There have been a lot of similar questions about this topic on this website, such as Gauge invariance is just a redundancy. Why is massive abelian gauge field renormalizable but massive non-abelian gauge field nonrenormalizable?. We know the propagator of massive vector field is like
\begin{equation}
-i\frac{g_{\mu \nu}-k_{\mu}k_{\nu}/m^{2}}{k^{2}-m^{2}}.
\end{equation}
And we know the propagator behaves as $O(1)$ at high momentum, so the power counting law breaks down and the theory is non-renormalizable.
However, I wonder, can we mimic what we do for $U(1)$ field: there we introduce gauge fixing by Faddeev-Popov method, then we get something like
\begin{equation}
\frac{-i}{k^{2}-m^{2}}(g_{\mu \nu}-(1-\xi)\frac{k_{\mu}k_{\nu}}{k^{2}-\xi m^{2}})
\end{equation}
(see this notes (62), but here I am NOT talking about Higgs mechanism, I just cite the calculating result of gauge fixing for massive boson field.)
By letting $\xi$ equal 1, we get
\begin{equation}
\frac{-ig_{\mu \nu}}{k^{2}-m^{2}}.
\end{equation}
It seems that we can solve the $O(1)$ difficulties at high momentum and it is renormalizable for the massive non-abelian gauge field.
I wonder if this idea makes any sense?
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