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Register a new userBaryon quadrupole moment in the 1/N(c) expansion of QCD
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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.
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The mass spectrum of the positive parity [56,2^+] baryons is studied in the 1/Nc expansion up to and including O(1/Nc) effects with SU(3) symmetry breaking implemented to first order. A total of eighteen mass relations result, several of which are tested with the available data. The breaking of spin-flavor symmetry is dominated by the hyperfine interactions, while spin-orbit effects are found to be small.
By employing the $1/N$ expansion, we compute the vacuum energy~$E(deltaepsilon)$ of the two-dimensional supersymmetric (SUSY) $mathbb{C}P^{N-1}$ model on~$mathbb{R}times S^1$ with $mathbb{Z}_N$ twisted boundary conditions to the second order in a SUSY-breaking parameter~$deltaepsilon$. This quantity was vigorously studied recently by Fujimori et al. using a semi-classical approximation based on the bion, motivated by a possible semi-classical picture on the infrared renormalon. In our calculation, we find that the parameter~$deltaepsilon$ receives renormalization and, after this renormalization, the vacuum energy becomes ultraviolet finite. To the next-to-leading order of the $1/N$ expansion, we find that the vacuum energy normalized by the radius of the~$S^1$, $R$, $RE(deltaepsilon)$ behaves as inverse powers of~$Lambda R$ for~$Lambda R$ small, where $Lambda$ is the dynamical scale. Since $Lambda$ is related to the renormalized t~Hooft coupling~$lambda_R$ as~$Lambdasim e^{-2pi/lambda_R}$, to the order of the $1/N$ expansion we work out, the vacuum energy is a purely non-perturbative quantity and has no well-defined weak coupling expansion in~$lambda_R$.
The masses of the negative parity SU(6) 70-plet baryons are analyzed in the 1/Nc expansion to order 1/Nc and to first order in SU(3) breaking. At this level of precision there are twenty predictions. Among them there are the well known Gell-Mann Okubo and equal spacing relations, and four new relations involving SU(3) breaking splittings in different SU(3) multiplets. Although the breaking of SU(6) symmetry occurs at zeroth order in 1/Nc, it turns out to be small. The dominant source of the breaking is the hyperfine interaction which is of order 1/Nc. The spin-orbit interaction, of zeroth order in 1/Nc, is entirely fixed by the splitting between the singlet states Lambda(1405) and Lambda(1520), and the spin-orbit puzzle is solved by the presence of other zeroth order operators involving flavor exchange.
We discuss the necessary, albeit not sufficient, conditions for tetraquark poles to occur in the 1/N expansion of QCD and find the minimum order at which such poles may appear. Assuming tetraquark poles, we find a new non-planar solution with the minimal number of topologies and tetraquark species. The solution implies narrow states. Mixing with quarkonium states is allowed so that P-wave tetraquarks with J^PC=1^-- would couple to e^+e^-.
Diquarks are found to have the right degrees of freedom to describe the tetraquark poles in hidden-charm to open-charm meson-meson amplitudes. Compact tetraquarks result as intermediate states in non-planar diagrams of the 1/N expansion and the corresponding resonances are narrower than what estimated before. The proximity of tetraquarks to meson-thresholds has an apparent role in this analysis and, in the language of meson molecules, an halving rule in the counting of states is obtained.
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