|
This article is cited in 28 scientific papers (total in 28 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.
Received: 25.11.2015
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
Linking options:
https://www.mathnet.ru/eng/jetpl4836 https://www.mathnet.ru/eng/jetpl/v103/i2/p83
|
Statistics & downloads: |
Abstract page: | 268 | Full-text PDF : | 34 | References: | 40 | First page: | 14 |
|