# HADRONIC INTERACTIONS IN LARGE N_c QCD: STUDIES OF EXCITED BARYON DECAYS AND SCATTERING RELATIONS

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2005-07-19##### Author

Dakin, Daniel C.

##### Advisor

Cohen, Thomas D

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Show full item record##### Abstract

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.

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