Dynamical Chiral Symmetry Breaking on the Light Front I. DLCQ Approach

TL;DR

This paper investigates dynamical chiral symmetry breaking on the light front using DLCQ in a chiral Yukawa model, revealing how nonperturbative solutions lead to condensates and mass generation.

Contribution

It demonstrates that the zero-mode constraint acts as a gap equation, enabling nonzero condensates and clarifying chiral transformation properties in light-front formalism.

Findings

Nonperturbative zero-mode solutions develop condensates

Masses of scalar and pseudoscalar bosons are calculated

PCAC relation and Q_5 nonconservation are derived

Abstract

Dynamical chiral symmetry breaking in the DLCQ method is investigated in detail using a chiral Yukawa model closely related to the Nambu-Jona-Lasinio model. By classically solving three constraints characteristic of the light-front formalism, we show that the chiral transformation defined on the light front is equivalent to the usual one when bare mass is absent. A quantum analysis demonstrates that a nonperturbative mean-field solution to the ``zero-mode constraint'' for a scalar boson (sigma) can develop a nonzero condensate while a perturbative solution cannot. This description is due to our identification of the ``zero-mode constraint'' with the gap equation. The mean-field calculation clarifies unusual chiral transformation properties of fermionic field, which resolves a seemingly inconsistency between triviality of the null-plane chiral charge Q_5|0>=0 and nonzero condensate. We also calculate masses of scalar and pseudoscalar bosons for both symmetric and broken phases, and eventually derive the PCAC relation and nonconservation of Q_5 in the broken phase.