Asymptotic Freedom of V-A Fermi Interaction

TL;DR

This paper demonstrates that the V-A Fermi interaction's scattering amplitude decreases logarithmically at high energies, restoring unitarity through a novel application of renormalization group methods to a non-renormalizable theory.

Contribution

It applies a previously developed summation method for asymptotics to the V-A Fermi interaction, deriving an RG equation that sums leading logarithms in a non-renormalizable context.

Findings

Amplitude decreases logarithmically with energy at high energies.

Restores unitarity in the V-A Fermi interaction.

Provides a new approach to non-renormalizable theories.

Abstract

We consider the V-A Fermi interaction and apply an earlier developed method for summing up the leading asymptotics for scattering amplitudes in non-renormalizable theories. We consider the amplitude of fermion-antifermion scattering and derive the corresponding RG equation that sums the leading logarithmic contributions just like in renormalizable models. Numerical solution of this equation in the asymptotic regime $s\sim t\sim u \sim E^2 \to \infty$ leads to amplitude logarithmically decreasing with energy, thus restoring the unitarity violated at the tree level.