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Register a new userExotic baryons and the large-Nc expansion
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P.V. Pobylitsa
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The status of exotic baryons is analyzed in the limit of a large number of colors Nc. Several toy models reproducing the main features of the large-Nc QCD are studied in order to clarify the recent controversy concerning the consistency of various approaches to the 1/Nc-expansion for exotic baryons. The analysis reveals several difficulties of the rigid-rotator approximation including the problems of this approximation in the description of exotic baryons.
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The masses of the negative parity 70-plet baryons are analyzed in large N_c QCD to order 1/N_c and to first order in SU(3) symmetry breaking. The existing experimental data are well reproduced and twenty new observables are predicted. The leading order SU(6) spin-flavor symmetry breaking is small and, as it occurs in the quark model, the subleading in 1/N_c hyperfine interaction is the dominant source of the breaking. It is found that the Lambda(1405) and Lambda(1520) are well described as three-quark states and spin-orbit partners. New relations between splittings in different SU(3) multiplets are found.
We show that the nonperturbative solution of the SU(2) linear sigma model field theory requires color number Nc=3. Also, we show that the three-point and four-point functions bootstrap (or nonperturbatively ``shrink) in the chiral limit to the tree amplitudes. Independently, we show that a chiral phase transition for Nf=2 requires Tc=180 MeV, consistent with the computer lattice value (173 +/- 8 MeV).
The partial decay widths of lowest lying negative parity baryons belonging to the 70-plet of SU(6) are analyzed in the framework of the 1/Nc expansion The channels considered are those with single pseudo-scalar meson emission. The analysis is carried out to sub-leading order in 1/Nc and to first order in SU(3) symmetry breaking. Conclusions about the magnitude of SU(3) breaking effects along with predictions for some unknown or poorly determined partial decay widths of known resonances are obtained.
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.
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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