Bag Models of Hadrons

During the early development of the quark model the light hadrons were treated as bound states of quarks moving nonrelativistically in a confining potential. However, it became clear that the nonrelativistic treatment was wanting. Ordinarily, nonrelativistic systems have excitation energies that are small compared to the component masses. In mesons and baryons, however, these energies are comparable to the quark masses of these models. As quantum chromodynamics (QCD), the SU(3) gauge theory of interacting colored quarks and gluons, grew in acceptance, the need for a new approach became even more compelling. Although it was hoped that the hadron spectroscopy, structure, and interaction could ultimately be deduced from first principles, the complexities of QeD compelled us to resort to approximate models, such as the Massachusetts Institute of Technology (MIT) bag model (1), the Stanford Linear Accelerator Center (SLAC) bag model (2), and the soliton bag model (3). These bag models attempt to incorporate three desirable features of hadronic structure that were omitted from the earlier nonrelativistic QCD approach: (a) the QCD property of short-distance asymptotic freedom, which on the one hand permits the use of perturbation theory in describing the short-distance interaction of quarks and gluons, and on the other hand forbids the propagation of colored fields to large distances; (b) the introduction of gluons as hadronic constituents and the mediators ofthe short-distance interaction between quarks; and (c) a relativistic and gauge-invariant framework. A variant of the MIT bag model, the hybrid chiral bag model (4), attempts to incorporate chiral symmetry, a feature of QCD missing also in the other bag models. In this brief, critical review we describe the good and bad features of bag models with principal emphasis upon the more developed MIT model. The MIT model has enjoyed more popularity because of its simplicity. However, most of its successes and its drawbacks are undoubtedly shared by the other models. The plan of the review is as follows. In the remainder of the introduction we discuss the relationship between the bag models and QCD, describing the various models briefly. In Section 2 we describe the method for obtaining the light hadron spectrum in the MIT model and discuss problems associated with the cavity approximation. A variety of bag states are described in Section 3. Bag interactions in Section 4 include the important subject of electromagnetic structure as well as bag-bag interactions and, in particular, pion-bag interactions. Finally, in Section 5, we review recent attempts at describing the vacuum structure of QCD and its relationship to future developments of bag models. For a quick introduction the casual reader may want to read the introductory and concluding sections and Sections 2.1 to 2.3. We have not attempted to be complete and have omitted some significant developments in the interest of coherence and brevity. The purpose of this review is to provide an entree to the literature and a critical discussion of key difficulties. There are several summary lectures and reviews (5- 10).