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Register a new userAnalysis of the [56,2^+] Baryon Masses in the 1/Nc Expansion
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The mass spectrum of the positive parity [56,2^+] baryons is studied in the 1/Nc expansion up to and including O(1/Nc) effects with SU(3) symmetry breaking implemented to first order. A total of eighteen mass relations result, several of which are tested with the available data. The breaking of spin-flavor symmetry is dominated by the hyperfine interactions, while spin-orbit effects are found to be small.
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The masses of the negative parity SU(6) 70-plet baryons are analyzed in the 1/Nc expansion to order 1/Nc and to first order in SU(3) breaking. At this level of precision there are twenty predictions. Among them there are the well known Gell-Mann Okubo and equal spacing relations, and four new relations involving SU(3) breaking splittings in different SU(3) multiplets. Although the breaking of SU(6) symmetry occurs at zeroth order in 1/Nc, it turns out to be small. The dominant source of the breaking is the hyperfine interaction which is of order 1/Nc. The spin-orbit interaction, of zeroth order in 1/Nc, is entirely fixed by the splitting between the singlet states Lambda(1405) and Lambda(1520), and the spin-orbit puzzle is solved by the presence of other zeroth order operators involving flavor exchange.
We compute the coefficients of the effective mass operator of the 1/Nc expansion for negative parity L=1 excited baryons using the Isgur-Karl model in order to compare the general approach, where the coefficients are obtained by fitting to data, with a specific constituent quark model calculation. We discuss the physics behind the fitted coefficients for the scalar part of the most general two-body quark-quark interaction. We find that both pion exchange and gluon exchange lead to the dominance of the same operator at the level of the effective mass operator, which is also observed from data.
We study the behavior with the number of colors (Nc) of the two poles associated to the Lambda(1405) resonance obtained dynamically within the chiral unitary approach. The leading order chiral meson-baryon interaction manifests a nontrivial Nc dependence for SU(3) baryons, which gives a finite attractive interaction in some channels in the large Nc limit. As a consequence, the SU(3) singlet (Kbar N) component of the Lambda(1405) survives in the large Nc limit as a bound state, while the other components dissolve into the continuum. The Nc dependence of the decay widths shows different behavior from the general counting rule for a qqq state, indicating the dynamical origin of the two poles for the Lambda(1405) resonance.
We propose a novel approach to study a possible role of the quantum chromodynamics vacuum in nuclear and hadron physics. Our proposal is essentially to introduce a candidate of the QCD vacuum through a gluon background field and calculate physical quantities as a function of the background field. In the present work we adopt the Copenhagen (spaghetti) vacuum. As a first application of the our approach, we investigate the effects of the Copenhagen vacuum on the ground-state baryon masses. We find that the baryon mass does depend on a parameter that characterizes the Copenhagen vacuum and satisfies the Gell-Mann-Okubo mass relation for the baryon octet. We also estimate the value of the parameter and discuss the chiral invariant nucleon mass in our framework.
The operator structures that can contribute to three-nucleon forces are classified in the 1/Nc expansion. At leading order in 1/Nc a spin-flavor independent term is present, as are the spin-flavor structures associated with the Fujita-Miyazawa three-nucleon force. Modern phenomenological three-nucleon forces are thus consistent with this O(Nc) leading force, corrections to which are suppressed by a power series in 1/Nc^2. A complete basis of operators for the three-nucleon force, including all independent momentum structures, is given explicitly up to next-to-leading order in the 1/Nc expansion.
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