6533b7d3fe1ef96bd12610de

RESEARCH PRODUCT

Large N-c Weinberg-Tomozawa interaction and negative parity s-wave baryon resonances

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It is shown that in the 70 and 700 SU(6) irreducible spaces, the SU(6) extension of the Weinberg-Tomozawa (WT) s-wave meson-baryon interaction incorporating vector mesons (hep-ph/0505233) scales as O(N-c(0)), instead of the well-known O(N-c(-1)) behavior for its SU(3) counterpart. However, the WT interaction behaves as order O(N-c(-1)) within the 56 and 1134 meson-baryon spaces. Explicit expressions for the WT couplings (eigenvalues) in the irreducible SU(2N(F)) spaces, for arbitrary N-F and N-c, are given. This extended interaction is used as a kernel of the Bethe Salpeter equation, to study the large N-c scaling of masses and widths of the lowest-lying negative parity s-wave baryon resonances. Analytical expressions are found in the N-c ->infinity limit, from which it can be deduced that resonance widths and excitation energies (M-R-M) behave as order O(N-c(0)), in agreement with model independent arguments, and moreover they fall in the 70-plet, as expected in constituent quark models for an orbital excitation. For the 56 and 1134 spaces, excitation energies and widths grow O(N-c(1/2)) indicating that such resonances do not survive in the large N-c limit. The relation of this latter N-c behavior with the existence of exotic components in these resonances is discussed. The interaction comes out repulsive in the 700.