A possible approach to the CEP
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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 CEP location

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A possible approach to the CEPlocation

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

  • Multiple solutions of the chiral order parameter, quark and pion meson effective mass

  • Summary and discussion


Introduction

  • QCD phase diagram (Hadron---QGP)

  • Tricritical point (TCP) and critical end point (CEP)

  • Methods to find the location of CEP


Formulation of the Nambu–Jona-Lasinio(NJL) model

The two flavor SU(2) NJL model Lagrangian density is defined as

with

the quark field,

the current quark mass.

Symmetry: (When =0 )


NJL model

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,


NJL model

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.


The phase diagram

Generally speaking, there are two ways to obtain the phase diagram

  • Landau theory of phasetransition


Boundary of two phases coexistence

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

thermodynamic relation

and baryon number density


Equilibrium condition:


as an order parameter


The multiple values of the chiral order parameter


The multiple values of the chiral order parameter


The quark effective mass

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


The quark effective mass


The pion meson mass

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


The pion meson mass


The pion meson mass


Summary and discussion

  • We analyze the chiral phase transition properties in the real physical world of the two flavor NJL model by the approach of analyzing the liquid-gas phase transition. And obtain the corresponding phase diagram .

  • In the first order phase transition region, the chiral order parameter, the quark effective mass and the thermal excitation pion meson have two physical values. With temperature

    increasing and quark chemical potential decreasing, two physical values close to each other and coincide at the CEP.

  • We advance a notion which is helpful to find the CEP. In the energy scan in the ultra-relativistic nuclear collision, if the happens on the first order phase transition region, the physical observable quantities related to chiral order parameter could appear the same character.


Thank you


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