Baryon mass splittings in the 1/Ncexpansion

Abstract

UCSD/PTH 95-01 hep-ph/9502227The I = 0, 1, 2, 3 mass splittings of the spin-1/2 octet and spin-3/2 decuplet baryons are analyzed in the 1/Nc expansion combined with perturbative flavor breaking. We show there is considerable experimental evidence that the baryon masses satisfy the hierarchy predicted by this expansion. Since flavor symmetry-breaking suppression factors alone are not sufficient to describe the observed hierarchy, we conclude that there is firm evidence for the 1/Nc expansion in the baryon masses. Our analysis differs from non-relativistic SU (6).

Baryon vector current in the chiral and1/Ncexpansions

“…Among the most relevant QCD operators studied in the 1/N c expansion are the Hamiltonian (baryon masses) [25,27], axial [6,7,10,23,28] and vector [29] currents and magnetic moments [8,9,28].…”

“…It is important to remark that expressions (25)- (27) have been truncated at the physical value N c = 3.…”

Excited baryons in large QCD

“…It contains an extra SU(2) Clebsch-Gordan coefficient which couples the angular momentum ℓ q of the excited quark to the angular momentum ℓ c of the excited core. The coefficients c ρ,η are the same in (6) and (8). They are defined in Refs.…”

“…The method is based on the result that, for N f flavors, the ground state baryons display an exact SU(2N f ) spinflavor symmetry in the large N c limit of QCD [ 3]. It has been applied with great success to the ground state baryons (N = 0 band), described by the symmetric representation 56 of SU (6), where N f = 3 [ 3,4,5,6,7,8,9]. For excited baryons this symmetry is broken.…”

Lattice baryons in the1/Nexpansion

“…There is an enormous (continuum) literature about spectroscopy and matrix elements for large N baryons. Assorted early references include [19][20][21][22][23], summarized in a review, Ref. [24].…”