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

Heavy Baryon Masses in Large N_c HQET

We argue that in the large N_c HQET, the masses of the s-wave low-spin heavy baryons equal to the heavy quark mass plus proton mass approximately. To the subleading order, the heavy baryon mass 1/N_c expansion not only has the same form, but also has the same coefficients as that of the light baryon. Based on this, numerical analysis is made.Comment: 7 pages, latex, no figures, to appear in Phys. Lett.

Naturalness of the Coleman-Glashow Mass Relation in the 1/N_c Expansion: an Update

A new measurement of the Xi^0 mass verifies the accuracy of the Coleman-Glashow relation at the level predicted by the 1/N_c expansion. Values for other baryon isospin mass splittings are updated, and continue to agree with the 1/N_c hierarchy.Comment: 6 pages, revte

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

Baryon masses at second order in large-NN chiral perturbation theory

We consider flavor breaking in the the octet and decuplet baryon masses at second order in large-$N$ chiral perturbation theory, where $N$ is the number of QCD colors. We assume that $1/N \sim 1/N_F \sim m_s / \Lambda \gg m_{u,d}/\Lambda, \alpha_{EM}$, where $N_F$ is the number of light quark flavors, and $m_{u,d,s} / \Lambda$ are the parameters controlling $SU(N_F)$ flavor breaking in chiral perturbation theory. We consistently include non-analytic contributions to the baryon masses at orders $m_q^{3/2}$, $m_q^2 \ln m_q$, and $(m_q \ln m_q) / N$. The $m_q^{3/2}$ corrections are small for the relations that follow from $SU(N_F)$ symmetry alone, but the corrections to the large-$N$ relations are large and have the wrong sign. Chiral power-counting and large-$N$ consistency allow a 2-loop contribution at order $m_q^2 \ln m_q$, and a non-trivial explicit calculation is required to show that this contribution vanishes. At second order in the expansion, there are eight relations that are non-trivial consequences of the $1/N$ expansion, all of which are well satisfied within the experimental errors. The average deviation at this order is 7 \MeV for the \De I = 0 mass differences and 0.35 \MeV for the \De I \ne 0 mass differences, consistent with the expectation that the error is of order $1/N^2 \sim 10\%$.Comment: 19 pages, 2 uuencoded ps figs, uses revte

Large N_c Limit of Spin-Flavor Breaking in Excited Baryon Levels

Spin-flavor symmetry breaking in the levels of excited Baryons are studied to leading order in the 1/$N_c$ expansion. This breaking occurs at zeroth order. For non-strange Baryons with a single quark excited, it is shown that to first order of perturbation theory the breaking is given by one 1-body operator (spin-orbit), and three 2-body operators, all involving the orbital angular momentum of the excited quark. Higher-body operators can be reduced to that set of operators. As illustration, p-wave Baryons are briefly discussed.Comment: 16 pages, one table, Latex file; title changed, some omitted operators have been included and corrections to the results have been mad

On Continuous Conformal Deformation of the SL(2)_4/U(1) Coset

We Describe a one-parameter family of c=1 CFT's as a continuous conformal deformation of the SL(2)_4/U(1) coset.Comment: LaTex file, 9 page

The Force Between Giant Magnons

We compute the force and torque between well-separated, slowly-moving Giant Magnons with arbitrary orientations on S^5. We propose an effective Hamiltonian for Giant Magnons in this regime

A Multiple Commutator Formula for the Sum of Feynman Diagrams

In the presence of a large parameter, such as mass or energy, leading behavior of individual Feynman diagrams often get cancelled in the sum. This is known to happen in large-$N_c$ QCD in the presence of a baryon, and also in the case of high-energy electron-electron as well as quark-quark scatterings. We present an exact combinatorial formula, involving multiple commutators of the vertices, which can be used to compute such cancellations. It is a non-abelian generalization of the eikonal formula, and will be applied in subsequent publications to study the consistency of large-$N_c$ QCD involving baryons, as well as high-energy quark-quark scattering in ordinary QCD.Comment: uu-encoded latex file with two postscript figure

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