Structure of Di-Ω Dibaryon

Previously, we extended our chiral SU（3） quark model to include the coupling between the quark and vector chiral fields [Nucl. Phys. A 727（2003）321]. Here we further study the structure of （ΩΩ）ST=oo dibaryon in the extended chiral SU（3） quark model by solving a resonating group method equation. The vector meson exchanges effect, hidden colour channel and colour screening effect are investigated, respectively. The results show that the （ΩΩ）ST=oo system is still the deeply bound state in the extended chiral SU（3） quark model in which the vector meson exchanges control the short-range quark-quark interaction, which is similar to the results obtained from the chiral SU（3） quark model. When the model space is enlarged by including the hidden colour channel, it is found that the energy of the hidden colour state ｜CC〉str=-6,ST=oo is much higher than that of the （ΩΩ）ST=oo state, thus the CC channel has little effect on the binding energy of （ΩΩ）ST=oo state. When the error function confinement potential is considered, the bound state property would not change largely. Fhrther, scalar meson mixing is considered. No matter whether θs= -18° or ideal mixing is taken, （ΩΩ）ST=oo state is still a bound state.     

Structures of（ΩΩ）0＋and（[1]Ω）1＋in Extended Chiral SU（3） Quark Model

The structures of (ΩΩ)0 and ([1]Ω)1 are studied in the extended chiral SU(3) quark model in which vector meson exchanges are included. The effect from the vector meson fields is very similar to that from the one-gluon exchange (OGE) interaction. Both in the chiral SU(3) quark model and in the extended chiral SU(3) quark model,di-omega (ΩΩ)0 is always deeply bound, with over one hundred MeV binding energy, and ([1]Ω)1 ‘s binding energy is around 20 MeV. An analysis shows that the quark exchange effect plays a very important role for making di-omega (ΩΩ)0 deeply bound.     

Structures of (ΩΩ)0 and (([1])Ω)1 in Extended Chiral SU(3) Quark Model

The structures of (ΩΩ)0 and (([1])Ω)1 are studied in the extended chiral SU(3) quark model in whichvector meson exchanges are included. The effect from the vector meson fields is very similar to that from the one-gluonexchange (OGE) interaction. Both in the chiral SU(3) quark model and in the extended chiral SU(3) quark model,di-omega (ΩΩ)0 is always deeply bound, with over one hundred MeV binding energy, and (([1])Ω)1 ‘s binding energyis around 20 MeV. An analysis shows that the quark exchange effect plays a very important role for making di-omega(ΩΩ)0 deeply bound.     

Chiral SU（3） Quark Model Study of Tetraquark States： cnn^-s^-/css^-s^-

The new members of the charm-strange family Dsj^＊（2317）, Dsj（2460）, and Ds（2632）, which have the surprising properties, are challenging the present models. Many theoretical interpretations have been devoted to this issue. Most authors suggest that they are not the conventional cs^- quark model states, but possibly are four-quark states, molecule states, or mixtures of a P-wave cs^- and a four-quark state. In this work, we follow the four-quark-state picture, and study the masses of cnn^-s^-/css^-s^- states （n is u or d quark） in the chiral SU（3） quark model. The numerical results show that the mass of the mixed four-quark state （cnn^-s^-/css^-s^-） with spin parity j^P ： 0^＋ might not be Ds （2632）. At the same time, we also conclude that Dsj^＊（2317） and Dsj（2460） cannot be explained as the pure four-quark state.     

QQqq Four-Quark Bound States in Chiral SU（3） Quark Model

Abstract The possibility of QQqq heavy-light four-quark bound states has been analyzed by means of the chiral SU（3） quark model, where Q is the heavy quark （c or b） and q is the light quark （u, d, or s）. We obtain a bound state for the bbnn configuration with quantum number JR=1^＋, I = 0 and for the ccnn （JR=1^＋, I=O） configuration, which is not bound but slightly above the D^＊ D^＊ threshold （n is u or d quark）. Meanwhile, we also conclude that a weakly bound state in bbnn system can also be found without considering the ehiral quark interactions between the two light quarks, yet its binding energy is weaker than that with the chiral quark interactions.     

Structures of NΩ and △Ω Dibaryons

We study the structures of NΩ and △Ω systems in the extended chiral SU（3） quark model by solving a resonating group method equation. The results show that both systems are weakly bound states and changed into unbound states if we consider the mixing of scalar mesons.     

△△ Dibaryon Structure in Extended Chiral SU（3） Quark Model

The structure of △△ dibaryon is studied in the extended chiral SU（3） quark model in which vector meson exchanges are included. The effect of the vector meson fields is very similar to that of the one-gluon exchange （OGE） interaction. Both in the chiral SU（3） quark model and in the extended chiral SU（3） quark model, the resultant mass of the △△ dibaryon is lower than the threshold of the △△ channel but higher than that of the △ Nπ channel.     

Low-Energy Kπ Phase Shifts in Chiral SU（3） Quark Model

The low-energy region kaon-pion S- and P-wave phase shifts with isospin I = 1/2 and I = 3/2 are dynamically studied in the chiral SU（3） quark model by solving a resonating group method equation. The model parameters are taken to be the values fitted by the energies of the baryon ground states and the kaon-nucleon elastic scattering phase shifts of different partial waves. As a preliminary study the s-channel qq^- annihilation interactions are not included since they only act in the very short range and are subsequently assumed to be unimportant in the low-energy domain. The numerical results are in qualitative agreement with the experimental data.     

Study of Σ~*-Δ Interactions

We study the Σ~*-Δ interaction in the chiral SU(3) quark model and in the extended chiral SU(3) quark model.In these two models,the short-range interaction mechanism are totally different,one is from the one-gluon exchange and another is from the vector meson exchange.The possible reasons of forming strangeness-1 bound states are given.Comparisons between the cases with and without quark exchange effect are made.The results show the quark exchange effect does give attractions to (Σ~*Δ)_(ST)=0 5/2 and (Σ~*Δ)_(ST)=3 1/2 systems,which means the special symmetry is important.Also,we make some analysis on chiral field effect,our results show that the σ exchange dominantly provides the attractive interaction for these two states.     

Quark-Antiquark and Diquark Condensates in Vacuum in a 2D Two-Flavor Gross-Neveu Model

The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio （NJL） model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the diquark ,condensates in vacuum also depends on Gs/Hs, the ratio of the coupling constants in scalar quarkantiquark and scalar diquark channel. Only the pure quark-antiquark condensates exist if Gs/Hs 〉 2/3, which is just the ratio of the color numbers of the quarks participating in the diquark and quark-antiquark condensates. The two condensates will coexist if 0 〈 Gs/Hs 〈 2/3. However, different from the 4D NJL model, the pure diquark condensates arise only at Gs/Hs = 0 and are not in a possibly finite region of Gs/Hs below 2/3.     

Quark-Antiquark and Diquark Condensates in Vacuum in Two-Flavor Four-Fermion Interaction Models with Any Color Number Nc

The color number Nc-dependence of the interplay between quark-antiquark condensates （q^-q） and diquark condensates （qq） in vacuum in two-flavor four-fermion interaction models is researched. The results show that the Gs-Hs （the coupling constant of scalar （q^-q）2-scalar （qq）2 channel） phase diagrams will be qualitatively consistent with the case of Nc = 3 as Nc varies in 4D Nambu-Jona-Lasinio model and 219 Gross Neveu （GN） model, However, in 3D GN model, the behavior of the Gs-Hp （the coupling constant of pseudoscalar （qq）^2 channel） phase diagram will obviously depend on No. The known characteristic that a 3D GN model does not have the coexistence phase of the condensates （q^-q） and （qq） is proven to appear only in the case of Nc ≤ 4. In all the models, the regions occupied by the phases containing the diquark condensates （qq） in corresponding phase diagrams will gradually decrease as Nc grows up and finally go to zero if Nc → ∞, i.e. in this limit only the pure （q^-q） phase could exist.     

Interplay Between Quark-Antiquark and Diquark Condensates in Vacuum in a Two-Flavor Nambu-Jona-Lasinio Model

By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.     

Phase transition between three- and two-flavor QCD?

We explore the possibility that QCD may undergo a phase transition as a function of the strange quark mass. This would hint towards models with ”spontaneous color symmetry breaking” in the vacuum. For two light quark flavors we classify possible colored quark-antiquark, diquark and gluon condensates that are compatible with a spectrum of integer charged states and conserved isospin and baryon number. The ”quark mass phase transition” would be linked to an unusual realization of baryon number in QCD₂ and could be tested in lattice simulations. We emphasize, however, that at the present stage the Higgs picture of the vacuum cannot predict a quark mass phase transition - a smooth crossover remains as a realistic alternative. Implications of the Higgs picture for the high-density phase transition in QCD₂ suggest that this transition is characterized by the spontaneous breaking of isospin for nuclear and quark matter. Received: 12 March 2001 / Revised version: 2 April 2003 / Published online: 2 June 2003 RID="a" ID="a" e-mail: C.Wetterich@thphys.uni-heidelberg.de     

Spontaneous electromagnetic superconductivity of vacuum in a strong magnetic field: evidence from the Nambu-Jona-Lasinio model

Using an extended Nambu-Jona-Lasinio model as a low-energy effective model of QCD, we show that the vacuum in a strong external magnetic field (stronger than 10(16) T) experiences a spontaneous phase transition to an electromagnetically superconducting state. The unexpected superconductivity of, basically, empty space is induced by emergence of quark-antiquark vector condensates with quantum numbers of electrically charged rho mesons. The superconducting phase possesses an anisotropic inhomogeneous structure similar to a periodic Abrikosov lattice in a type-II superconductor. The superconducting vacuum is made of a new type of vortices which are topological defects in the charged vector condensates. The superconductivity is realized along the axis of the magnetic field only. We argue that this effect is absent in pure QED.     

Diquark condensation in dense adjoint matter

We study SU(2) lattice gauge theory at non-zero chemical potential with one staggered quark flavor in the adjoint representation. In this model the fermion determinant, although real, can be both positive and negative. We have performed numerical simulations using both hybrid Monte Carlo and two-step multibosonic algorithms, the latter being capable of exploring sectors with either determinant sign. We find that the positive determinant sector behaves like a two-flavor theory, with the chiral condensate rotating into a two-flavor diquark condensate for , implying a superfluid ground state. Good agreement is found with analytical predictions made using chiral perturbation theory. In the ‘full’ model there is no sign of either onset of baryon density or diquark condensation for the range of chemical potentials we have considered. The impact of the sign problem has prevented us from exploring the true onset transition and the mode of diquark condensation, if any, for this model. Received: 28 September 2001 / Published online: 23 November 2001     

Non-perturbative corrections to one-gluon exchange quark potentials

The leading non-perturbative QCD corrections to the one-gluon exchange quark-quark, quark-antiquark and pair-excitation potentials are derived by using a covariant form of non-local two-quark and two-gluon vacuum expectation values. Our numerical calculation indicates that the correction of quark and gluon condensates to the quark-antiquark potential improves the heavy quarkonium spectra to some degree.     

Nonperturbative corrections of quark and gluon condensates to QCD inspired quark potentials

We adopt the Lorentz gauge to derive the non-local two-gluon vacuum expectation value (VEV) with translational invariance. By means of the obtained non-local two-gluon VEV, the leading nonperturbative QCD corrections to one gluon exchange quark-quark, quark-antiquark and pair-excitation potentials are given by employing non-vanishing vacuum condensates of quarks and gluons to modify the free gluon propagator. The linear, cubic and Yukawa-type terms in quark-quark potential appear automatically. In the pair-excitation potential with , the linear, square and cubic terms arise from the nonzero quark and gluon condensates. Received: 22 June 1998 / Revised version: 10 August 1998 / Published online: 29 October 1998     

The Quarkonium Potential Within the Short and Intermediate Range in QCD

A quark-antiquark potential is calculated by involving vacuum condensates up to dimension-6 in QCD in the background fields. The underlying assumption is that a gluon (quark) propagates, not in the empty space, but through the physics vacuum, filled with the background fields. The interactions of the gluon with the background fidds manifest themselves as the corrections of vacuum condensates to the free gluon propagator. It is shown that these corrections extend the potential from the short distances to the intermediate range. Indeed, with some reasonable parameters, the resulting potential is similar to those popular phenomenological potentials in shape in the region of 0.1 < γ < 1 fm.