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

Chiral solitons from dimensional reduction of Chern-Simons gauged non-linear Schr\"odinger model of FQHE: classical and quantum aspects

The soliton structure of a gauge theory recently proposed to describe chiral excitations in the Fractional Quantum Hall Effect is investigated. A new type of non-linear derivative Schr\"odinger equation emerges as an effective description of the system that supports novel chiral solitons. We discuss the classical properties of solutions with vanishing and non-vanishing boundary conditions (dark solitons) and we explain their relation to integrable systems. The quantum analysis is also addressed in the framework of a semiclassical approximation improved by Renormalization Group arguments.Comment: 39 page, RevTeX, 6 figure

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

Properties of "35" Spin-(5/2) Baryon Resonances in a Model with Broken SU(3)

We investigate the properties of a set of J =(5/2)^+ resonances appearing in a 35-dimensional representation of SU(3), as proposed by Abers, Balázs, and Hara. A simple dynamical calculation gives an estimate for the mass differences within the supermultiplet. The matrix elements for the SU(3) allowed decays into meson plus resonance are given in terms of one parameter and the SU(3)-violating matrix elements for decay into meson plus baryon are given by two parameters

General S-Matrix Methods for Calculation of Perturbations on the Strong Interactions

Recently, the authors proposed an on-the-mass-shell, S-matrix method for computing the effects of small perturbations on the masses and coupling constants of strongly interacting particles. In the present paper, the method is generalized to the multichannel case. The use of group-theoretical techniques in reducing the complexity of the method is described in detail

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