Chiral Symmetry and the Constituent Quark Model: A Null-Plane Point of View

Abstract

In order to clarify the connection between {\it current} and {\it constituent} quarks (of u,d,s flavors), several authors have used the lightlike chiral $SU(3)\otimes SU(3)$ algebra as a central concept. This literature is reviewed here with the goal of offering an introduction to the subject within a convenient, unified framework. It is shown that the null-plane Hamiltonian for free massive fermions is chirally symmetric, provided only that the particles have equal masses ($SU(3)$ limit). In the free quark model, hadrons can be classified by a chiral $SU(3)\otimes SU(3)$ algebra, the generators of which are current lightlike charges. Naturally, QCD interactions break chiral symmetry, and the axial nonsinglet charges are not conserved. This remains true in the 'chiral limit' (zero quark masses), signalling the spontaneous breakdown of chiral symmetry. The actual generators of the $SU(3)\otimes SU(3)$ classification of physical hadrons are obtained from the current charges by means of a unitary transformation. Under this transformation, quarks of the same flavor and of opposite helicities mix to form a constituent quark. The functional form of this unitary transformation can be strongly constrained on the basis of symmetry arguments. This analysis is potentially rich in phenomenological applications, and a few are presented here. The author offers also some new theoretical results. No prior knowledge of light-cone formalism on the part of the reader is assumed.