Leonid P. Kaptari 8th APCTP-BLTP JINR Joint Workshop

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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