Finite Nc Results for F/D Ratios of the Baryon Vertices and I=J Rule

الأصل · EN

We calculate the F/D ratios of spin-nonflip baryon vertex for an arbitrary number of color degrees of freedom Nc both in the non-relativistic quark model with the SU(6) spin-flavor symmetry and in the chiral soliton model with SU(3) flavor symmetry. We find that the spin-nonflip F/D ratio tends to -1 in the limit of Nc → ∞. We show that this leading value F/D= -1 of spin-nonflip baryon vertex in the 1/Nc expansion corresponds to the isoscalar dominance while the well known leading value F/D=1/3 of the spin-flip vertex corresponds to the isovector dominance. We discuss origins of the dominance of isovector in spin-flip and isoscalar in spin-nonflip baryon vertices, referred to as the I=J rule. In terms of the matrix elements of the operator which transform as the generator λ⁸ of the SU(3) symmetry we derive the model independent isoscalar formula for baryon vertices and apply this to the mass formula and the isoscalar part of the baryon magnetic moments. The same Okubo-Gell-Mann mass relation and its refined relation among the octet baryons as the one for the case Nc=3 is derived model independently for arbitrary color degrees of freedom Nc. Contrary to λ⁸,