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Matching the quark model to the 1/Nc expansion

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 Added by Carlos Luis Schat
 Publication date 2010
  fields
and research's language is English




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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.



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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.
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.
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