A class of the NSVZ renormalization schemes for $\mathcal{N}=1$ SQED

Abstract

For the $\mathcal{N}=1$ supersymmetric electrodynamics we investigate renormalization schemes in which the NSVZ equation relating the $\beta$-function to the anomalous dimension of the matter superfields is valid in all loops. We demonstrate that there is an infinite set of such schemes. They are related by finite renormalizations which form a group and are parameterized by one finite function and one arbitrary constant. This implies that the NSVZ $\beta$-function remains unbroken if the finite renormalization of the coupling constant is related to the finite renormalization of the matter superfields by a special equation derived in this paper. The arbitrary constant corresponds to the arbitrariness of choosing the renormalization point. The results are illustrated by explicit calculations in the three-loop approximation.

arXiv comment12 pages

References in corpus (18)

• Scheme dependence and the NSVZ $\beta$-function
• $N=1$ supersymmetry and the three loop gauge beta function
• NSVZ scheme with the higher derivative regularization for N=1 SQED
• The connection between the DRED and NSVZ renormalisation schemes
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams
• The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions
• Scheme independent consequence of the NSVZ relation for N=1 SQED with N_f flavors
• Lagrange Multipliers and Couplings in Supersymmetric Field Theory
• Precision Calculations in Supersymmetric Theories
• Non-renormalization of the $V\bar{c}c$-vertices in $\mathcal{N}=1$ supersymmetric theories
• Exact Adler Function in Supersymmetric QCD
• Three-loop NSVZ relation for terms quartic in the Yukawa couplings with the higher covariant derivative regularization
• The NSVZ scheme for $\mathcal{N}=1$ SQED with $N_f$ flavors, regularized by the dimensional reduction, in the three-loop approximation
• Derivation of the exact expression for the D function in N=1 SQCD
• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
• NSVZ-like scheme for the photino mass in softly broken $\mathcal{N}=1$ SQED regularized by higher derivatives
• Structure of quantum corrections in $\mathcal{N}=1$ supersymmetric gauge theories

Cited by in corpus (19)

• The all-loop perturbative derivation of the NSVZ $\beta$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions
• The $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives as an integral of double total derivatives
• Two-loop renormalization of the matter superfields and finiteness of $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• On-shell renormalization scheme for $\mathcal{N}=1$ SQED and the NSVZ relation
• The NSVZ relations for $\mathcal{N}=1$ supersymmetric theories with multiple gauge couplings
• The NSVZ $\beta$-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities
• Three-loop contribution of the Faddeev-Popov ghosts to the $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories and the NSVZ relation
• Three-loop verification of a new algorithm for the calculation of a $\beta$-function in supersymmetric theories regularized by higher derivatives for the case of $\mathcal{N}=1$ SQED
• The higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• Three-loop $\beta$-functions and two-loop anomalous dimensions for MSSM regularized by higher covariant derivatives in an arbitrary supersymmetric subtraction scheme
• Finiteness of the two-loop matter contribution to the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• Exact $\beta$-functions for $\mathcal{N}=1$ supersymmetric theories finite in the lowest loops
• Operator mixing in massless QCD-like theories and Poincare'-Dulac theorem
• Finiteness of the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories: the two-loop verification
• Riemann $\zeta (4)$ function contributions to $O\left({{\alpha }_s}^5\right)$ terms of Adler D-function and Bjorken polarized sum rule in $SU\left(N_c\right)$ QCD: results and consequences
• Quantum properties of gauge theories with extended supersymmetry formulated in $\mathcal{N}=1$ superspace
• Non-perturbative SQED beta function using functional renormalization group approach and the NSVZ exact beta function