Advertisement

On epsilon expansions of four-loop non-planar massless propagator diagrams

  • R. N. LeeEmail author
  • A. V. Smirnov
  • V. A. Smirnov
Regular Article - Theoretical Physics

Abstract

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter ϵ=(4−d)/2 up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.). We observe only multiple zeta values in our results.

Keywords

High Energy Phys Dimensional Regularization Master Integral Feynman Integral Multiple Zeta 
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.

References

  1. 1.
    P.A. Baikov, K.G. Chetyrkin, Nucl. Phys. B 837, 186 (2010) [arXiv:1004.1153 [hep-ph]] MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 2.
    J. Blumlein, D.J. Broadhurst, J.A.M. Vermaseren, Comput. Phys. Commun. 181, 582 (2010) [arXiv:0907.2557 [math-ph]] MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    F. Brown, Commun. Math. Phys. 287, 925 (2009) [arXiv:0804.1660 [math.AG]] ADSzbMATHCrossRefGoogle Scholar
  4. 4.
    I. Bierenbaum, S. Weinzierl, Eur. Phys. J. C 32, 67 (2003) ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes. Math. Res. Lett. 5, 497 (1998) MathSciNetzbMATHGoogle Scholar
  6. 6.
    A.B. Goncharov, Multiple polylogarithms and mixed Tate motives [arXiv:math/0103059]
  7. 7.
    R.N. Lee, Nucl. Phys. B 830, 474 (2010) [arXiv:0911.0252 [hep-ph]] ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    O.V. Tarasov, Phys. Rev. D 54, 6479 (1996) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    R.N. Lee, A.V. Smirnov, V.A. Smirnov, J. High Energy Phys. 1004, 020 (2010) [arXiv:1001.2887 [hep-ph]] MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    R.N. Lee, A.V. Smirnov, V.A. Smirnov, Nucl. Phys. B, Proc. Suppl. 205–206, 308 (2010) [arXiv:1005.0362 [hep-ph]] CrossRefGoogle Scholar
  11. 11.
    R.N. Lee, Nucl. Phys. B, Proc. Suppl. 205–206, 135 (2010) [arXiv:1007.2256 [hep-ph]] CrossRefGoogle Scholar
  12. 12.
    R.N. Lee, I.S. Terekhov, J. High Energy Phys. 1101, 068 (2011) [arXiv:1010.6117 [hep-ph]] ADSCrossRefGoogle Scholar
  13. 13.
    R.N. Lee, V.A. Smirnov, J. High Energy Phys. 1102, 102 (2011) [arXiv:1010.1334 [hep-ph]] ADSCrossRefMathSciNetGoogle Scholar
  14. 14.
    K.G. Chetyrkin, F.V. Tkachov, Nucl. Phys. B 192, 159 (1981) ADSCrossRefGoogle Scholar
  15. 15.
    A.V. Smirnov, J. High Energy Phys. 0810, 107 (2008) [arXiv:0807.3243 [hep-ph]] ADSCrossRefGoogle Scholar
  16. 16.
    T. Binoth, G. Heinrich, Nucl. Phys. B 585, 741 (2000) MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. 17.
    T. Binoth, G. Heinrich, Nucl. Phys. B 680, 375 (2004) ADSzbMATHCrossRefGoogle Scholar
  18. 18.
    T. Binoth, G. Heinrich, Nucl. Phys. B 693, 134 (2004) ADSzbMATHCrossRefGoogle Scholar
  19. 19.
    G. Heinrich, Int. J. Modern Phys. A 23, 10 (2008) [arXiv:0803.4177] MathSciNetCrossRefGoogle Scholar
  20. 20.
    J. Carter, G. Heinrich, arXiv:1011.5493 [hep-ph]
  21. 21.
    C. Bogner, S. Weinzierl, Comput. Phys. Commun. 178, 596 (2008) [arXiv:0709.4092 [hep-ph]] MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 22.
    C. Bogner, S. Weinzierl, Nucl. Phys. B, Proc. Suppl. 183, 256 (2008) [arXiv:0806.4307 [hep-ph]] MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    A.V. Smirnov, M.N. Tentyukov, Comput. Phys. Commun. 180, 735 (2009) [arXiv:0807.4129 [hep-ph]] ADSzbMATHCrossRefGoogle Scholar
  24. 24.
    A.V. Smirnov, V.A. Smirnov, M. Tentyukov, Comput. Phys. Commun. 182, 790 (2011) [arXiv:0912.0158 [hep-ph]] MathSciNetADSzbMATHCrossRefGoogle Scholar
  25. 25.
    A.V. Smirnov, M. Tentyukov, Nucl. Phys. B 837, 40 (2010) [arXiv:1004.1149 [hep-ph]] MathSciNetADSzbMATHCrossRefGoogle Scholar
  26. 26.
    H.R.P. Ferguson, D.H. Bailey, S. Arno, Math. Comput. 68, 351 (1999). NASA–Ames Technical Report, NAS–96–005 MathSciNetADSzbMATHCrossRefGoogle Scholar
  27. 27.
    D. Maitre, Comput. Phys. Commun. 174, 222 (2006) [arXiv:hep-ph/0507152] ADSCrossRefGoogle Scholar
  28. 28.
    E. Remiddi, J.A.M. Vermaseren, Int. J. Mod. Phys. A 15, 725 (2000) hep-ph/9905237 MathSciNetADSzbMATHCrossRefGoogle Scholar
  29. 29.
    D.J. Broadhurst, Eur. Phys. J. C 8, 311 (1999) ADSGoogle Scholar
  30. 30.
    J. Fleischer, M.Yu. Kalmykov, Phys. Lett. B 470, 168 (1999) ADSCrossRefGoogle Scholar
  31. 31.
    M.Yu. Kalmykov, Nucl. Phys. B 718, 276 (2005) ADSzbMATHCrossRefGoogle Scholar
  32. 32.
    M.Yu. Kalmykov, B.A. Kniehl, Nucl. Phys. B, Proc. Suppl. 205-206, 129 (2010) [arXiv:1007.2373 [math-ph]] MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2011

Authors and Affiliations

  1. 1.Budker Institute of Nuclear Physics and Novosibirsk State UniversityNovosibirskRussia
  2. 2.Scientific Research Computing CenterMoscow State UniversityMoscowRussia
  3. 3.Skobeltsyn Institute of Nuclear Physics of Moscow State UniversityMoscowRussia
  4. 4.Institut für Theoretische TeilchenphysikKITKarlsruheGermany

Personalised recommendations