Strings, quarks, diquarks, baryons, exotic mesons and glueballs
Conrad J. Burden · ANU Open Research (Australian National University) · 1982
The string model of hadron structure is studied, principally at the classical level. The Nielsen-Olesen vortex is taken as a prototype string and the problem of a semi-infinite static U(l) vortex terminating in a fixed monopole is considered. An attempt is made to calculate the flux lines at distances from the vortex greater than the ’penetration length'. The SU(3)/Z3 vortex ending in a monopole is also considered and the problem is shown to reduce to the same set of non-linear equations as the U(l) case provided certain criteria are met. A model is then considered in which hadrons are built up from infinitesimally thin relativistic Nambu strings. Strings meet three at a time, consistent with the idea that the strings are the strong coupling limit of SU(3)/Z3 vortices. They can also terminate at quarks or antiquarks described by Dirac fields restricted to the world line traced out by the string end. The Nambu string equation is solved for motion corresponding to rigid body rotation about the z-axis. One class of these solutions, the planar solutions, allows for new hadrons to be constructed from the above model. In particular, two types of exotic meson and one type of glueball, each of which have asymptotically straight ChewFrautschi plots can be built up. Possible baryon configurations consistent with the above model are examined. Chew-Frautschi plots are found for baryons containing a quark and a diquark at the extremities of a straight rigidly rotating string. Quantum numbers for the diquark field are obtained by adding those for two individual quark fields. The leading trajectory for the quark-diquark configuration is found to be energetically more favourable than previously established trajectories for the linear and Y-shaped baryon configurations. In order to describe more accurately the coupling of two quark fields at the string end to form a diquark field, two methods are suggested. The first method involves combining two restricted Dirac equations using a variant of the de Broglie fusion method. The resulting equation describing the spin 0 diquark is the KleinGordon equation restricted to the world line. However, the spin 1 diquark equation differs from the restricted Proca-de Broglie equation. Both the spin 0 and spin 1 equations are derivable from Lagrangians, so in principle there is nothing to prevent a rigorous treatment of the classical quark-diquark string baryon being carried out. It is also shown that Grassmann algebra valued quark fields can be incorporated within the fusion method. The second method involves the restriction of a free 16- component Duffin-Kemmer-Petiau field to a world line. The restricted field splits into a scalar and a vector part, but it is shown that these are not descriptions of spin 0 and spin 1 diquark fields.