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

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dc.creatorTakamura, Akira
dc.creatorSawada, Shoji
dc.creatorMatsui, Yoshimitsu
dc.creatorKitakado, Shinsaku
dc.date1995-06-09
dc.date.accessioned2026-07-07T03:57:43Z
dc.date.available2026-07-07T03:57:43Z
dc.descriptionWe calculate the $F/D$ ratios of spin-nonflip baryon vertex for an arbitrary number of color degrees of freedom $N_c$ 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 $N_c \to \infty$. We show that this leading value $F/D= -1$ of spin-nonflip baryon vertex in the $1/N_c$ 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. \par In terms of the matrix elements of the operator which transform as the generator $λ^8$ 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 $N_c=3$ is derived model independently for arbitrary color degrees of freedom $N_c$. Contrary to $λ^8$,
dc.description25pages, LaTeX file, with uuencoded 3 postscript figures
dc.identifierhttps://arxiv.org/abs/hep-ph/9506275
dc.identifierhttp://arxiv.org/abs/hep-ph/9506275
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/45549
dc.subjectHigh Energy Physics - Phenomenology
dc.titleFinite $N_c$ Results for $F/D$ Ratios of the Baryon Vertices and $I=J$ Rule
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