Evaluation of two-loop self-energy basis integrals using differential equations

Physical Review D

Volumn 68, Issue 7, 2003, Pages

  Martin, Stephen P ^a,b  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

^b FERMI NATIONAL ACCELERATOR LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; CALCULATION; ENERGY; MATHEMATICAL COMPUTING; MOLECULAR WEIGHT;

EID: 0344924857     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.68.075002     Document Type: Article

References (63)

1. See for example, "ATLAS detector and physics performance. Technical design report. Vol. 2," CERN-LHCC-99-15
2. and V. Drollinger and A. Sopczak, Eur. Phys. J. C 3, N1 (2001).
3. For discussions of the present status of the problem, see G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich, and G. Weiglein, Eur. Phys. J. C 28, 133 (2003);
4. S.P. Martin, Phys. Rev. D 66, 096001 (2002);
5. S.P. Martin, Phys. Rev. D 67, 095012 (2003).
6. O.V. Tarasov, Nucl. Phys. B502, 455 (1997).
7. G. Weiglein, R. Scharf, and M. Bohm, Nucl. Phys. B416, 606 (1994).
8. A. Ghinculov and Y.P. Yao, Nucl. Phys. B516, 385 (1998);
9. Phys. Rev. D 63, 054510 (2001).
10. F.V. Tkachov, Phys. Lett. 100B, 65 (1981);
11. K.G. Chetyrkin and F.V. Tkachov, Nucl. Phys. B192, 159 (1981).
12. O.V. Tarasov, Phys. Rev. D 54, 6479 (1996).
13. R. Scharf, Würzburg Diploma thesis, as quoted in [17].
14. J.L. Rosner, AIP Conf. Proc. 44, 11 (1967).
15. J. van der Bij and M.J. Veltman, Nucl. Phys. B231, 205 (1984).
16. D.J. Broadhurst, Z. Phys. C 47, 115 (1990).
17. A. Djouadi, Nuovo Cimento A 100, 357 (1988).
18. B.A. Kniehl, Nucl. Phys. B347, 86 (1990).
19. N. Gray, D.J. Broadhurst, W. Grafe, and K. Schilcher, Z. Phys. C 48, 673 (1990).
20. C. Ford and D.R.T. Jones, Phys. Lett. B 274, 409 (1992).
21. C. Ford, I. Jack, and D.R.T. Jones, Nucl. Phys. B387, 373 (1992).
22. R. Scharf and J.B. Tausk, Nucl. Phys. B412, 523 (1994).
23. F.A. Berends and J.B. Tausk, Nucl. Phys. B421, 456 (1994).
24. J. Fleischer, A.V. Kotikov, and O.L. Veretin, Nucl. Phys. B547, 343 (1999).
25. S.P. Martin, Phys. Rev. D 65, 116003 (2002).
26. V.A. Smirnov, Commun. Math. Phys. 134, 109 (1990).
27. A.I. Davydychev and J.B. Tausk, Nucl. Phys. B397, 123 (1993).
28. D.J. Broadhurst, J. Fleischer, and O.V. Tarasov, Z. Phys. C 60, 287 (1993).
29. A.I. Davydychev, V.A. Smirnov, and J.B. Tausk, Nucl. Phys. B410, 325 (1993).
30. F.A. Berends, A.I. Davydychev, V.A. Smirnov, and J.B. Tausk, Nucl. Phys. B439, 536 (1995).
31. F.A. Berends, A.I. Davydychev, and V.A. Smirnov, Nucl. Phys. B478, 59 (1996).
32. A. Czarnecki and V.A. Smirnov, Phys. Lett. B 394, 211 (1997).
33. M. Beneke and V.A. Smirnov, Nucl. Phys. B522, 321 (1998).
34. F.A. Berends, A.I. Davydychev, and N.I. Ussyukina, Phys. Lett. B 426, 95 (1998).
35. A.I. Davydychev and V.A. Smirnov, Nucl. Phys. B554, 391 (1999).
36. J. Fleischer, M.Y. Kalmykov, and A.V. Kotikov, Phys. Lett. B 462, 169 (1999).
37. M. Caffo, H. Czyz, and E. Remiddi, Nucl. Phys. B581, 274 (2000);
38. M. Caffo, H. Czyz, and E. Remiddi, Nucl. Phys. B611, 503 (2001).
39. S. Groote and A.A. Pivovarov, Nucl. Phys. B580, 459 (2000).
40. D. Kreimer, Phys. Lett. B 273, 277 (1991).
41. F.A. Berends, M. Buza, M. Bohm, and R. Scharf, Z. Phys. C 63, 227 (1994).
42. A. Ghinculov and J.J. van der Bij, Nucl. Phys. B436, 30 (1995).
43. A. Czarnecki, U. Kilian, and D. Kreimer, Nucl. Phys. B433, 259 (1995).
44. S. Bauberger, F.A. Berends, M. Bohm, and M. Buza, Nucl. Phys. B434, 383 (1995).
45. S. Bauberger, M. Bohm, G. Weiglein, F.A. Berends, and M. Buza, Nucl. Phys. B (Proc. Suppl.) 37B, 95 (1994).
46. S. Bauberger and M. Bohm, Nucl. Phys. B445, 25 (1995).
47. G. Passarino, Nucl. Phys. B619, 257 (2001).
48. A.V. Kotikov, Phys. Lett. B 254, 158 (1991).
49. A.V. Kotikov, Phys. Lett. B 259, 314 (1991).
50. E. Remiddi, Nuovo Cimento A 110, 1435 (1997).
51. M. Caffo, H. Czyz, S. Laporta, and E. Remiddi, Nuovo Cimento A 111, 365 (1998).
52. M. Caffo, H. Czyz, S. Laporta, and E. Remiddi, Acta Phys. Pol. B 29, 2627 (1998).
53. M. Caffo, H. Czyz, and E. Remiddi, Nucl. Phys. B634, 309 (2002).
54. M. Caffo, H. Czyz, and E. Remiddi, "Numerical evaluation of master integrals from differential equations," hep-ph/0211178, talk given at RADCOR 2002.
55. R. Mertig and R. Scharf, Comput. Phys. Commun. 111, 265 (1998).
56. L. Lewin, Polylogarithms and Associated Functions (Elsevier North Holland, New York, 1981).
57. K.S. Kolbig, SIAM J. Math. Anal. 17, 1232 (1986).
58. G. 't Hooft and M.J. Veltman, Nucl. Phys. B44, 189 (1972);
59. W.A. Bardeen, A.J. Buras, D.W. Duke, and T. Muta, Phys. Rev. D 18, 3998 (1978).
60. W. Siegel, Phys. Lett. 84B, 193 (1979);
61. D.M. Capper, D.R.T. Jones, and P. van Nieuwenhuizen, Nucl. Phys. B167, 479 (1980).
62. I. Jack et al., Phys. Rev. D 50, 5481 (1994).
63. G. Passarino and M.J. Veltman, Nucl. Phys. B160, 151 (1979).