The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation

Abstract

We calculate the Adler $D$-function for $\mathcal{N}=1$ SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the $D$-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for $\mathcal{N}=1$ SQCD is found in this scheme to the order $O({\alpha }_s^2)$. The problem of scheme-dependence of the $D$-function and the NSVZ-like equation is briefly discussed.

25 pages, 2 figures; the version accepted for publication in Nuclear Physics B

References in corpus (13)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Muon g-2 Theory: the Hadronic Part
• 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
• 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
• One-loop polarization operator of the quantum gauge superfield for $\mathcal{N}=1$ SYM regularized by higher derivatives
• Factorization of integrals defining the two-loop beta-function for the general renormalizable N=1 SYM theory, regularized by the higher covariant derivatives, into integrals of double total derivatives
• NSVZ-like scheme for the photino mass in softly broken $\mathcal{N}=1$ SQED regularized by higher derivatives
• Riemann $\zeta (3)$- terms in perturbative QED series, conformal symmetry and the analogies with structures of multiloop effects in N=4 supersymmetric Yang-Mills theory

Cited by in corpus (25)

• New form of the NSVZ relation at the two-loop level
• The all-loop perturbative derivation of the NSVZ $\beta$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions
• New form of the exact NSVZ $\beta$-function: the three-loop verification for terms containing Yukawa couplings
• A class of the NSVZ renormalization schemes for $\mathcal{N}=1$ SQED
• 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
• Two-loop renormalization of the Faddeev--Popov ghosts in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• The NSVZ $\beta$-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities
• Two-Loop Cutoff Renormalization of 4-D Yang-Mills Effective Action
• 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
• Two-loop renormalisation of gauge theories in $4D$ Implicit Regularisation and connections to dimensional methods
• Explicit Cutoff Regularization in Coordinate Representation
• Three-loop $\beta$-functions and two-loop anomalous dimensions for MSSM regularized by higher covariant derivatives in an arbitrary supersymmetric subtraction scheme
• Supersymmetric Tools in Yang-Mills Theories at Strong Coupling: the Beginning of a Long Journey
• Exact $\beta$-functions for $\mathcal{N}=1$ supersymmetric theories finite in the lowest loops
• Finiteness of the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories: the two-loop verification
• Structure of quantum corrections in $\mathcal{N}=1$ supersymmetric gauge theories
• Non-renormalizable theories and finite formulation of QFT
• Exact results in explicit three-loop calculations using higher derivatives for $\mathcal{N}=1$ SQCD