Z2×S6 symmetry of the two-loop diagram

  • D. T. Barfoot
  • D. J. Broadhurst
Article

Abstract

The generic two-loop diagram of massless scalar field theory ind dimensions, with propagators raised to powers {αi|i=1,5} is shown to have a symmetry groupZ2×S6 corresponding to reflection and permutation of six linear combinations of the six parameters. The expansion about αi=d/4=1 is given to the level required for six-loop renormalization. All but five of the coefficients are obtained from products of one-loop diagrams. All but one are expressed in terms of the Riemann zeta function.

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References

  1. 1.
    O.V. Tarasov, A.A. Vladimirov, A.Y. Zharkov: Phys. Lett. 93B (1980) 429Google Scholar
  2. 2.
    S.G. Gorishny, A.L. Kataev, S.A. Larin: Dubna preprint P2-87-185 (1987)Google Scholar
  3. 3.
    K.G. Chetyrkin, S.G. Gorishny, S.A. Larin, F.V. Tkachov: Phys. Lett. 132B (1983) 351; INR preprint P-0453 (1986); D.I. Kazakov: Phys. Lett. 133B (1983) 406Google Scholar
  4. 4.
    G.'t Hooft, M. Veltmann: Nucl. Phys. B44, (1972) 189Google Scholar
  5. 5.
    K.G. Chetyrkin, F.V. Tkachov: Nucl. Phys. B192 (1981) 159Google Scholar
  6. 6.
    D.I. Kazakov: TM Φ 58 (1984) 343; Dubna lecture notes E3-84-410 (1984)Google Scholar
  7. 7.
    S.G. Gorishny, A.P. Isaev: TM Ф 62 (1985) 345Google Scholar
  8. 8.
    D.J. Broadhurst: Phys. Lett. 164B (1985) 356Google Scholar
  9. 9.
    D.J. Broadhurst: Z. Phys. C—Particles and Fields 32 (1986) 249Google Scholar
  10. 10.
    K.G. Chetyrkin, A.L. Kataev, F.V. Tkachov: Nucl. Phys. B174 (1980) 345; A.E. Terrano: Phys. Lett. 93B (1980) 424Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • D. T. Barfoot
    • 1
  • D. J. Broadhurst
    • 1
  1. 1.The Open UniversityMilton KeynesEngland

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