Properties of the vacuum expectation values in $R_{\xi }$ and general gauge

We have investigated the renormalization group evolution and the perturbative expansion of the vacuum expectation value(VEV) of the Abelian Higgs model both in the $R_{\xi }$ and the general gauge which extrapolate between the Fermi and the $\overline{R_{\xi }}$ gauge. In the $R_{\xi }$ gauge, the gamma function of the VEV was different from that of the scalar field. On the contrary, the gamma function of the VEV was the same as that of the scalar field in general gauge. Both in the $R_{\xi }$ and $\overline{R_{\xi }}$ gauge, the two-loop VEVs have an IR divergence in the Landau gauge($\xi =0$) and these IR divergences do not occur when $\xi \ne 0$.