Abstract
For the general renormalizable mathcal{N}=1 supersymmetric gauge theory we investigate renormalization of the Faddeev-Popov ghosts using the higher covariant derivative regularization. First, we find the two-loop anomalous dimension defined in terms of the bare coupling constant in the general ξ-gauge. It is demonstrated that for doing this calculation one should take into account that the quantum gauge superfield is renormalized in a nonlinear way. Next, we obtain the two-loop anomalous dimension of the Faddeev-Popov ghosts defined in terms of the renormalized coupling constant and examine its dependence on the subtraction scheme.
Highlights
For the β-function in the form of the geometric series
To obtain the NSVZ scheme with the higher derivative regularization one should include into the renormalization constants only powers of ln Λ/μ, where Λ is the dimensionful parameter of the regularized theory playing the role of the UV cut-off and μ is the renormalization scale
In this paper the two-loop anomalous dimension of the Faddeev-Popov ghosts is obtained for the general renormalizable N = 1 supersymmetric gauge theory, regularized by higher covariant derivatives
Summary
We will calculate the two-loop anomalous dimension of the Faddeev-Popov ghosts defined in terms of the bare couplings. The matter is that it is necessary to take into account the one-loop renormalization of this parameter, while in the two-loop diagrams in the case F (V ) = V with the considered accuracy it can be set to 0 together with the other similar parameters Having this in mind, we can construct the superdiagrams contributing to the two-point Green function of the Faddeev-Popov ghosts in the considered approximation. Note that the quintic vertices containing two external ghost legs and three legs of the quantum gauge superfield (which may arise due to the nonlinear form of the function F (V )) are not essential in the considered approximation In principle, they can appear in the two-loop diagrams, but the corresponding contributions to the two-loop ghost anomalous dimension vanish if we choose F (V ) = V.
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