HADRONIC INTERACTIONS IN LARGE N_c QCD: STUDIES OF EXCITED BARYON DECAYS AND SCATTERING RELATIONS
Dakin, Daniel C.
Cohen, Thomas D
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Decays and scattering events are two of the principal ways to learn about particle physics. Decays, in which a particle spontaneously disintegrates and we examine the debris, are quantified by a decay width. The decay of a resonance state provides information about the structure of the state and the interaction between its components. In particular, we can learn about the dynamics of quarks and gluons by studying the decay of hadrons. Scattering, in which particles are directed towards each other and interact, are quantified by partial-wave amplitudes. These amplitudes give us information about the interaction between the scattered particles. In principle, all of hadronic physics follows from quantum chromodynamics (QCD), which describes the interactions of quarks and gluons. However, the techniques of perturbation theory are not applicable to QCD at low energy because the strong coupling constant (the natural choice for the expansion parameter) is large at the energy scale of hadronic physics. A powerful model-independent method is the 1/N_c expansion in which the number of quark color degrees of freedom (N_c) is treated as a large number. This thesis presents the application of the 1/N_c expansion to the calculation of physical observables for excited baryons, pion-nucleon scattering, and pion photoproduction. The framework of the contracted SU(4) group that emerges in large N_c QCD is applied to the study of excited baryon decays. The N_c power scaling of the excited baryon's decay width depends on the symmetry of its spin-flavor wavefunction. The scaling with N_c for different symmetries is discussed in the context of a quark-shell model that permits mixing of different symmetry types. The subtle issues concerning the legitimacy of applying the contracted SU(4) group theory to excited baryons are discussed. The contracted SU(4) spin-flavor symmetry severely restricts the angular momentum and isospin dependence of partial-wave amplitudes. The consequences of this restriction on pion-nucleon scattering and pion photoproduction are discussed. In particular, model-independent linear relations among different hadronic scattering amplitudes holding to leading order in 1/N_c are obtained and compared with experimental data. The group-theoretic structure of large N_c QCD allows for a systematic expansion of scattering amplitudes in powers of 1/N_c which leads to model-independent relations holding to next-to-leading order in 1/N_c. These relations are derived and shown to compare more favorably with experiments to the extent expected for the 1/N_c expansion.