One-loop calculation of the $\beta$-function in the modified formulation of the Yang–Mills theory

In the one-loop approximation for the modified Yang–Mills theory, we calculate contributions to the two- and three-point Green's functions of the gauge field $A_\mu$, to the Green's function of the anticommuting fields $e$ and $b$, and to the vertex function $\Gamma_{Aeb}$. We find the renormalization constants $Z_1$ and $Z_2$ and the corresponding constants $\overline Z_1$ and $\overline Z_2$ for the anticommuting fields and show that they satisfy the same equation as in the standard Yang–Mills theory. We demonstrate that the $\beta$-functions in the standard and modified theories coincide.