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

High Energy Physics - Phenomenology;High Energy Physics - Theory