Cross Section and Effective Potential in Asymptotically Free Scalar Field Theories

TL;DR

This paper investigates asymptotically free scalar field theories by calculating scattering amplitudes, cross sections, and the effective potential, revealing how nonpolynomial interactions affect high-energy behavior and symmetry breaking.

Contribution

It introduces the computation of scattering amplitudes and effective potential in non-trivial scalar theories, highlighting effects of nonpolynomial interactions on renormalization and symmetry.

Findings

High-energy cross section scaling differs from pure phi^4 theory

Radiative corrections can eliminate classical symmetry breaking

No evidence of radiatively induced symmetry breaking observed

Abstract

In an effort to understand the physical implications of the newly discovered non-trivial directions in scalar field theory, we compute lowest order scattering amplitudes, cross sections, and the 1-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 2-->2 cross section is studied and found to differ significantly from that of pure phi^4 theory. From the 1-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.