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Pis'ma v Zh. Èksper. Teoret. Fiz., 2016, Volume 103, Issue 2, Pages 83–87 (Mi jetpl4836)  

This article is cited in 15 scientific papers (total in 15 papers)

FIELDS, PARTICLES, AND NUCLEI

Structure of three-loop contributions to the $\beta$-function of $\mathcal{N}=1$ SQED with $N_f$ flavors, regularized by the dimensional reduction

S. S. Aleshina, A. L. Kataevb, K. V. Stepanyantza

a Physical Faculty Lomonosov MSU, Department of Theoretical Physics, 119991 Moscow, Russia
b Institute for Nuclear Research of the RAS, 117312 Moscow, Russia

Abstract: In the case of using the higher derivative regularization for $N=1$ supersymmetric quantum electro-dynamics (SQED) with $N_f$ flavors the loop integrals giving the $\beta$-function are integrals of double total derivatives in the momentum space. This feature allows to reduce one of the loop integrals to an integral of the $\delta$-function and to derive the NSVZ relation for the renormalization group functions defined in terms of the bare coupling constant. In this paper 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 $\beta$-function proportional to $(N_f)^2$ we find the structures analogous to integrals of the $\delta$-singularities. After adding the scheme-independent terms proportional to $(N_f)^1$ we obtain the known result for the three-loop $\beta$-function.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00647_
14-01-00695_
Ministry of Education and Science of the Russian Federation -2835.2014.2
The work of A.K. was supported by the RFBR grant #14-01-00647 and also by the grant for the Leading Scientific Schools NS-2835.2014.2. The work of K.S. was supported by the RFBR grant #14-01-00695.


DOI: https://doi.org/10.7868/S0370274X16020016

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English version:
Journal of Experimental and Theoretical Physics Letters, 2016, 103:2, 77–81

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Received: 25.11.2015
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Citation: S. S. Aleshin, A. L. Kataev, K. V. Stepanyantz, “Structure of three-loop contributions to the $\beta$-function of $\mathcal{N}=1$ SQED with $N_f$ flavors, regularized by the dimensional reduction”, Pis'ma v Zh. Èksper. Teoret. Fiz., 103:2 (2016), 83–87; JETP Letters, 103:2 (2016), 77–81

Citation in format AMSBIB
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\by S.~S.~Aleshin, A.~L.~Kataev, K.~V.~Stepanyantz
\paper Structure of three-loop contributions to the $\beta$-function of $\mathcal{N}=1$ SQED with $N_f$ flavors, regularized by the dimensional reduction
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2016
\vol 103
\issue 2
\pages 83--87
\mathnet{http://mi.mathnet.ru/jetpl4836}
\crossref{https://doi.org/10.7868/S0370274X16020016}
\elib{http://elibrary.ru/item.asp?id=26126462}
\transl
\jour JETP Letters
\yr 2016
\vol 103
\issue 2
\pages 77--81
\crossref{https://doi.org/10.1134/S0021364016020028}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Stepanyantz K., 19Th International Seminar on High Energy Physics (Quarks-2016), Epj Web of Conferences, 125, eds. Andrianov V., Matveev V., Rubakov V., Kim V., Andrianov A., Fitkevich M., E D P Sciences, 2016, UNSP 05014  crossref  isi  scopus
    2. Stepanyantz K.V., Nucl. Phys. B, 909 (2016), 316–335  crossref  mathscinet  zmath  isi  elib  scopus
    3. Aleshin S.S., Kazantsev A.E., Skoptsov M.B., Stepanyantz K.V., J. High Energy Phys., 2016, no. 5, 014  crossref  isi  elib  scopus
    4. I. V. Nartsev, K. V. Stepanyantz, JETP Letters, 105:2 (2017), 69–73  mathnet  crossref  crossref  isi  elib
    5. S. S. Aleshin, I. O. Goriachuk, A. L. Kataev, K. V. Stepanyantz, Phys. Lett. B, 764 (2017), 222–227  crossref  zmath  isi  scopus
    6. V. Yu. Shakhmanov, K. V. Stepanyantz, Nucl. Phys. B, 920 (2017), 345–367  crossref  mathscinet  zmath  isi  scopus
    7. I. V. Nartsev, K. V. Stepanyantz, J. High Energy Phys., 2017, no. 4, 047  crossref  mathscinet  isi  scopus
    8. A. E. Kazantsev, M. B. Skoptsov, K. V. Stepanyantz, Mod. Phys. Lett. A, 32:36 (2017), 1750194  crossref  mathscinet  zmath  isi  scopus
    9. V. Yu. Shakhmanov, K. V. Stepanyantz, Phys. Lett. B, 776 (2018), 417–423  crossref  mathscinet  zmath  isi  scopus
    10. A. L. Kataev, A. E. Kazantsev, K. V. Stepanyantz, Nucl. Phys. B, 926 (2018), 295–320  crossref  mathscinet  zmath  isi  scopus
    11. A. E. Kazantsev, V. Yu. Shakhmanov, K. V. Stepanyantz, J. High Energy Phys., 2018, no. 4, 130  crossref  mathscinet  zmath  isi
    12. A. E. Kazantsev, M. D. Kuzmichev, N. P. Meshcheriakov, S. V. Novgorodtsev, I. E. Shirokov, M. B. Skoptsov, K. V. Stepanyantz, J. High Energy Phys., 2018, no. 6, 020  crossref  mathscinet  isi  scopus
    13. S. S. Aleshin, Phys. Part. Nuclei, 49:5 (2018), 966–968  crossref  isi  scopus
    14. K. Stepanyantz, XXV International Conference on Integrable Systems and Quantum Symmetries (ISQS-25), Journal of Physics Conference Series, 965, IOP Publishing Ltd, 2018, UNSP 012039  crossref  isi  scopus
    15. Aleshin S.S., Kataev A.L., Stepanyantz K.V., J. High Energy Phys., 2019, no. 3, 196  crossref  isi  scopus
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