Abstract
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.
Highlights
One of the subtle problems in quantum field theory (QFT) is the gauge invariance of physical quantities
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
It is generally believed that physical quantities, such as the S-matrix elements, the physical masses, the energy density of a physical state, and the decay rate of a false vacuum, are gauge invariant the quantum field theory can be quantized in an arbitrary gauge
Summary
One of the subtle problems in quantum field theory (QFT) is the gauge invariance of physical quantities. The minimum value of the effective potential is a physical quantity Another interesting observation is that the pole masses in the CW model are not gauge invariant at one-loop order, but the ratio of the pole masses of the scalar meson and the vector meson are gauge invariant [4]. We show that the pole mass of the vector meson in the CW model is gauge invariant at one-loop order after including the daisy resummation effects in the propagator and in the effective potential. This result is the novel contribution of the present article. We give some details of our calculation in Appendixes A, B, and C
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