The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction

Abstract

The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD in the $\overline{\mbox{DR}}$ scheme is calculated starting from the three-loop result recently obtained with the higher covariant derivative regularization. For this purpose, for the theory regularized by higher derivatives we find a subtraction scheme in which the Green functions coincide with the ones obtained with the dimensional reduction and the modified minimal subtraction prescription for the renormalization of the SQCD coupling constant and of the matter superfields. Also we calculate the $D$-function in the $\overline{\mbox{DR}}$ scheme for all renormalization constants (including the one for the electromagnetic coupling constant which appears due to the SQCD corrections). It is shown that the results do not satisfy the NSVZ-like equation relating the $D$-function to the anomalous dimension of the matter superfields. However, the NSVZ-like scheme can be constructed with the help of a properly tuned finite renormalization. It is also demonstrated that the three-loop $D$-function defined in terms of the bare couplings with the dimensional reduction does not satisfy the NSVZ-like equation for an arbitrary renormalization prescription. We also investigate a possibility to present the results in the form of the $\beta$-expansion and the scheme dependence of this expansion.

25 pages, 2 figures, 1 table, improved conclusion, version accepted for publication in JHEP

References in corpus (49)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• Naive nonabelianization and resummation of fermion bubble chains
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• Muon g-2 Theory: the Hadronic Part
• Scheme dependence and the NSVZ $\beta$-function
• $N=1$ supersymmetry and the three loop gauge beta function
• Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
• Corrections of order ${\alpha }_s^3$ to $R_{had}$ in pQCD with light gluinos
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• Testing non-perturbative strong interaction effects via the Adler function
• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• NSVZ scheme with the higher derivative regularization for N=1 SQED
• The connection between the DRED and NSVZ renormalisation schemes
• Three-loop $\beta$-function for N=1 supersymmetric electrodynamics, regularized by higher derivatives
• Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams
• Background field calculations and nonrenormalization theorems in 4d supersymmetric gauge theories and their low-dimensional descendants
• 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
• Generalization of the BLM procedure and its scales in any order of pQCD
• Lagrange Multipliers and Couplings in Supersymmetric Field Theory
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Precision Calculations in Supersymmetric Theories
• Calculation of two-loop beta-function for general N=1 supersymmetric Yang--Mills theory with the higher covariant derivative regularization
• Non-renormalization of the $V\bar{c}c$-vertices in $\mathcal{N}=1$ supersymmetric theories
• One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization
• Exact Adler Function in Supersymmetric QCD
• Manifestly N=2 supersymmetric regularization for N=2 supersymmetric field theories
• The higher derivative regularization and quantum corrections in $\mathcal{N}=2$ supersymmetric theories
• Three-loop NSVZ relation for terms quartic in the Yukawa couplings with the higher covariant derivative regularization
• The NSVZ beta-function and the Schwinger-Dyson equations for N=1 SQED with N_f flavors, regularized by higher derivatives
• The SUSY-QCD beta function to three loops
• 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
• New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
• One-loop polarization operator of the quantum gauge superfield for $\mathcal{N}=1$ SYM regularized by higher derivatives
• Precise measurement of $R_{\text{uds}}$ and $R$ between 1.84 and 3.72 GeV at the KEDR detector
• New form of the exact NSVZ $\beta$-function: the three-loop verification for terms containing Yukawa couplings
• Structure of three-loop contributions to the beta-function of N=1 SQED with N_f flavors, regularized by the dimensional reduction
• A class of the NSVZ renormalization schemes for $\mathcal{N}=1$ SQED
• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
• Two-loop renormalization of N=1 supersymmetric electrodynamics, 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
• Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules
• Exact renormalization of the photino mass in softly broken $\mathcal{N}=1$ SQED with $N_f$ flavors regularized by higher derivatives
• Setting the Renormalization Scale in pQCD: Comparisons of the Principle of Maximum Conformality with the Sequential Extended Brodsky-Lepage-Mackenzie Approach
• Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit
• On the BLM scale-fixing procedure, its generalizations and "genuine" higher order corrections
• The $\{\beta \}$-expansion formalism in perturbative QCD and its extension

Cited by in corpus (10)

• 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
• 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
• The higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories
• Ambiguities of the principle of maximum conformality procedure for hadron collider processes
• The $\overline{\mathrm{MS}}$-scheme ${\alpha }_s^5$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold $\{\beta \}$-expanded representation
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function