Dynamical chiral symmetry breaking on the light front: DLCQ approach - art. no. 045009

Dynamical chiral symmetry breaking in the discretized light-cone quantizati on method is investigated in detail using a chiral Yukawa model closely rel ated to the Nambu-Jona-Lasinio model. By classically solving three constrai nts characteristic of the light-front formalism, we show that the chiral tr ansformation defined on the light front is equivalent to the usual one when the bare mass is absent. A quantum analysis demonstrates that a nonperturb ative mean-field solution to the "zero-mode constraint'' for a scalar boson a can develop a nonzero condensate [sigma] = -(lambda/N)[<(Psi)over bar>Ps i] not equal 0 while a perturbative solution cannot. This description is du e to our identification of the "zero-mode constraint" with the gap equation . The mean-field calculation clarifies unusual chiral transformation proper ties of the fermionic field, which resolves a seeming inconsistency between the triviality of the null-plane chiral charge Q(5)(LF)\0] = 0 and the non zero condensate [<(Psi)over bar>Psi] not equal 0. We also calculate masses of scalar and pseudoscalar bosons for both symmetric and broken phases, and eventually derive the relation of partial conservation of axial vector cur rent and nonconservation of Q(5)(LF) in the broken phase.