Radiative Corrections as the Origin of Spontaneous Symmetry Breaking

TLDR

The simplest model exhibiting radiative‑induced symmetry breaking is massless scalar electrodynamics, where the scalar sector’s symmetry exceeds that of the full Lagrangian. The study investigates whether radiative corrections can trigger spontaneous symmetry breaking in theories whose tree‑level analysis shows no such breaking, and outlines how to apply the method in those cases. The authors compute the scalar‑to‑vector mass ratio as a power series in the electromagnetic coupling and show that the method extends to theories where tree‑level symmetry breaking is suggested but its details remain unclear. For small couplings the theory behaves like an Abelian Higgs model, exhibiting spontaneous symmetry breaking that yields massive vector and scalar mesons, with the scalar‑to‑vector mass ratio given by \((3/2\pi)(e^{2}/4\pi)\), and analogous qualitative results are obtained for non‑Abelian gauge theories.

Abstract

We investigate the possibility that radiative corrections may produce spontaneous symmetry breakdown in theories for which the semiclassical (tree) approximation does not indicate such breakdown. The simplest model in which this phenomenon occurs is the electrodynamics of massless scalar mesons. We find (for small coupling constants) that this theory more closely resembles the theory with an imaginary mass (the Abelian Higgs model) than one with a positive mass; spontaneous symmetry breaking occurs, and the theory becomes a theory of a massive vector meson and a massive scalar meson. The scalar-to-vector mass ratio is computable as a power series in $e$, the electromagnetic coupling constant. We find, to lowest order, $\frac{{m}^{2}(S)}{{m}^{2}(V)}=(\frac{3}{2\ensuremath{\pi}})(\frac{{e}^{2}}{4\ensuremath{\pi}})$. We extend our analysis to non-Abelian gauge theories, and find qualitatively similar results. Our methods are also applicable to theories in which the tree approximation indicates the occurrence of spontaneous symmetry breakdown, but does not give complete information about its character. (This typically occurs when the scalar-meson part of the Lagrangian admits a greater symmetry group than the total Lagrangian.) We indicate how to use our methods in these cases.