1Ncexpansion for baryons

A systematic expansion in $\frac{1}{N_c}$ is constructed for baryons in QCD. Predictions of the $\frac{1}{N_c}$ expansion at leading and subleading order for baryon axial vector current coupling constant ratios such as $\frac{F}{D}$, baryon masses, and magnetic moments are derived. The baryon sector of QCD has a light quark spin-flavor symmetry at leading order in $\frac{1}{N_c}$. The formalism of induced representations for contracted Lie algebras is introduced to explain the consequences of this symmetry. Relations are first derived for the case of two quark flavors. The generalization of the large $N_c$ expansion to three flavors is subtle and is treated using several complementary methods. The $\frac{1}{N_c}$ expansion severely restricts the form of SU(3) breaking in the baryon sector. Extrapolation of the large $N_c$ results to $N_c=3\mathrm{}$ permits a quantitative comparison with experimental data. Deviations of the measured quantities from exact spin-flavor symmetry predictions are accurately described by the subleading $\frac{1}{N_c}$ corrections. Implications of the $\frac{1}{N_c}$ expansion for baryon chiral perturbation theory are discussed.