Abstract
The quadrupole moments of ground state baryons are discussed in the framework of the 1/N(c) expansion of QCD, where N(c) is the number of color charges. Theoretical expressions are first provided assuming an exact SU(3) flavor symmetry, and then the effects of symmetry breaking are accounted for to linear order. The rather scarce experimental information available does not allow a detailed comparison between theory and experiment, so the free parameters in the approach are not determined. Instead, some useful new relations among quadrupole moments, valid even in the presence of first-order symmetry breaking, are provided. The overall predictions of the 1/N(c) expansion are quite enlightening.
Highlights
Understanding the structure of baryons is still a daunting task in quantum chromodynamics (QCD)
The most interesting static properties of baryons, e.g., masses, magnetic moments, matter and charge radii, etc., fall in the nonperturbative regime of QCD so analytic calculations of these properties are not possible because the theory is strongly coupled at low energies, with no small expansion parameter
The analysis of the magnetic moments of baryons presents an opportunity to shed light on an accurate test of QCD, and there are an important number of works on the subject; the approaches include, among others, the quark model [1,2,3,4,5,6,7], QCD sum rules [8,9,10,11], the 1=Nc expansion, where Nc is the number of color charges [12,13,14,15,16], chiral perturbation theory [17,18,19,20,21,22,23,24,25,26,27], the combined expansion in 1=Nc and chiral corrections [28,29], and lattice QCD [30], to name but a few
Summary
Understanding the structure of baryons is still a daunting task in quantum chromodynamics (QCD). Accounted for in Sec. IV; the detailed construction of baryon operators which make up the series is described for each flavor representation present in the tensor product of the quadrupole moment and the perturbation to identify redundant operators. IV; the detailed construction of baryon operators which make up the series is described for each flavor representation present in the tensor product of the quadrupole moment and the perturbation to identify redundant operators This assumption is not used in the present analysis; instead the full operator basis is used here This might be counterproductive due to the larger number of free parameters introduced, it leads to interesting relations among quadrupole moments which can not be determined otherwise. Because the baryon matrix elements of the spin-flavor generators (2) can be taken as the values in the nonrelativistic quark model, this convention is usually referred to as the quark representation [45]
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