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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 14 scientific papers (total in 14 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_à14-01-00695_à Ministry of Education and Science of the Russian Federation ÍØ-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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Document Type: Article
Received: 25.11.2015
Language: English

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
\Bibitem{AleKatSte16} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000374066200001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962920866} `

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Stepanyantz K., “Some aspects of N = 1 SYM renormalization”, 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
2. Stepanyantz K.V., Nucl. Phys. B, 909 (2016), 316–335
3. Aleshin S.S., Kazantsev A.E., Skoptsov M.B., Stepanyantz K.V., “One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization”, J. High Energy Phys., 2016, no. 5, 014
4. I. V. Nartsev, K. V. Stepanyantz, “NSVZ-like scheme for the photino mass in softly broken $N=1$ SQED regularized by higher derivatives”, JETP Letters, 105:2 (2017), 69–73
5. S. S. Aleshin, I. O. Goriachuk, A. L. Kataev, K. V. Stepanyantz, Phys. Lett. B, 764 (2017), 222–227
6. V. Yu. Shakhmanov, K. V. Stepanyantz, “Three-Loop NSVZ Relation For Terms Quartic in the Yukawa Couplings With the Higher Covariant Derivative Regularization”, Nucl. Phys. B, 920 (2017), 345–367
7. I. V. Nartsev, K. V. Stepanyantz, “Exact renormalization of the photino mass in softly broken $\mathcal{N}=1$ SQED with $N_f$ flavors regularized by higher derivatives”, J. High Energy Phys., 2017, no. 4, 047
8. A. E. Kazantsev, M. B. Skoptsov, K. V. Stepanyantz, “One-Loop Polarization Operator of the Quantum Gauge Superfield For N=1 SYM Regularized By Higher Derivatives”, Mod. Phys. Lett. A, 32:36 (2017), 1750194
9. Shakhmanov V.Yu., Stepanyantz K.V., “New Form of the Nsvz Relation At the Two-Loop Level”, Phys. Lett. B, 776 (2018), 417–423
10. Kataev A.L., Kazantsev A.E., Stepanyantz K.V., “The Adler D-Function For N=1 SQCD Regularized By Higher Covariant Derivatives in the Three-Loop Approximation”, Nucl. Phys. B, 926 (2018), 295–320
11. Kazantsev A.E., Shakhmanov V.Yu., Stepanyantz K.V., “New Form of the Exact Nsvz Beta-Function: the Three-Loop Verification For Terms Containing Yukawa Couplings”, J. High Energy Phys., 2018, no. 4, 130
12. Kazantsev A.E., Kuzmichev M.D., Meshcheriakov N.P., Novgorodtsev S.V., Shirokov I.E., Skoptsov M.B., Stepanyantz K.V., “Two-Loop Renormalization of the Faddeev-Popov Ghosts in N=1 Supersymmetric Gauge Theories Regularized By Higher Derivatives”, J. High Energy Phys., 2018, no. 6, 020
13. Aleshin S.S., “Nsvz Relation and the Dimensional Reduction in N=1 Sqed”, Phys. Part. Nuclei, 49:5 (2018), 966–968
14. Stepanyantz K., Xxv International Conference on Integrable Systems and Quantum Symmetries (Isqs-25), Journal of Physics Conference Series, 965, IOP Publishing Ltd, 2018
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