Search

In this paper, we use the self-consistent mean field approximation to study the Quantum Chromodynamics (QCD) phase transition. In the self-consistent mean field approximation of the Nambu–Jona-Lasinio (NJL) model, a parameter [Formula: see text] is introduced, which reflects the weight of “direct” channel and the “exchange” channel and needs to be determined by experiments (as mentioned in a recent work [T. Zhao, W. Zheng, F. Wang, C.-M. Li, Y. Yan, Y.-F. Huang and H.-S. Zong, Phys. Rev. D 100, 043018 (2019)], the results with [Formula: see text] are in good agreement with astronomical observation data on the latest binary neutron star merging. This indicates that the contribution of “exchange” channel should be considered, and [Formula: see text] is a possible choice). By comparing the results with different parameter [Formula: see text]’s ([Formula: see text], [Formula: see text] and [Formula: see text]), we study the influence of “exchange” channel on the behavior of the solutions of the quark gap equation and the critical point of chiral phase transition. Our results show that the second-order chiral phase turns to the crossover from the chiral limit to the non-chiral limit around [Formula: see text] in the case of [Formula: see text]. The difference of the quark mass with different [Formula: see text]’s mainly occurs in the intermediate temperatures for the different fixed chemical potentials. At zero temperature and the chemical potential [Formula: see text] there will be two solutions (including a meta-stable solution) of gap equation with [Formula: see text], and as [Formula: see text] increases it will be only one solution left (the meta-stable solution will disappear until [Formula: see text]). Besides, the discrepancy of the critical temperature (above which the pseudo-Wigner solution and negative Nambu solution will disappear) in the three cases of [Formula: see text] will become large when the chemical potential increases.

The nucleon–antinucleon interaction is studied by using resonating-group-method in the framework of two constituent quark models: the chiral quark model and the quark delocalization color screening model, which can give a good description of baryon properties and nucleon–nucleon interaction. The experimental data of proton–antiproton S-wave elastic scattering cross-section can be well reproduced by adjusting properly one-gluon annihilation coupling constant. With the fixed model parameters, a dynamical calculation of all possible S-wave nucleon–antinucleon states with channel-coupling is performed. The calculated results show that the effect of channel-coupling is not strong to form a bound state as indicated by a strong enhancement at threshold of [Formula: see text] in J/ψ radiative decay.

To look for nonstrange dibaryon resonances, a systematic calculation of nucleon–nucleon scattering phase shifts of two interacting baryon clusters of quarks with explicit coupling to NΔ and ΔΔ states is done. Two phenomenological nonrelativistic quark models giving similar low-energy NN properties are found to give significantly different dibaryon resonance structures. In the chiral quark model, the dibaryon system does not resonate in the NNS waves. In the quark delocalization color screening model, the S wave NN resonances appear with nucleon size b = 0.6. There is a IJ = 12NΔ resonance state in the [Formula: see text] scattering phase shifts at 2168 MeV in this model. Both quark models give an IJ = 03 ΔΔ resonance, which is a promising candidate for the explanation of the ABC structure at ~ 2.36 GeV in the production cross section of the reaction pn → dππ by the CELSIUS-WASA collaboration. None of the quark models used has any bound NΔP states that might generate odd-parity resonances.

The extended quark delocalization color screening model, which incorporates Goldstone–boson-exchange with soft cutoff, and chiral quark model are employed to do a systematic dynamical calculation of six-quark systems with strangeness. The two models give similar results, although they have different attraction mechanisms. Comparing with the previous calculation of the extended quark delocalization color screening model, in which the Goldstone–bosons are introduced with hard cutoff, the present calculation obtains a little large binding energies for most of the states. However, the conclusions are the same. The calculations show that NΩ state with IJ = 1/2, 2 is a good dibaryon candidate with narrow width, and ΩΩ state with IJ = 00 is a stable dibaryon against the strong interaction. The calculations also reveal several other possible dibaryon candidates with high angular momentum, ΔΣ*(1/2, 3), ΔΞ*(1, 3), etc. These states may have too wide width to be observed experimentally.

Three representations of Nambu–Jona-Lasinio interaction Lagrangians are constructed by Fierz transformation, and gap equation and critical end point in these three representations at finite temperature and finite chemical potential are studied. We find that the values of the quark mass and the critical end point are different in these three representations because of the consideration of Hartree–Fock approximation in our calculation.

A transformation table between physical bases including hidden color channels and symmetry bases for nonstrange six-quark systems is provided by using fractional parentage expansion method. By solving a coupled-channel equation, in the framework of the resonating group method (RGM), the effect of hidden color channels to all nonstrange six-quark systems is examined. It is shown that the overall effects from hidden color channels would reduce the energies of systems. For ΔΔ systems, the greatest decrease is about 20 MeV. Effects of hidden color on the masses of NN systems have been found to be about 1 MeV. However, we should emphasize that such a minor change for NN system is not negligible. We also give the most favorable hidden color channels for NN system.

The spectroscopy of S-wave heavy-baryons containing one, two or three heavy quarks is investigated in a constituent quark model. We solve the Schrödinger equation for three particles exactly by means of a Gaussian expansion method. The calculated results of heavy-baryon spectra with a single heavy quark are consistent with the experimental data.

We expand Salamanca SU (2) chiral quark model to SU (3) one and calculate promising dibaryon candidates with strangeness S=-3,-6 in the framework of resonating group method. We find that, besides ΩΩ, the mass of NΩ state is about 23–38 MeV lower than its threshold, it might appear as a bound state or a narrow resonance. The effect of K and η exchanges on the masses of strangeness and nonstrangeness systems has been studied and found to be negligible for nonstrangeness systems. However this effect brings some changes (about tens of MeV) on the masses of strangeness systems. We have also studied the sensitivities of binding energy and root mean square radius to the mass of s-quark.

A relativistic quark potential model is used to do a systematic search for quasi-stable dibaryon states in the $u$, $d$, and $s$ three flavor world. Flavor symmetry breaking and channel coupling effects are included and an adiabatic method and fractional parentage expansion technique are used in the calculations. The relativistic model predicts dibaryon candidates completely consistent with the nonrelativistic model., Comment: 12 pages, latex, no figures

The effect of correction for center-of-mass motion on the quark delocalization model of baryon-baryon interactions is to make the effective interaction a little less attractive; the correction is minor. The intermediate range behavior of the color screening potential is not critical for obtaining an intermediate attractive baryon-baryon interaction. The cluster model and molecular single quark bases give exactly the same results.

The $p\bar{\Lambda}$ systems with J=0 and J=1 are dynamically investigated within the framework of two constituent quark models: the chiral quark model and the quark delocalization color screening model. The model parameters are taken from our previous work, which gave a good description of the proton-antiproton S-wave elastic scattering cross section experimental data. The $p\bar{\Lambda}$ elastic scattering processes with coupling to $p\bar{\Sigma}$ state are studied. The results show that, there is no s-wave bound state as indicated by an enhancement near the threshold of $p\bar{\Lambda}$ in $J/\psi$ decay. However, a $IJ = {1/2}0$ $p\bar{\Sigma}$ resonance state is given in the quark delocalization color screening model., Comment: 7 pages, 3 figures

The properties of bottomonia are investigated in detail in the constituent quark model. The wave functions of bottomonia are obtained by solving Dirac equation and Schrödinger equation. The potentials between quark and antiquark include color confinement (linear and quadratic) and one-gluon-exchange. Based on the obtained wave functions, the electromagnetic and two-photon decay, electric dipole transition, and hadronic width of bottomonia are calculated. The calculated results are in a good agreement with the experimental data. The results also show that the nonrelativistic and relativistic version of quark model can all describe the properties of bottomonia.