1. Leonid P. Kaptari 8th APCTP-BLTP JINR Joint Workshop
Bogoliubov Lab. Theor. Phys .JINR, Dubna
Leonid P. Kaptari
8th APCTP-BLTP JINR Joint Workshop
June 29 ~ July 04 , 2014
Hanwha Resort, Jeju Island, Korea
co-authors:S.M. Dorkin (BLTP), B. Kaempfer(HZD, Germany)
(PRC 89 (2014); Few Body Syst.49, Few Body Syst.49, Few Body Syst.42…)
Analytical properties ....
June 29-July 04,
2014

2. MOTIVATION Fundamental Theory of strong Interaction: QCD confinement !
Leonid P. Kaptari
MOTIVATION
Fundamental Theory of strong Interaction: QCD confinement !
Analytical properties ....
June 29-July 04, Jeju
2014

3. MOTIVATION QGP signals (GSI, RHIC, NICA ..) “Inverse” processes
Leonid P. Kaptari
MOTIVATION
QGP signals (GSI, RHIC, NICA ..)
“Inverse” processes
Dense matter
Freeze-out
Heavy Ion
collisions
Mesons in vacuum and at finite temperatures: BSE.
Analytical properties ....
June 29-July 04, Jeju
2014

4. L.P. Kaptari
Analytical properties ....
June 29-July 04,
2014

5. Rainbow approximation ( ) + effective model for gluon propagator:
Leonid P. Kaptari
Rainbow approximation ( ) + effective model for gluon propagator:
Analytical properties ....
June 29-July 04, Jeju
2014

6. L.P. Kaptari
RESULTS
Analytical properties ....
2014
June 29-July 04,

7. RESULTS BSE domain 2014 L.P. Kaptari (5MeV) (1GeV)
Analytical properties ....
June 29-July 04,
2014

8. Analytical continuation (numerical)
L.P. Kaptari
Analytical continuation (numerical)
rays along f=const
Laurent series DSE at complex external
momenta
Analytical properties ....
June 29-July 04,
2014

9. ? Example: F(z)=z*=x-iy y x 2014 L.P. Kaptarix
Analytical properties ....
June 29-July 04,
2014

10. ? Example: F(x,y)=(x,-y) y x 2014 L.P. Kaptari
Analytical properties ....
June 29-July 04,
2014

12. QUALITATIVE RESULT QCD confinement ! (no confinement) 2014
Leonid P. Kaptari
QUALITATIVE RESULT
QCD confinement !
(no confinement)
Analytical properties ....
June 29-July 04, Jeju
2014

13. L.P. Kaptari
Analytical properties ....
June 29-July 04,
2014

14. 2014 Analytical properties .... June 29-July 04, Jeju
Leonid P. Kaptari
Analytical properties ....
June 29-July 04, Jeju
2014

15. L.P. Kaptari
SUMMARY
Analytical properties of solutions of the truncated DS equation for the Euclidean complex momentum domain have been analyzed.
It is found that, within the ladder rainbow kernel, the solutions A(p^2), B(p^2) are analytical functions everywhere, while the propagation functions sv,s (p^2) contain poles (an infinite number!) at negative Re(P^2)
the exact position of the poles and the corresponding residues of sv,s (p^2) can be found by applying Rouche’s theorem and computing the Cauchy integrals
the knowledge of the exact positions of poles and residues of sv,s (p^2) allows one to separate from the propagator functions their analytical part (for numerical calculations) and dipole terms (for explicit integration in BSE)
The knowledge of the analytical structure of the quark propagators is important for designing appropriate phenomenological kernels since it is related to such fundamental characteristics of QCD as confinement and dynamical chiral symmetry breaking phenomena encoded in the chiral condensate being the trace of the quark propagator.
Our further investigations are aimed at study of the analytical properties of the quark propagators and solutions of the DSE+BSE at finite temperatures with the ultimate goal of investigations of mesons properties in hot matter and possible signals of QGP