Modeling the QCD ground state in the Hartree-Fock-Bogoliubov approximation

Abstract

We study quark behavior in a strong stochastic gluon field. Based on the procedure of the averaged description, we derive the effective Hamiltonian and find its ground state in the Hartree-Fock-Bogoliubov approximation. We compare different model Hamiltonians. We discuss the chiral limit transition in detail in the example of the Keldysh model.

Quantum liquids resulting from quark systems with four-quark interaction

“…The next curves and the ones following upwards correspond to temperatures T = 10 MeV, T = 50 MeV (an upper curve) with a step T = 10 MeV. Let us also remember that the pressure of the vacuum for the NJL model was estimated in [9][10][11] to be 40-50 MeV/fm 3 , which is quite consistent with that obtained in the bag model. It was also demonstrated that there is a region of instability within a certain interval of the Fermi momenta generated by the anomalous behavior of pressure d P/dn < 0 (see also [33][34][35][36]).…”

“…It is the latter that is implied in a scenario of chiral invariance restoration under extreme temperatures higher than 100 MeV and with a highly diluted quark ensemble. We have already noted (see also [9][10][11]) that the momentum p θ , which corresponds to the strongest quark-antiquark attraction d sin θ/d p = 0, …”

“…But for our purposes here it would be quite enough restrict ourselves with this simple form. The effective interactions mentioned above appear in a natural way by the coarse-grained description of the system with handling the corresponding averaging procedure, and having in mind that the vacuum gluon field changed stochastically (for example, in the form of instanton liquid; see [9][10][11]). But this elaboration of the effective Hamiltonian resulting from the first principles of quantum chromodynamics (QCD) will be unessential for us, as will be demonstrated below.…”

“…Below we analyze respective data in more detail including the situation with nonzero temperature. The energy (and, hence, the pressure) of the ensemble is a discontinuous functional of the quark current mass (see [9][10][11]) in the KKB model. The integrands in (8) are then estimated as follows:…”

“…Dealing with the definition of an induced quark mass (9) and presenting the trigonometric factors via the quark dynamical mass we find the ensemble pressure as…”