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 TMF, 2003, Volume 134, Number 3, Pages 430–446 (Mi tmf169)

Two-Loop Anomalous Dimension of $N=1$ Supersymmetric Quantum Electrodynamics Regularized Using Higher Covariant Derivatives

A. A. Soloshenko, K. V. Stepanyantz

M. V. Lomonosov Moscow State University

Abstract: We calculate the two-loop anomalous dimension in the $N=1$ supersymmetric electrodynamics regularized through the higher covariant derivative method using the minimum subtraction scheme and show that the result is independent of the form of the regularizing term but does depend on the ratio between the masses $M$ of the Pauli–Villars fields and the dimensional constant $\Lambda$ in the regularizing term. We propose a simple subtraction scheme in which the result is independent of the parameters of the regularization used.

Keywords: regularization, higher covariant derivatives, counterterms

DOI: https://doi.org/10.4213/tmf169

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English version:
Theoretical and Mathematical Physics, 2003, 134:3, 377–391

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Revised: 28.05.2002

Citation: A. A. Soloshenko, K. V. Stepanyantz, “Two-Loop Anomalous Dimension of $N=1$ Supersymmetric Quantum Electrodynamics Regularized Using Higher Covariant Derivatives”, TMF, 134:3 (2003), 430–446; Theoret. and Math. Phys., 134:3 (2003), 377–391

Citation in format AMSBIB
\Bibitem{SolSte03} \by A.~A.~Soloshenko, K.~V.~Stepanyantz \paper Two-Loop Anomalous Dimension of $N=1$ Supersymmetric Quantum Electrodynamics Regularized Using Higher Covariant Derivatives \jour TMF \yr 2003 \vol 134 \issue 3 \pages 430--446 \mathnet{http://mi.mathnet.ru/tmf169} \crossref{https://doi.org/10.4213/tmf169} \transl \jour Theoret. and Math. Phys. \yr 2003 \vol 134 \issue 3 \pages 377--391 \crossref{https://doi.org/10.1023/A:1022653506397} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000182047100008} 

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• http://mi.mathnet.ru/eng/tmf/v134/i3/p430

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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. K. V. Stepanyantz, “Anomaly Problem in the $N=1$ Supersymmetric Electrodynamics as a Consequence of the Inconsistency of the Dimensional Reduction Method”, Theoret. and Math. Phys., 140:1 (2004), 939–957
2. A. A. Soloshenko, K. V. Stepanyantz, “Three-Loop $\beta$-Function of $N=1$ Supersymmetric Electrodynamics Regularized by Higher Derivatives”, Theoret. and Math. Phys., 140:3 (2004), 1264–1282
3. K. V. Stepanyantz, “Investigating the anomaly puzzle in $N=1$ supersymmetric electrodynamics”, Theoret. and Math. Phys., 142:1 (2005), 29–47
4. A. B. Pimenov, K. V. Stepanyantz, “Four-loop verification of an algorithm for summing Feynman diagrams in the $N{=}1$ supersymmetric electrodynamics”, Theoret. and Math. Phys., 147:2 (2006), 687–697
5. K. V. Stepanyantz, “Summation of diagrams in $N=1$ supersymmetric electrodynamics regularized by higher derivatives”, Theoret. and Math. Phys., 146:3 (2006), 321–334
6. K. V. Stepanyantz, “Contribution of matter fields to the Gell-Mann–Low function for the $N=1$ supersymmetric Yang–Mills theory regularized by higher covariant derivatives”, Theoret. and Math. Phys., 150:3 (2007), 377–392
7. A. B. Pimenov, K. V. Stepanyantz, “Two-loop Gell-Mann–Low function of the $N=1$ supersymmetric Yang–Mills theory regularized by higher covariant derivatives”, Theoret. and Math. Phys., 155:3 (2008), 848–861
8. Soloshenko AA, Stepan'yants KV, “Schwinger-Dyson Equations for N=1 Supersymmetric Yang-Mills Theory”, Moscow University Physics Bulletin, 63:3 (2008), 189–192
9. Pimenov, AB, “REGULARIZATION BY HIGHER DERIVATIVES AND QUANTUM CORRECTION FOR N=1 SUPERSYMMETRIC THEORIES”, Russian Physics Journal, 51:5 (2008), 444
10. Kataev A.L. Stepanyantz K.V., “Nsvz Scheme with the Higher Derivative Regularization for N=1 Sqed”, Nucl. Phys. B, 875:2 (2013), 459–482
11. Kataev A.L. Stepanyantz K.V., “Scheme Independent Consequence of the Nsvz Relation For N=1 Sqed With N-F Flavors”, Phys. Lett. B, 730 (2014), 184–189
12. Shakhmanov V.Yu. Stepanyantz K.V., “Three-Loop Nsvz Relation For Terms Quartic in the Yukawa Couplings With the Higher Covariant Derivative Regularization”, Nucl. Phys. B, 920 (2017), 345–367
13. 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
14. 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
15. Aleshin S.S. Kataev A.L. Stepanyantz K.V., “The Three-Loop Adler D-Function For N=1 Sqcd Regularized By Dimensional Reduction”, J. High Energy Phys., 2019, no. 3, 196
16. Kataev A.L. Kazantsev A.E. Stepanyantz K.V., “On-Shell Renormalization Scheme For N=1 Sqed and the Nsvz Relation”, Eur. Phys. J. C, 79:6 (2019), 477
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