Cancellation of Infrared Divergences in $e^{+}e^{-}\rightarrow q\bar{q}g$ in Light Front Coherent State Formalism

TL;DR

This paper demonstrates that infrared divergences in the process $e^{+}e^{-} ightarrow qar{q}g$ within Light Front QCD are canceled at the amplitude level by employing a coherent state basis, providing a new approach to IR divergence management.

Contribution

The paper introduces a coherent state formalism for Light Front QCD that explicitly cancels infrared divergences at the amplitude level for the process $e^{+}e^{-} ightarrow qar{q}g$.

Findings

IR divergences are canceled using the coherent state basis.

Constructed the coherent state formalism for LFQCD.

Verified divergence cancellation at $ ext{O}(g^3)$ in light-cone-time-ordered perturbation theory.

Abstract

We address the issue of cancellation of infrared (IR) divergences at the amplitude level in Light Front Quantum Chromodynamics (LFQCD) using the coherent state formalism. We consider the process $e^{+}e^{-}\rightarrow q\bar{q}g$ upto $\mathcal{O}(g^3)$ in light-cone-time-ordered Hamiltonian perturbation theory and show that IR divergences in S-matrix elements appear due to vanishing energy denominators. We construct the coherent state formalism for LFQCD and explicitly show that these divergences are cancelled when a coherent state basis is used for calculating the S-matrix elements.