Abstract
We consider \(\mathcal{N} = 1\) supersymmetric quantum electrodynamics (SQED) with \({{N}_{f}}\) flavors regularized by higher derivatives. The new program is used to calculate the contributions to the anomalous dimension of matter superfields up to the three-loop approximation. Using this calculation and the well-known NSVZ relation, we obtain the \(\beta \)-function of this theory in the four-loop approximation. Then, we study scheme-dependence of these results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
L. Mihaila, “Precision calculations in supersymmetric theories,” Adv. High Energy Phys. 2013, 607807 (2013).
L. V. Avdeev and O. V. Tarasov, “The three loop beta function in the N = 1, N = 2, N = 4 supersymmetric Yang-Mills theories,” Phys. Lett. B 112, 356 (1982).
I. Jack, D. R. T. Jones, and C. G. North, “N=1 supersymmetry and the three loop anomalous dimension for the chiral superfield,” Nucl. Phys. B 473, 308 (1996).
W. Siegel, “Inconsistency of supersymmetric dimensional regularization,” Phys. Lett. B 94, 37 (1980).
L. V. Avdeev and A. A. Vladimirov, “Dimensional regularization and supersymmetry,” Nucl. Phys. B 219, 262 (1983).
A. A. Slavnov, “Invariant regularization of nonlinear chiral theories,” Nucl. Phys. B 31, 301–315 (1971).
V. K. Krivoshchekov, “Invariant regularizations for supersymmetric gauge theories,” Theor. Math. Phys. 36, 745 (1978).
P. C. West, “Higher derivative regulation of supersymmetric theories,” Nucl. Phys. B 268, 113 (1986).
V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Beta function in supersymmetric gauge theories: instantons versus traditional approach,” Phys. Lett. B 166, 329 (1986).
K. V. Stepanyantz, “Derivation of the exact NSVZ β‑function in N = 1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams,” Nucl. Phys. B 852, 71 (2011).
K. Stepanyantz, “The all-loop perturbative derivation of the NSVZ β-function and the NSVZ scheme in the non-abelian case by summing singular contributions,” Eur. Phys. J. C 80, 911 (2020).
A. L. Kataev and K. V. Stepanyantz, “NSVZ Scheme with the higher derivative regularization for 𝒩 = 1 SQED,” Nucl. Phys. B 875, 459 (2013).
J. A. Campbell and A. C. Hearn, “Symbolic analysis of Feynman diagrams by computer,” J. Comput. Phys. 5, 280 (1970).
T. Kreuzberger, W. Kummer, and M. Schweda, “SUSYCAL: a program for symbolic computations in supersymmetric theories,” Comput. Phys. Commun. 58, 89–104 (1990).
A. F. Ferrari, “SusyMath: a Mathematica package for quantum superfield calculations,” Comput. Phys. Commun. 176, 334–346 (2007).
I. Shirokov, “Computer algebra calculations in supersymmetric electrodynamics,” Programming and Computer Software (in press). arXiv:2209.05295 [hep-th].
I. E. Shirokov and K. V. Stepanyantz, “The three-loop anomalous dimension and the four-loop -function for SQED regularized by higher derivatives,” J. High Energy Phys. 2204, 108 (2022).
M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Exact Gell–Mann-Low function in supersymmetric electrodynamics,” Phys. Lett. B. 166, 334 (1986).
S. S. Aleshin, I. S. Durandina, D. S. Kolupaev, D. S. Korneev, M. D. Kuzmichev, N. P. Meshcheriakov, S. V. Novgorodtsev, I. A. Petrov, V. V. Shatalova, I. E. Shirokov, V. Y. Shirokova, and K. V. Stepanyantz, “Three-loop verification of a new algorithm for the calculation of a β-function in supersymmetric theories regularized by higher derivatives for the case of SQED,” Nucl. Phys. B 956, 115020 (2020).
J. L. Rosner, “Higher-order contributions to the divergent part of Z(3) in a model quantum electrodynamics,” Ann. Phys. 44, 11 (1967).
A. L. Kataev and K. V. Stepanyantz, “Scheme independent consequence of the NSVZ relation for N = 1 SQED with N f flavors,” Phys. Lett. B 730, 184 (2014).
ACKNOWLEDGMENTS
The author expresses his gratitude to K.V. Stepanyantz for his significant help during this study, as well as for careful reading of the work and useful comments.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declares that he has no conflicts of interest.
Rights and permissions
About this article
Cite this article
Shirokov, I.E. Multiloop Calculations in 𝒩 = 1 SQED with Nf Flavours Regularized by Higher Derivatives. Phys. Part. Nuclei Lett. 20, 268–271 (2023). https://doi.org/10.1134/S1547477123030639
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1547477123030639