Gauge invariance of the vector meson mass in the Coleman-Weinberg model

We revisit the problem of gauge invariance in Coleman-Weinberg model which a $U(1)$ symmetry is driven spontaneously broken by radiative corrections. It was noticed previous work that masses this are not invariant at one-loop order. In our analysis, we use dressed propagators scalars include resummation self-energy correction to tree-level propagator. calculate vector meson using these propagators. find pole mass calculated propagator vacuum determined effective potential with daisy diagrams.