Advertisement

Automated computation of one-loop integrals in massless theories

  • A. vanHameren
  • J. Vollinga
  • S. Weinzierl
theoretical physics

Abstract.

We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory, and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The number of external legs of the loop integrals is not restricted. All calculations are done within dimensional regularization.

Keywords

Field Theory Elementary Particle Quantum Field Theory Particle Acceleration Scalar Integral 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F.A. Berends, W.T. Giele, Nucl. Phys. B 306, 759 (1988)CrossRefGoogle Scholar
  2. 2.
    F.A. Berends, W.T. Giele, H. Kuijf, Phys. Lett. B 232, 266 (1989)CrossRefGoogle Scholar
  3. 3.
    F.A. Berends, H. Kuijf, B. Tausk, W.T. Giele, Nucl. Phys. B 357, 32 (1991)CrossRefGoogle Scholar
  4. 4.
    F. Caravaglios, M. Moretti, Phys. Lett. B 358, 332 (1995), hep-ph/9507237CrossRefGoogle Scholar
  5. 5.
    F. Caravaglios, M.L. Mangano, M. Moretti, R. Pittau, Nucl. Phys. B539, 215 (1999), hep-ph/9807570Google Scholar
  6. 6.
    P. Draggiotis, R.H.P. Kleiss, C.G. Papadopoulos, Phys. Lett. B 439, 157 (1998), hep-ph/9807207CrossRefGoogle Scholar
  7. 7.
    P.D. Draggiotis, R.H.P. Kleiss, C.G. Papadopoulos, Eur. Phys.J. C 24, 447 (2002), hep-ph/0202201Google Scholar
  8. 8.
    T. Stelzer, W.F. Long, Comput. Phys. Commun. 81, 357 (1994), hep-ph/9401258CrossRefGoogle Scholar
  9. 9.
    A. Pukhov et al. , (1999), hep-ph/9908288Google Scholar
  10. 10.
    F. Yuasa et al. , Prog. Theor. Phys. Suppl. 138, 18 (2000), hep-ph/0007053Google Scholar
  11. 11.
    W.B. Kilgore, W.T. Giele, Phys. Rev. D 55, 7183 (1997), hep-ph/9610433CrossRefGoogle Scholar
  12. 12.
    Z. Nagy, Phys. Rev. Lett. 88, 122003 (2002), hep-ph/0110315CrossRefPubMedGoogle Scholar
  13. 13.
    Z. Nagy, Phys. Rev. D 68, 094002 (2003), hep-ph/0307268CrossRefGoogle Scholar
  14. 14.
    J. Campbell, R.K. Ellis, Phys. Rev. D 65, 113007 (2002), hep-ph/0202176CrossRefGoogle Scholar
  15. 15.
    W. Beenakker et al. , Nucl. Phys. B 653, 151 (2003), hep-ph/0211352CrossRefGoogle Scholar
  16. 16.
    S. Dawson, C. Jackson, L.H. Orr, L. Reina, D. Wackeroth, Phys. Rev. D 68, 034022 (2003), hep-ph/0305087CrossRefGoogle Scholar
  17. 17.
    V. Del Duca, W. Kilgore, C. Oleari, C. Schmidt, D. Zeppenfeld, Phys. Rev. Lett. 87, 122001 (2001), hep-ph/0105129CrossRefPubMedGoogle Scholar
  18. 18.
    V. Del Duca, W. Kilgore, C. Oleari, C. Schmidt, D. Zeppenfeld, Nucl. Phys. B 616, 367 (2001), hep-ph/0108030CrossRefGoogle Scholar
  19. 19.
    A. Brandenburg, S. Dittmaier, P. Uwer, S. Weinzierl, Nucl. Phys. Proc. Suppl. 135, 71 (2004), hep-ph/0408137CrossRefGoogle Scholar
  20. 20.
    D.E. Soper, Phys. Rev. Lett. 81, 2638 (1998), hep-ph/9804454CrossRefGoogle Scholar
  21. 21.
    D.E. Soper, Phys. Rev. D 62, 014009 (2000), hep-ph/9910292CrossRefGoogle Scholar
  22. 22.
    G. Passarino, Nucl. Phys. B 619, 257 (2001), hep-ph/0108252CrossRefGoogle Scholar
  23. 23.
    A. Ferroglia, M. Passera, G. Passarino, S. Uccirati, Nucl. Phys. B 650, 162 (2003), hep-ph/0209219CrossRefGoogle Scholar
  24. 24.
    Z. Nagy, D.E. Soper, JHEP 09, 055 (2003), hep-ph/0308127CrossRefGoogle Scholar
  25. 25.
    A. Denner, S. Dittmaier, Nucl. Phys. B 658, 175 (2003), hep-ph/0212259CrossRefGoogle Scholar
  26. 26.
    S. Dittmaier, Nucl. Phys. B 675, 447 (2003), hep-ph/0308246CrossRefGoogle Scholar
  27. 27.
    W.T. Giele, E.W.N. Glover, JHEP 04, 029 (2004), hep-ph/0402152CrossRefGoogle Scholar
  28. 28.
    W. Giele, E.W.N. Glover, G. Zanderighi, Nucl. Phys. Proc. Suppl. 135, 275 (2004), hep-ph/0407016CrossRefGoogle Scholar
  29. 29.
    F. del Aguila, R. Pittau, JHEP 07, 017 (2004), hep-ph/0404120CrossRefGoogle Scholar
  30. 30.
    R. Pittau, hep-ph/0406105Google Scholar
  31. 31.
    T. Binoth, G. Heinrich, N. Kauer, Nucl. Phys. B 654, 277 (2003), hep-ph/0210023CrossRefGoogle Scholar
  32. 32.
    T. Binoth, Nucl. Phys. Proc. Suppl. 135, 270 (2004), hep-ph/0407003CrossRefGoogle Scholar
  33. 33.
    A. van Hameren, C.G. Papadopoulos, Acta Phys. Polon. B 35, 2601 (2004), hep-ph/0410189Google Scholar
  34. 34.
    R. Pittau, Comput. Phys. Commun. 104, 23 (1997), hep-ph/9607309CrossRefGoogle Scholar
  35. 35.
    R. Pittau, Comput. Phys. Commun. 111, 48 (1998), hep-ph/9712418CrossRefGoogle Scholar
  36. 36.
    S. Weinzierl, Phys. Lett. B 450, 234 (1999), hep-ph/9811365CrossRefGoogle Scholar
  37. 37.
    Z. Bern, L.J. Dixon, D.A. Kosower, Nucl. Phys. B 412, 751 (1994), hep-ph/9306240CrossRefGoogle Scholar
  38. 38.
    T. Binoth, J.P. Guillet, G. Heinrich, Nucl. Phys. B 572, 361 (2000), hep-ph/9911342CrossRefGoogle Scholar
  39. 39.
    J. Fleischer, F. Jegerlehner, O.V. Tarasov, Nucl. Phys. B 566, 423 (2000), hep-ph/9907327CrossRefGoogle Scholar
  40. 40.
    G. Duplancic, B. Nizic, Eur. Phys. J. C 35, 105 (2004), hep-ph/0303184Google Scholar
  41. 41.
    J. Collins, Renormalization (Cambridge University Press, 1984)Google Scholar
  42. 42.
    G. ‘t Hooft, M.J.G. Veltman, Nucl. Phys. B 44, 189 (1972)CrossRefGoogle Scholar
  43. 43.
    Z. Bern, D.A. Kosower, Nucl. Phys. B 379, 451 (1992)CrossRefGoogle Scholar
  44. 44.
    S. Weinzierl, hep-ph/9903380Google Scholar
  45. 45.
    Z. Bern, A. De Freitas, L. Dixon, H.L. Wong, Phys. Rev. D 66, 085002 (2002), hep-ph/0202271CrossRefGoogle Scholar
  46. 46.
    Z. Kunszt, A. Signer, Z. Trocsanyi, Nucl. Phys. B 411, 397 (1994), hep-ph/9305239CrossRefGoogle Scholar
  47. 47.
    A. Signer, Ph.D. thesis, Diss. ETH Nr. 11143 (1995)Google Scholar
  48. 48.
    S. Catani, M.H. Seymour, Z. Trocsanyi, Phys. Rev. D 55, 6819 (1997), hep-ph/9610553CrossRefGoogle Scholar
  49. 49.
    G. Passarino, M.J.G. Veltman, Nucl. Phys. B 160, 151 (1979)CrossRefGoogle Scholar
  50. 50.
    R.G. Stuart, Comput. Phys. Commun. 48, 367 (1988)CrossRefGoogle Scholar
  51. 51.
    R.G. Stuart, A. Gongora, Comput. Phys. Commun. 56, 337 (1990)CrossRefGoogle Scholar
  52. 52.
    G. Devaraj, R.G. Stuart, Nucl. Phys. B 519, 483 (1998), hep-ph/9704308CrossRefGoogle Scholar
  53. 53.
    G.J. van Oldenborgh, J.A.M. Vermaseren, Z. Phys. C 46, 425 (1990)CrossRefGoogle Scholar
  54. 54.
    A.I. Davydychev, Phys. Lett. B 263, 107 (1991)CrossRefGoogle Scholar
  55. 55.
    O.V. Tarasov, Phys. Rev. D 54, 6479 (1996), hep-th/9606018CrossRefGoogle Scholar
  56. 56.
    O.V. Tarasov, Nucl. Phys. B 502, 455 (1997), hep-ph/9703319CrossRefGoogle Scholar
  57. 57.
    J.M. Campbell, E.W.N. Glover, D.J. Miller, Nucl. Phys. B 498, 397 (1997), hep-ph/9612413CrossRefGoogle Scholar
  58. 58.
    Z. Bern, A.G. Morgan, Nucl. Phys. B 467, 479 (1996), hep-ph/9511336CrossRefGoogle Scholar
  59. 59.
    D.B. Melrose, Nuovo Cim. 40, 181 (1965)Google Scholar
  60. 60.
    W.L. van Neerven, J.A.M. Vermaseren, Phys. Lett. B 137, 241 (1984)CrossRefGoogle Scholar
  61. 61.
    G. ‘t Hooft, M.J.G. Veltman, Nucl. Phys. B 153, 365 (1979)CrossRefGoogle Scholar
  62. 62.
    A. Denner, U. Nierste, R. Scharf, Nucl. Phys. B 367, 637 (1991)CrossRefGoogle Scholar
  63. 63.
    Z. Bern, L.J. Dixon, D.A. Kosower, Phys. Lett. B 302, 299 (1993), hep-ph/9212308CrossRefGoogle Scholar
  64. 64.
    N.I. Ussyukina, A.I. Davydychev, Phys. Lett. B 298, 363 (1993)CrossRefGoogle Scholar
  65. 65.
    H.J. Lu, C.A. Perez, SLAC-PUB-5809Google Scholar
  66. 66.
    Z. Bern, L. Dixon, D.A. Kosower, S. Weinzierl, Nucl. Phys. B 489, 3 (1997), hep-ph/9610370CrossRefGoogle Scholar
  67. 67.
    G. Duplancic, B. Nizic, Eur. Phys. J. C 20, 357 (2001), hep-ph/0006249Google Scholar
  68. 68.
    G. Duplancic, B. Nizic, Eur. Phys. J. C 24, 385 (2002), hep-ph/0201306Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  • A. vanHameren
    • 1
  • J. Vollinga
    • 1
  • S. Weinzierl
    • 1
  1. 1.Institut für PhysikUniversität MainzMainzGermany

Personalised recommendations