Finiteness of the two-loop matter contribution to the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives

Abstract

For a general renormalizable $\mathcal{N}=1$ supersymmetric gauge theory with a simple gauge group we verify the ultraviolet (UV) finiteness of the two-loop matter contribution to the triple gauge-ghost vertices. These vertices have one leg of the quantum gauge superfield and two legs corresponding to the Faddeev--Popov ghost and antighost. By an explicit calculation made with the help of the higher covariant derivative regularization we demonstrate that the sum of the corresponding two-loop supergraphs containing a matter loop is not UV divergent in the case of using a general $\xi$-gauge. In the considered approximation this result confirms the recently proved theorem that the triple gauge-ghost vertices are UV finite in all orders, which is an important ingredient of the all-loop perturbative derivation of the Novikov-Shifman-Vainshtein-Zakharov relation.

17 pages, 5 figures, version accepted for publication in Physical Review D

References in corpus (16)

• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• 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
• The higher derivative regularization and quantum corrections in $\mathcal{N}=2$ supersymmetric theories
• The NSVZ beta-function and the Schwinger-Dyson equations for N=1 SQED with N_f flavors, regularized by higher derivatives
• Derivation of the exact expression for the D function in N=1 SQCD
• New form of the NSVZ relation at the two-loop level
• One-loop polarization operator of the quantum gauge superfield for $\mathcal{N}=1$ SYM regularized by higher derivatives
• On-shell renormalization scheme for $\mathcal{N}=1$ SQED and the NSVZ relation
• 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
• One-loop effective potential in the non-local supersymmetric gauge theory
• On supersymmetric gauge theories with higher derivatives and nonlocal terms in the matter sector
• On the one-loop effective potential in nonlocal supersymmetric theories

Cited by in corpus (6)

• The NSVZ relations for $\mathcal{N}=1$ supersymmetric theories with multiple gauge couplings
• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• 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
• Quantum properties of gauge theories with extended supersymmetry formulated in $\mathcal{N}=1$ superspace
• A condition for the reduction of couplings in the $P=\frac{1}{3}Q$ supersymmetric theories