Infrared Divergences in $e^{+}e^{-}\rightarrow 2\; jets$ in the Light Front Coherent State Formalism

TL;DR

This paper demonstrates that using coherent states in light front QCD calculations effectively cancels infrared divergences in the $e^{+}e^{-} o 2$ jets process at order $g^2$, improving the understanding of IR issues in this framework.

Contribution

It introduces a coherent state basis approach in light front Hamiltonian perturbation theory to cancel IR divergences in QCD scattering processes.

Findings

IR divergences cancel when using coherent states instead of Fock states

Explicit calculation shows divergence cancellation at order $g^2$

Method improves IR divergence handling in light front QCD

Abstract

We study infrared (IR) divergences in light front quantum chromodynamics using a coherent state basis in light front time-ordered Hamiltonian perturbation theory. In computation of the S-matrix elements in Hamiltonian formalism, the IR divergences appear in the form of vanishing energy denominators. We consider the process $e^{+}e^{-}\rightarrow 2\; jets$ at $\mathcal{O}(g^{2})$ in strong coupling, construct the coherent state representing the outgoing particles, and explicitly show that the `true' IR divergences cancel to this order when the matrix elements are calculated between coherent states instead of Fock states.