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Asymptotic Freedom of V-A Fermi Interaction

A. T. Borlakov, D. I. Kazakov

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.

Asymptotic Freedom of V-A Fermi Interaction

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 leads to amplitude logarithmically decreasing with energy, thus restoring the unitarity violated at the tree level.
Paper Structure (4 sections, 21 equations, 4 figures)

This paper contains 4 sections, 21 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Fermi theory in spinor helicity formalism
  3. Numerical solution of RG equation in asymptotic regime
  4. Discussion

Figures (4)

  • Figure 1: The Feynman diagram for the fermion-antifermion scattering amplitude. All momenta are incoming.
  • Figure 2: The schematic form of the recurrence relation for the four-point function. The bubbles surrounded by the dotted lines denote the corresponding counter terms
  • Figure 3: The function $A(y)$ as a numerical solution of equation (\ref{['EqA']})
  • Figure 4: The differential cross-section in the SM and in Fermi theory as a function of $s$. The unitarity bound is also shown for reference.