A possible approach to the CEP location. Juan Xiong Supervisor: Prof. Jiarong Li IOPP-CCNU 2010-04. Outline. Introduction Formulation of the NJL model Boundary of two phases coexistence and the phase diagram
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A possible approach to the CEPlocation
Supervisor: Prof. Jiarong Li
The two flavor SU(2) NJL model Lagrangian density is defined as
the quark field,
the current quark mass.
Symmetry: (When =0 )
Define the chiral condensate
The Schwinger-Dyson equation of quark self-energy in the Hartree approximation has the following form,
is the quark propagator in momentum space,
After a direct calculation in imaginary time finite temperature
field theory formalism, the chiral condensate reads:
The NJL grand potential from the Hartree propagator:
In the above formula
is the Hartree quasi-particle
energy of the quark.
are the Fermi-Dirac
distribution for the antiquark and quark, respectively.
Generally speaking, there are two ways to obtain the phase diagram
The QCD chiral phase transition and the liquid-gas phase transition belong to one universal class. As usual, the pressure is defined such that its value is zero in the vacuum state
The net quark number density could be calculated with the
and baryon number density
The constituent quark mass
origins from the quark and antiquark
Interaction and is determined by the energy gap in the energy spectrum
of quasi-particle excitations
In the NJL model, meson is the quark-antiquark thermal excitation.
Under the standard Hartree Fock approximation (HFA) +random phase approximation (RPA), the full correlation function of pion meson has the form
is the polarization tensor of the pion meson which reads
In the NJL model,
can be easily calculated by solving the equation
increasing and quark chemical potential decreasing, two physical values close to each other and coincide at the CEP.