan, and S. Joe Lattice Methods for Multiple Integration 1994 Oxford Univ. Press Oxford
27. J. Fujimoto, M. Igarashi, N. Nakazawa, Y. Shimizu, and K. Tobimatsu Prog. Theor. Phys. 100 Suppl. 1990 1
28. G.J. van Oldenborgh Comput. Phys. Comm. 58 1991 1
29. S. Kawabata Comput. Phys. Comm. 41 1986 127
30. Comput. Phys. Comm. 88 1995 309
31. Numbers are obtained though a private communication with D. Kreimer. His calculation is performed based on the method described in: D. Kreimer Phys. Lett. B 273 1991 277
32. S. Bauberger, and M. Böhm Nucl. Phys. B 445 1995 25
33. D. Kreimer Phys. Lett. B 292 1992 341
34. A. Frink, U. Kilian, and D. Kreimer Nucl. Phys. B 488 1997 426
35. Y. Kurihara, J. Fujimoto, T. Ishikawa, K. Kato, S. Kawabata, T. Munehisa, and H. Tanaka Nucl. Phys. B 654 2003 301
36. Mathematica ver.5.0, Wolfram Research, Inc.