The di-hyperon state in the quark cluster model

The di-hyperon state (DH) predicted by Jaffe in the MIT bag model is studied in the non-relativistic quark cluster model. The resonating group method is applied to the ΛΛ, NΞ and ΣΣ coupled channels problem. No stable bound state is found below the lowest ΛΛ threshold but a sharp resonance with spin-parity 0⁺ is predicted just below the NΞ threshold. The structure of the state is similar to that of the flavour SU₃ singlet state and the attractive nature of the color magnetic interaction in this state is responsible for the appearance of the resonance. The difference between the present model and the bag model which predicted a strongly bound state is attributed to the difference in the mechanism of confinement for these two models.     

Three-nucleon interaction in a quark cluster model

Taking into account the quark structure of the nucleons, a new three-nucleon potential is derived. It contains two parts: the pairwise interactions and a three-nucleon force. The pairwise interactions are described by the NN potentials of the quark-compound-bag model in the off-shell generalized form. The three-body force has the form of a separable potential which has a pole singularity on the energy axis. The residue at the pole is determined by the three-nucleon vertex given explicitly through all possible intermediate states formed by the 6q and 9q bags. The solution of the three-nucleon problem is obtained in an analytical form by means of the known solution of the problem with ordinary pairwise interaction. It is shown that: (i) the 9q bag is an additional source of an attractive interaction between three nucleons; (ii) the pole singularity of the three-nucleon force exhibits a resonance structure of the three-nucleon scattering amplitude; (iii) the total and partial widths of the quasi-discrete level are defined by the three-nucleon vertex. Some consequences of the new potential are discussed.     

Non-relativistic quark cluster model of the isospin-violating two-nucleon interaction

The violations of isospin symmetry induced in the two-nucleon system at the quark level by the mass difference between up and down quarks are studied in a quark cluster model. Quark dynamics are treated by means of the standard non-relativistic quark model with a quark hamiltonian consisting of a confining harmonic potential, eventually corrected for anharmonicities, and a spin-dependent potential truncated to the contact-gluon-exchange hyperfine interaction. The resonating group method is adopted to treat the six-quark system and we restrict ourselves to configurations of two three-quark clusters with nucléon quantum numbers. π- and σ-meson-mediated quark interactions are tentatively considered in an attempt to achieve a good matching to the empirical strong NN potentials. We supply explicit formulas for the various kernels. Equivalent adiabatic potentials are calculated for the pp, np and nn systems in low partial waves. We also solve the resonating group scattering equations for these systems and give predictions for phase observables and low-energy parameters.     

Explicit form of the effectiveN-N potential from the quark cluster model

We derive an effectiveN-N potential from a microscopic quark Hamiltonian using the quark cluster model. We construct it in an explicit analytical form, which is expressed only by nuclear variables and which can be used in nuclear structure calculations. To this end we first solve the equation of motion for the six-quark system with a microscopic quark Hamiltonian that includes the quadratic-confinement, one-gluon-, and one-pion-exchange potentials. We then eliminate the quark (internal) degrees of freedom explicitly and express them implicitly in terms of an effectiveN-N potential. The equation of motion for the two-nucleon system is then described by a Schrödinger equation with an effectiveN-N potential. In addition to the one-pion-exchange potential, this effectiveN-N potential contains thequark-exchange potential, which represents the quark-exchange processes associated with a gluon or a pion exchange. This quark-exchange potential is incorporated into the effectiveN-N potential through nonlocal and isospin-dependent terms, which produce a short-range repulsion in theN-N interaction. We give the explicit analytical form of this quark-exchange potential so that it can be used in the nuclear structure calculations.Supported by the DFG under contract number Fa 67/10-5Dedicated to Prof. Erich Schmid on the occasion of his 60th birthday     

A study of six quark cluster states in chiral SU(3) quark model

The energies of the (0S)⁶ six quark cluster states are calculated in the chiral SU(3) quark model. The results show that some states with high strangeness have more attraction from the chiral SU(3) coupling, and this feature is interesting in discussing if there exists some new narrow width six quark states. Further, we did a RGM calculation to study some multi-strangeness dibaryon states. We found that ΩΩ dibaryon is a deeply bound state and ΞΩ dibaryon is slightly bound.     

Some implications of the quark model for high energy scattering

The expressions for total scattering cross sections obtained from the quark model are expressed in a simple form which shows the dependence of the results on the assumptions. The results are shown to depend only on the value of six constants or “charges” defined for each hadron and to be otherwise independent of the structure. Any model which gives the same values of these charges gives the same result as the quark model. In particular, the results for processes which have odd signature t-channel quantum numbers hold in a quark model even with arbitrary mixtures of additional quarkantiquark pairs in the hadron wave function, provided that B, Y, and I are conserved.     

Binding energy in model classical field theories

The energy of two external sources bound by self-interacting scalar “glue” is studied classically in a spatially one-dimensional model. When the self-interaction is treated exactly, some surprising results are obtained. In particular, for self-interactions with a bounded potential and for certain strengths of the external sources, we find “confinement” by an infinitely deep well of finite radius.     

Low energy theorems in a nonlocal chiral quark model at finite temperature

We solve the Dyson equation and the Bethe-Salpeter equation for a nonlocal effective quark interaction kernel which is instantaneous and separable. The momentum-dependent dynamical quark mass, the scalar and pseudoscalar meson masses, the pion decay constant and the quark meson coupling constant are calculated at finite temperature in the Hartree approximation for the quark self energy. We obtain relations between these quantities, which coincide to leading order in the current quark mass (m ₀/Δm) with the basic low energy theorems: the Goldstone theorem, the Gell-Mann-Oakes-Renner relation and the Goldberger-Treimann relation at finite temperature. A formula for the σ?π mass gap is obtained which exhibits an additional contribution from the momentum dependence of the quark mass.     

Regge trajectories in the quark model

We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\) ) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.     

Recent experimental data and the size of the quark in the constituent quark model

We use the constituent quark model (CQM) to describe CDF data on double parton cross section and HERA data on the ratio cross section of elastic and inelastic diffractive productions. Our estimate shows that the radius of the constituent quark turns out to be rather small, GeV^-2, in accordance with the assumption on which CQM is based. Received: 14 April 2002 / Published online: 9 August 2002     

The spin-symmetry of the quark model

Corrections to the exact heavy–quark symmetry results are expected to come from the inverse powers of the heavy-quark mass. We show, by an explicit calculation using the quark model, that the breaking of the spin symmetry is suppressed by other kinematic effects even when the quark masses are not heavy. Received: 21 January 1999 / Published online: 20 May 1999     

Spin distributions in the quark parton model

Spin-dependent parton distributions are described in a broken SU(6) quark parton model. The model predicts definite forms for the spin-dependent structure functions in deep inelastic lepton-nucleon scattering and leads to several relations between Regge intercepts and couplings. Resonance electroproduction at large momentum transfer is explored via Bloom-Gilman duality.