In the framework of a simple nonrelativistic potential model, we have previously studied the stability of a system of two quarks and two antiquarks of identical light flavor. Here, we extend our analysis to quarks ͑antiquarks͒ of different masses and discuss the role of heavy flavors on the stability of the system. This analysis is performed by using a simple variational method which proved powerful in the treatment of other few-body systems. We compare our results with other results from the literature and single out a few characteristics of the spectrum of the tetraquarks.
Using the 1/N c expansion of QCD we analyze the spectrum of positive parity resonances with strangeness S = 0, −1, −2 and -3 in the 2-3 GeV mass region, supposed to belong to the [56, 4 + ] multiplet. The mass operator is similar to that of [56, 2 + ], previously studied in the literature.The analysis of the latter is revisited. In the [56, 4 + ] multiplet we find that the spin-spin term brings the dominant contribution and that the spin-orbit term is entirely negligible in the hyperfine interaction, in agreement with constituent quark model results. More data are strongly desirable, especially in the strange sector in order to fully exploit the power of this approach. * e-mail address: nmatagne@ulg.ac.be † e-mail address: fstancu@ulg.ac.be 1 I. INTRODUCTIONThe 1/N c expansion of QCD [1,2,3,4] has been proved a useful approach to study baryon spectroscopy. It has been applied to the ground state baryons [5,6,7,8,9,10,11] as well as to excited states, in particular to the negative parity spin-flavor [70, 1 − ] multiplet (N = 1 band) [12,13,14,15,16,17], to the positive parity Roper resonance belonging to [56', 0 + ] (N = 2 band) [18] and to the [56, 2 + ] multiplet (N = 2 band) [19]. In this approach the main features of the constituent quark model emerge naturally and in addition, new information is provided, as for example, on the spin-orbit problem.In this study we explore its applicability to the [56, 4 + ] multiplet (N = 4 band) for the first time. The number of experimentally known resonances in the 2-3 GeV region [20], expected to belong to this multiplet is quite restricted. Among the five possible candidates there are two four-star resonances, N(2220)9/2 + and ∆(2420)11/2 + , one three-star resonance Λ(2350)9/2 + , one two-star resonance ∆(2300)9/2 + and one one-star resonance ∆(2390)7/2 + . This is an exploratory study which will allow us to make some predictions.In constituent quark models the N = 4 band has been studied so far either in a large harmonic oscillator basis [21] or in a variational basis [22]. We shall show that the present approach reinforces the conclusion that the spin-orbit contribution to the hyperfine interaction can safely be neglected in constituent quark model calculations.The properties of low energy hadrons are interpreted to be a consequence of the spontaneous breaking of chiral symmetry [23]. For highly excited hadrons, as the ones considered here, there are phenomenological arguments to believe that the chiral symmetry is restored.This would imply a weakening (up to a cancellation) of the spin-orbit and tensor interactions [24]. Then the main contribution to the hyperfine interaction remains the spin-spin term. II. THE WAVE FUNCTIONSThe N = 4 band contains 17 multiples having symmetries (56), (70) with ℓ = 4 (see Table 2 of Ref. [22]) to a spin-flavor symmetric wave function. This giveswhere S, S z are the spin and its projection, d labels an SU(3) representation (here 8 and 10), Y, I, I z stand for the hypercharge, isospin and its projection and J, J z for ...
We present the evolution of the shell structure of nuclei in Hartree-Fock calculations using Skyrme's density-dependent effective nucleon-nucleon interaction. The role of the tensor part of the Skyrme interaction to the Hartree-Fock spin-orbit splitting in spherical spin unsaturated nuclei is reanalyzed. The contribution of a finite range tensor force to the spin-orbit splitting in closed shell nuclei is calculated. It is found that the exact matrix elements of a Gaussian and of a one-pion exchange tensor potential could be written as a product Skyrme's short range expression times a suppression factor which is almost constant for closed shell nuclei with mass number A ≥ 48. The suppression factor is ∼ 0.15 for the one-pion exchange potential.
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