Dynamical Chiral Symmetry Breaking on the Light Front.II. The Nambu--Jona-Lasinio Model

Abstract

An investigation of dynamical chiral symmetry breaking on the light front is made in the Nambu--Jona-Lasinio model with one flavor and N colors. Analysis of the model suffers from extraordinary complexity due to the existence of a "fermionic constraint," i.e., a constraint equation for the bad spinor 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 introduce a bilocal formulation to solve the fermionic constraint by the 1/N expansion. Systematic 1/N expansion of the fermion bilocal operator is realized by the boson expansion method. The leading (bilocal) fermionic constraint becomes a gap equation for a chiral condensate and thus if we choose a nontrivial solution of the gap equation, we are in the broken phase. As a result of the nonzero chiral condensate, we find unusual chiral transformation of fields and nonvanishing of the light-front chiral charge. A leading order eigenvalue equation for a single bosonic state is equivalent to a leading order fermion-antifermion bound-state equation. We analytically solve it for scalar and pseudoscalar mesons and obtain their light-cone wavefunctions and masses. All of the results are entirely consistent with those of our previous analysis on the chiral Yukawa model.

23 pages, REVTEX, the version to be published in Phys.Rev.D; Some clarifications in discussion of the LC wavefunctions added

References in corpus (2)

• NJL model on the light cone and pion structure function
• Dynamical Chiral Symmetry Breaking on the Light Front I. DLCQ Approach

Cited by in corpus (9)

• Heavy Quarkonium in a Holographic Basis
• Transverse lattice calculation of the pion light-cone wavefunctions
• Statistical Physics and Light-Front Quantization
• Hadronic structure on the light-front VIII. Light scalar and vector mesons
• Hadronic structure on the light-front VII. Pions and kaons and their partonic distributions
• Chiral Symmetry in Light-front QCD
• Light Mesons on the Light Front
• Vector Mesons on the Light Front
• Different scenarios of dynamical chiral symmetry breaking in the interacting instanton liquid model via flavor symmetry breaking