Cross section and effective potential in asymptotically free scalar field theories

Abstract

In an effort to understand the physical implications of the newly discovered nontrivial directions in scalar field theory, we compute lowest order scattering amplitudes, cross sections, and the one-loop effective potential. To lowest order, the primary effect of the nonpolynomial nature of the theories is a renormalization of the field. The high-energy scaling of the $\stackrel{\ensuremath{\rightarrow}}{2}2$ cross section is studied and found to differ significantly from that of pure ${\ensuremath{\varphi}}^{4}$ theory. From the one-loop effective potential we determine that in some cases radiative corrections destroy classical symmetry breaking, resulting in a phase boundary between symmetry broken and unbroken theories. No radiatively induced symmetry breaking is observed.