Dynamical chiral symmetry breaking on the light front. II. The Nambu-Jona-Lasinio model - art. no. 105016

An investigation of dynamical chiral symmetry breaking on the light front i s made in the Nambu-Jona-Lasinio model with one flavor and N colors. The an alysis of the model suffers from extraordinary complexity due to the existe nce of a "fermionic constraint," i.e., a constraint equation for the bad sp inor component. However, to solve this constraint is of special importance. In classical theory, we can exactly solve it and then explicitly check the property of "light-front chiral transformation." In quantum theory, we int roduce a bilocal formulation to solve the fermionic constraint by the 1/N e xpansion. Systematic 1/N expansion of the fermion bilocal operator is reali zed by the boson expansion method. The leading (bilocal) fermionic constrai nt becomes a gap equation for a chiral condensate and thus if we choose a n ontrivial solution of the gap equation, we are in the broken phase. As a re sult of the nonzero chiral condensate, we find an unusual chiral transforma tion of fields and nonvanishing of the light-front chiral charge. A leading -order eigenvalue equation for a single bosonic state is equivalent to a le ading-order fermion-antifermion bound-state equation. We analytically solve it for scalar and pseudoscalar mesons and obtain their light-cone wave fun ctions and masses. All of the results are entirely consistent with those of our previous analysis on the chiral Yukawa model.