Hyperfine Mass Splittings of Baryons Containing a Heavy Quark in Large N QCD

The hyperfine mass splittings of baryons containing a heavy quark are derived at leading order in large $N$ QCD. Hyperfine splittings either preserve or violate heavy quark spin symmetry. Previous work proves that the splittings which preserve heavy quark spin symmetry are proportional to ${\bf J}^2$ at order $1/N$, where $J$ is the angular momentum of the light degrees of freedom of the baryon. This work proves that the splittings which violate heavy quark spin symmetry are proportional to ${\bf J} \cdot {\bf S_Q}$ at order $1/(N m_Q)$ in the $1/N$ and $1/m_Q$ expansions.Comment: (8 pages, no figures, uses harvmac), UCSD/PTH 93-2

Baryon Masses in the 1/N Expansion

The masses of baryons and heavy quark baryons are studied analytically in an expansion in 1/N, SU(3) flavor symmetry breaking and heavy-quark symmetry breaking. The measured baryon masses are in striking agreement with the 1/N hierarchy.Comment: Lattice 2000 (Spectrum

Baryon-Pion Couplings from Large-N QCD

We derive a set of consistency conditions for the pion-baryon coupling constants in the large-N limit of QCD. The consistency conditions have a unique solution which are precisely the values for the pion-baryon coupling constants in the Skyrme model. We also prove that non-relativistic $SU(2N_f)$ spin-flavor symmetry (where $N_f$ is the number of light flavors) is a symmetry of the baryon-pion couplings in the large-N limit of QCD. The symmetry breaking corrections to the pion-baryon couplings vanish to first order in $1/N$. Consistency conditions for other couplings, such as the magnetic moments are also derived.Comment: (12 pages, 2 figs, uses harvmac and uufiles), UCSD/PTH 93-1

Light Quark Spin-Flavor Symmetry for Baryons Containing a Heavy Quark in Large N QCD

The couplings and interactions of baryons containing a heavy quark are related by light quark spin-flavor symmetry in the large $N$ limit. The single pion coupling constant which determines all heavy quark baryon-pion couplings is equal to the pion coupling constant for light quark baryons. Light quark symmetry relations amongst the baryon couplings are violated at order $1/N^2$. Heavy quark spin-flavor symmetry is used in conjunction with large $N$ light quark spin-flavor symmetry to determine the couplings of the degenerate doublets of heavy quark baryons.Comment: (14 pages, 2 figs, uses harvmac and uufiles), UCSD/PTH 93-1

Baryon Chiral Perturbation Theory in the 1/N Expansion

The chiral Lagrangian for baryons is formulated in an expansion in 1/N_c. The chiral Lagrangian implements the contracted spin-flavor symmetry of large-N_c baryons as well as nonet symmetry of the leading planar diagrams. Large-N_c consistency conditions ensure that chiral loop corrections are suppressed in 1/N_c through exact cancellation of chiral loop graphs to fixed orders in 1/N_c. Application of 1/N_c baryon chiral perturbation theory to the flavor-27 baryon mass splittings and the baryon axial vector currents are considered as examples.Comment: 10 pages, Invited talk, The Phenomenology of Large-N_c QCD, to be published Proceedings of the Institute of Nuclear Theor

On Losing One\u27s Illusions

Non-fiction by Connie Jenkins

Large-N Baryons, Chiral Loops, and the Emergence of the Constituent Quark

Meson loop corrections to baryon axial currents are computed in the 1/N expansion. It is already known that the one-loop corrections are suppressed by a factor 1/N; here it is shown that the two-loop corrections are suppressed by (1/N)^2. To leading order, these corrections are exactly what would be calculated in the constituent quark model. Some applications are discussed

Semiclassical Meson-Baryon Dynamics from Large-Nc QCD

The large-$N_c$ limit of the meson-baryon effective Lagrangian is shown to reduce to a semiclassical field theory. A chiral bag structure emerges naturally in the $N_c\rightarrow \infty$ limit. A possible connection between the chiral bag picture and the Skyrme model is discussed. The classical meson-baryon theory is used to reproduce the $M_\pi^3$ non-analytic correction to the baryon mass obtained previously as a loop correction in chiral perturbation theory.Comment: (13 pages, 1 figure, uses harvmac and uufiles), UCSD/PTH 94-1