Functional Integration and High Energy Scattering of Particles with Anomalous Magnetic Moments in Quantum Field Theory

TL;DR

This paper uses functional integration to analyze high-energy pion-nucleon scattering with anomalous magnetic moments, deriving an eikonal amplitude that includes spin-flip effects and addresses renormalization issues at asymptotic energies.

Contribution

It introduces a novel application of functional integration to nonrenormalizable quantum field theory, deriving an eikonal representation for scattering amplitudes with anomalous magnetic moments.

Findings

Derived an eikonal form of the scattering amplitude at high energies.

Identified additional spin-flip terms due to anomalous magnetic moments.

Showed renormalization issues do not arise in the asymptotic limit.

Abstract

The functional integration method is used for studying the scattering of a scalar pion on nucleon with the anomalous magnetic moment in the framework of nonrenomalizable quantum field theory. In the asymptotic region s {\to} {\infty}, |t| << s the representation of eikonal type for the amplitude of pion-nucleon scattering is obtained. The anomalous magnetic moment leads to additional terms in the amplitude which describe the spin flips in the scattering process. It is shown that the renormalization problem does not arise in the asymptotic s {\to} {\infty} since the unrenomalized divergences disappear in this approximation. Coulomb interference is considered as an application.