Advertisement

JETP Letters

, Volume 103, Issue 2, pp 77–81 | Cite as

Structure of three-loop contributions to the β-function of N = 1 supersymmetric QED with N f flavors regularized by the dimensional reduction

  • S. S. Aleshin
  • A. L. Kataev
  • K. V. StepanyantzEmail author
Fields, Particles, and Nuclei

Abstract

In the case of using the higher derivative regularization for N = 1 supersymmetric quantum electrodynamics (SQED) with N f flavors, the loop integrals giving the β-function are integrals of double total derivatives in themomentum space. This feature allows reducing one of the loop integrals to an integral of the δ-function and deriving the Novikov–Shifman–Vainshtein–Zakharov relation for the renormalization group functions defined in terms of the bare coupling constant. We consider N = 1 SQED with N f flavors regularized by the dimensional reduction in the \(\overline {DR} \)-scheme. Evaluating the scheme-dependent three-loop contribution to the β-function proportional to (N f)2 we find the structures analogous to integrals of the δ-singularities. After adding the schemeindependent terms proportional to (N f)1, we obtain the known result for the three-loop β-function.

Keywords

Dimensional Reduction JETP Letter High Derivative Loop Integral Renormalization Group Function 
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.
    V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B 229, 381 (1983).ADSCrossRefGoogle Scholar
  2. 2.
    D. R. T. Jones, Phys. Lett. B 123, 45 (1983).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    A. I. Vainshtein, V. I. Zakharov, and M. A. Shifman, JETP Lett. 42, 224 (1985).ADSMathSciNetGoogle Scholar
  4. 4.
    V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Phys. Lett. B 166 (1986) 329; Sov. J. Nucl. Phys. 43, 294 (1986).ADSCrossRefGoogle Scholar
  5. 5.
    M. A. Shifman and A. I. Vainshtein, Nucl. Phys. B 277, 456 (1986); Sov. Phys. JETP 64, 428 (1986).ADSCrossRefGoogle Scholar
  6. 6.
    M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Phys. Lett. B 166, 334 (1986).ADSCrossRefGoogle Scholar
  7. 7.
    K. V. Stepanyantz, Nucl. Phys. B 852, 71 (2011).ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    K. V. Stepanyantz, J. High Energy Phys. 1408, 096 (2014).ADSCrossRefGoogle Scholar
  9. 9.
    A. A. Slavnov, Nucl. Phys. B 31, 301 (1971).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    A. A. Slavnov, Theor. Math. Phys. 13, 1064 (1972).CrossRefGoogle Scholar
  11. 11.
    V. K. Krivoshchekov, Theor. Math. Phys. 36, 745 (1978).MathSciNetCrossRefGoogle Scholar
  12. 12.
    P. C. West, Nucl. Phys. B 268, 113 (1986).ADSCrossRefGoogle Scholar
  13. 13.
    A. A. Soloshenko and K. V. Stepanyantz, Theor. Math. Phys. 140, 1264 (2004).CrossRefGoogle Scholar
  14. 14.
    A. V. Smilga and A. Vainshtein, Nucl. Phys. B 704, 445 (2005).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    A. B. Pimenov, E. S. Shevtsova, and K. V. Stepanyantz, Phys. Lett. B 686, 293 (2010).ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    K. V. Stepanyantz, arXiv:1108.1491 [hep-th].Google Scholar
  17. 17.
    A. E. Kazantsev and K. V. Stepanyantz, J. Exp. Theor. Phys. 120, 618 (2015).ADSCrossRefGoogle Scholar
  18. 18.
    I. L. Buchbinder and K. V. Stepanyantz, Nucl. Phys. B 883, 20 (2014).ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    I. L. Buchbinder, N. G. Pletnev, and K. V. Stepanyantz, Phys. Lett. B 751, 434 (2015).ADSCrossRefGoogle Scholar
  20. 20.
    M. Shifman and K. Stepanyantz, Phys. Rev. Lett. 114, 051601 (2015).ADSCrossRefGoogle Scholar
  21. 21.
    M. Shifman and K. V. Stepanyantz, Phys. Rev. D 91, 105008 (2015).ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    A. L. Kataev and K. V. Stepanyantz, Nucl. Phys. B 875, 459 (2013).ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    A. L. Kataev and K. V. Stepanyantz, Phys. Lett. B 730, 184 (2014).ADSCrossRefGoogle Scholar
  24. 24.
    A. L. Kataev and K. V. Stepanyantz, Theor. Math. Phys. 181, 1531 (2014).MathSciNetCrossRefGoogle Scholar
  25. 25.
    W. Siegel, Phys. Lett. B 84, 193 (1979).ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    W. Siegel, Phys. Lett. B 94, 37 (1980).ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    L. V. Avdeev, G. A. Chochia, and A. A. Vladimirov, Phys. Lett. B 105, 272 (1981).ADSCrossRefGoogle Scholar
  28. 28.
    L. V. Avdeev and A. A. Vladimirov, Nucl. Phys. B 219, 262 (1983).ADSCrossRefGoogle Scholar
  29. 29.
    L. Mihaila, Adv. High Energy Phys. 2013, 607807 (2013).MathSciNetCrossRefGoogle Scholar
  30. 30.
    I. Jack, D. R. T. Jones, and C. G. North, Phys. Lett. B 386, 138 (1996).ADSCrossRefGoogle Scholar
  31. 31.
    K. G. Chetyrkin, A. L. Kataev, and F. V. Tkachov, Nucl. Phys. B 174, 345 (1980).ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    I. Jack, D. R. T. Jones, and C. G. North, Nucl. Phys. B 486, 479 (1997).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2016

Authors and Affiliations

  • S. S. Aleshin
    • 1
  • A. L. Kataev
    • 2
  • K. V. Stepanyantz
    • 1
    Email author
  1. 1.Department of Theoretical Physics, Faculty of PhysicsMoscow State UniversityMoscowRussia
  2. 2.Institute for Nuclear ResearchRussian Academy of SciencesMoscowRussia

Personalised recommendations