Quantum Field Theory in the Limit x << 1

TL;DR

This paper investigates the high momentum behavior of quantum field theories with cubic interactions in the limit x << 1, using renormalization group techniques, and derives asymptotic scattering amplitudes consistent with Regge theory.

Contribution

It introduces a matrix renormalization approach for theories with multiple fields and derives explicit Regge trajectories in the asymptotic limit.

Findings

Asymptotic scaling forms match Regge theory predictions.

Matrix renormalization is necessary for multi-field interactions.

Explicit Regge trajectories are calculated for scalar theories.

Abstract

The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions involving more than one field where it is found that a matrix renormalization is necessary. Asymptotic scaling forms, in agreement with Regge theory, are derived for the elastic two-particle scattering amplitude and verified in one-loop renormalization group improved perturbation theory, corresponding to the summation of leading logs to all orders. We give explicit forms for the Regge trajectories of different scalar theories in this approximation and determine the signatures.