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The massless two-loop two-point function

  • I. Bierenbaum
  • S. Weinzierl
theoretical physics

Abstract.

We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter \(\varepsilon\). As a side product, we show that in the Laurent expansion of the two-loop integral only rational numbers and multiple zeta values occur. Our method of calculation obtains the two-loop integral as a convolution product of two primitive one-loop integrals. We comment on the generalization of this product structure to higher loop integrals.

Keywords

Convolution Rational Number Regularization Parameter Product Structure Side Product 
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.

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References

  1. 1.
    S.G. Gorishnii, S.A. Larin, L.R. Surguladze, F.V. Tkachov, Comput. Phys. Commun. 55, 381 (1989)CrossRefGoogle Scholar
  2. 2.
    S.A. Larin, F.V. Tkachov, J.A.M. Vermaseren, NIKHEF-H-91-18Google Scholar
  3. 3.
    K.G. Chetyrkin, A.L. Kataev, F.V. Tkachov, Nucl. Phys. B 174, 345 (1980)CrossRefMathSciNetGoogle Scholar
  4. 4.
    D.I. Kazakov, Phys. Lett. B 133, 406 (1983)CrossRefGoogle Scholar
  5. 5.
    D.I. Kazakov, Theor. Math. Phys. 58, 223 (1984)Google Scholar
  6. 6.
    D.I. Kazakov, Theor. Math. Phys. 62, 84 (1985)Google Scholar
  7. 7.
    D.J. Broadhurst, Z. Phys. C 32, 249 (1986)Google Scholar
  8. 8.
    D.T. Barfoot, D.J. Broadhurst, Z. Phys. C 41, 81 (1988)MathSciNetGoogle Scholar
  9. 9.
    A.V. Kotikov, Phys. Lett. B 375, 240 (1996), hep-ph/9512270CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    D.J. Broadhurst, J.A. Gracey, D. Kreimer, Z. Phys. C 75, 559 (1997), hep-th/9607174CrossRefMathSciNetGoogle Scholar
  11. 11.
    D.J. Broadhurst, Nucl. Phys. Proc. Suppl. 116, 432 (2003), hep-ph/0211194CrossRefzbMATHGoogle Scholar
  12. 12.
    S.G. Gorishnii, A.P. Isaev, Theor. Math. Phys. 62, 232 (1985)Google Scholar
  13. 13.
    V.A. Smirnov (2002), hep-ph/0209177Google Scholar
  14. 14.
    S. Weinzierl (2003), hep-th/0305260Google Scholar
  15. 15.
    A.G. Grozin (2003), hep-ph/0307297Google Scholar
  16. 16.
    S. Moch, P. Uwer, S. Weinzierl, J. Math. Phys. 43, 3363 (2002), hep-ph/0110083CrossRefGoogle Scholar
  17. 17.
    S. Weinzierl, Comput. Phys. Commun. 145, 357 (2002), math-ph/0201011CrossRefzbMATHGoogle Scholar
  18. 18.
    G. ‘t Hooft, M.J.G. Veltman, Nucl. Phys. B 44, 189 (1972)CrossRefGoogle Scholar
  19. 19.
    F.V. Tkachov, Phys. Lett. B 100, 65 (1981)MathSciNetGoogle Scholar
  20. 20.
    K.G. Chetyrkin, F.V. Tkachov, Nucl. Phys. B 192, 159 (1981)CrossRefGoogle Scholar
  21. 21.
    T. van Ritbergen, R.G. Stuart, Nucl. Phys. B 564, 343 (2000), hep-ph/9904240CrossRefGoogle Scholar
  22. 22.
    D. Kreimer, Ann. Phys. 303, 179 (2003), hep-th/0211136CrossRefzbMATHGoogle Scholar
  23. 23.
    D. Kreimer, Nucl. Phys. Proc. Suppl. 116, 392 (2003), hep-ph/0211188CrossRefzbMATHGoogle Scholar
  24. 24.
    D. Kreimer (2003), hep-th/0306020Google Scholar
  25. 25.
    V.A. Smirnov, Phys. Lett. B 567, 193 (2003), hep-ph/0305142CrossRefGoogle Scholar
  26. 26.
    C. Bauer, A. Frink, R. Kreckel, J. Symbolic Computation 33, 1 (2002), cs.sc/0004015CrossRefzbMATHGoogle Scholar
  27. 27.
    J.A.M. Vermaseren, Int. J. Mod. Phys. A 14, 2037 (1999), hep-ph/9806280CrossRefMathSciNetzbMATHGoogle Scholar
  28. 28.
    E. Remiddi, J.A.M. Vermaseren, Int. J. Mod. Phys. A 15, 725 (2000), hep-ph/9905237CrossRefMathSciNetzbMATHGoogle Scholar
  29. 29.
    J. Blümlein, S. Kurth, Phys. Rev. D 60, 014018 (1999), hep-ph/9810241CrossRefGoogle Scholar
  30. 30.
    H.N. Minh, M. Petitot, Discrete Math. 217, 273 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  31. 31.
    S.G. Gorishnii, A.L. Kataev, S.A. Larin, Phys. Lett. B 259, 144 (1991)CrossRefGoogle Scholar
  32. 32.
    L.R. Surguladze, M.A. Samuel, Phys. Rev. Lett. 66, 560 (1991), Erratum 66, 2416 (1991)CrossRefGoogle Scholar
  33. 33.
    A. Erdélyi, Higher transcendental functions, Vol. I (McGraw Hill, 1953)Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • I. Bierenbaum
    • 1
  • S. Weinzierl
    • 2
  1. 1.Institut für PhysikUniversität MainzMainzGermany
  2. 2.Dipartimento di FisicaUniversitá di Parma, INFN Gruppo Collegato di ParmaParmaItaly

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