Infrared divergence on the light-front and dynamical Higgs mechanism

TL;DR

This paper investigates the dynamical Higgs mechanism on the light-front in a (1+1)D model, addressing infrared divergence issues by introducing a cutoff, and demonstrates that gauge bosons acquire mass dynamically.

Contribution

It highlights the importance of handling infrared divergences beyond zero modes for studying dynamical symmetry breaking on the light-front.

Findings

Infrared divergence caused by internal momentum is crucial for LF symmetry breaking.

Introducing a non-Lorentz invariant infrared cutoff avoids divergence issues.

Gauge bosons gain mass dynamically on the light-front.

Abstract

Dynamical Higgs mechanism on the light-front (LF) is studied using a (1+1) dimensional model, with emphasis on the infrared divergence problem. The consideration of the zero mode $ k^+ = 0 $ is not sufficient for investigating dynamical symmetry breaking on the LF. It also needs to treat properly an infrared divergence caused by internal momentum $ p^+ \to 0 ~ (p^+ \neq 0) $ in the continuum limit. In order to avoid the divergence, we introduce an infrared cutoff function $ F_{\rm IR} (p, \Lambda) $ which is not Lorentz invariant. It is then shown that the gauge boson obtains mass dynamically on the LF.