A Dual Quark Model with Spin

Citation

Ellis, Stephen Dean (1971) A Dual Quark Model with Spin. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/G3AD-N729. https://resolver.caltech.edu/CaltechTHESIS:04202018-125942170

Abstract

A dual quark model is developed from the usual Veneziano model by explicitly including the Dirac spin of the quarks. Resonances appear without the parity doubling and new ghosts present in previous models with spin. This is accomplished by eliminating the contributions of the negative parity components (MacDowell-twins) of the spin quarks 1/2 through the introduction of fixed J-plane cuts. The resonances belong to an SU₆ symmetric spectrum identical, on the leading trajectory, with that of the usual static symmetrical quark model. All resonances couple via SU_6w x O_2Lz symmetric vertices and the model factorizes with essentially the same degeneracy as the usual Veneziano model. As a consequence of requiring these two features the model acquires further new structure which is studied in detail in terms of the asymptotic behavior of the model. This new structure leads to unavoidable "background" contributions to the imaginary parts of the amplitudes not present in previous dual models. This situation is examined and interpreted in the language of Finite Energy Sum Rules.

In order to test the basic features of the model explicit calculations are made for the case of pion-nucleon scattering in the Regge limit. To make the numerical work easier a somewhat simplified version of the model is used. Although the results of the calculations are suggestive of reasonable J-plane structure for the various amplitudes, i.e., the location of Regge pole-fixed cut interference is reasonable from the standpoint of the data, the overall kinematic behavior of the amplitudes is definitely not compatible with what is measured. However, it is noted that this kinematic behavior depends strongly on those details of the model which were simplified in the present study. If such models are to be unambiguously and successfully tested against data, future studies must treat these details more completely and realistically, including both unitarity and symmetry breaking effects.

Thesis Files