Critical Scaling and a Dynamical Higgs Boson

In a quantum electrodynamics theory that is realized by critical scaling and anomalous dimensions, the action is not chiral invariant and there are no dynamical Goldstone or Higgs boson bound states. In the mean-field approximation to a chiral invariant four-fermion theory the associated mean-field sector action is not chiral invariant either and it also possesses no dynamical bound states, with Goldstone and Higgs bosons instead being generated by an accompanying four-fermion residual interaction. In this paper we show that if a critical scaling electrodynamics in which the dimension $d_{\theta}$ of $\bar{\psi}\psi$ is reduced from three to two is augmented with a four-fermion interaction, precisely because it possesses no dynamical bound states the electrodynamic sector can be reinterpreted as a mean-field approximation to a larger theory that is chiral symmetric. And with $d_{\theta}=2$ we show in this larger theory there is a residual interaction that then does generate dynamical Goldstone and Higgs bosons in scattering amplitudes that are completely finite. While the dynamically generated Goldstone boson is massless, the dynamically induced Higgs boson is found to be a narrow resonance just above threshold, with its width being a diagnostic that could potentially enable one to distinguish between a dynamical Higgs boson and an elementary one.