Internal symmetries and bootstrap models

Abstract

Chapter 1 serves ms a brief introduction to the ideas which form the subject of this thesis, internal symmetry, bootstraps, duality and the quark model. In Chapters 2 and 3 we survey predictions for internal symmetries made from (^N)/D bootstraps and the duality hypothesis respectively. Both approaches predict a Lie group structure and predict the meson representations. In addition the duality equations imply that the baryons transform as two-quark composites. A phenomenological choice of a subset of the duality constraints can be made which has a physical three-quark solution. Symmetry breaking is discussed in both cases. In Chapter 4 we contrast the predictions surveyed in the previous two chapters. Duality requires exchange degeneracies among trajectories of different multiplet8 but these do not result from (^N)/D models. In the dual case the even-signature, isosinglet trajectories are identified with mixed f, f' states, degenerate with the W,Ѳ respectively, whereas bootstrap models always produce a high-lying singlet trajectory which is most naturally identified with the Pomeron. It is argued that these differences make it unlikely that dual models can be deduced in any simple way from the bootstrap hypothesis. An (^N)/D quark model with meson exchanges is examined in Chapter 5. With the assumption that the quark mass is much larger than the meson mass, a singlet meson trajectory is obtained which lies an order of magnitude above the octet trajectories. This result is unaltered if symmetry breaking of any order is allowed. These difficulties are not removed by treating the particle exchange forces as perturbations to a background term. It is concluded that these results together with the known difficulties of obtaining physical slopes and intercepts imply that this type of quark model should probably be discarded.