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Diffusion and local deconfinement in relativistic systems Georg Wolschin Universität Heidelberg, Theor. Physics Georg Wolschin.

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Presentation on theme: "Diffusion and local deconfinement in relativistic systems Georg Wolschin Universität Heidelberg, Theor. Physics Georg Wolschin."— Presentation transcript:

1 Diffusion and local deconfinement in relativistic systems Georg Wolschin Universität Heidelberg, Theor. Physics http://wolschin.uni-hd.de Georg Wolschin Universität Heidelberg, Theor. Physics http://wolschin.uni-hd.de

2 YITP2/052 Topics  Relativistic Diffusion Model for R(E T,y): net baryons and produced charged hadrons  Transverse energy and rapidity distributions at SIS, AGS, SPS and RHIC energies  Indications for local deconfinement and local thermal equilibrium (QGP formation) at RHIC (and possibly SPS) energies ?  Collective longitudinal expansion

3 YITP2/053 Indications for local deconfinement/qgp? Fig. Courtesy U Frankfurt 1.Yes, in central collisions of Au-Au at √s=200 GeV/particle pair, the partons in 14% of the incoming baryons are likely to be deconfined. [cf. GW, Phys. Rev. C 69, 024906(2004)] 2.Yes, most of the produced particles are in local thermal equilibrium [cf. M. Biyajima et al., nucl-th/0309075 (2003) )]

4 YITP2/054 Relativistic Diffusion Model Nonequilibrium- statistical approach to relativistic many-body collisions Macroscopic distribution function R(y,t) for the rapidity y Coupled to a corresponding evolution eq. for p T, or E T -The drift function J(y) determines the shift of the mean rapidity towards the equilibrium value - The diffusion coefficient D(t) accounts for the broadening of the distributions due to interactions and particle creations. It is related to J(y) via a dissipation-fluct. Theorem.

5 YITP2/055 Linear RDM The rapidity relaxation time  y determines the peak positions The rapidity diffusion coefficient D y is calculated from  y and the equilibrium temperature T in the weak-coupling limit - For  =1,q=2- =1 and a linear drift function J(y) = (y eq -y)/  y the mean value becomes and the variance is with

6 YITP2/056 RDM:p-induced transverse energy spectra RDM-calculation for 200GeV p + Au Selected weighted solutions of the transport eq. at various impact parameters b NA 35 data scaled to 4  acceptance GW, Z. Phys. A 355, 301 (1996)

7 YITP2/057 Transverse energy spectra: SPS RDM-prediction @SPS energies, p L =157.7 A GeV  S NN = 17.3 GeV NA 49 data scaled to 4  acceptance Calorimeter data, integrated over all particle species

8 YITP2/058 Rapidity density distributions: Net protons, SIS Linear Relativistic Diffusion Model- calculations @SIS energies Ni-Ni, E cm = 1.06-1.93 A GeV; FOPI data: bell- shaped distributions (dashed: thermal equil.) GW, Eur. Phys. Lett. 47, 30 (1999)

9 YITP2/059 Rapidity density distributions: Net protons @AGS Linear Relativistic Diffusion Model- calculations @AGS energies Si-Al, p L = 14.6 GeV/c; Au-Au, p L = 11.4 GeV/c; E 814/ E877 data GW, Eur. Phys. Lett. 47, 30 (1999)

10 YITP2/0510 Central Collisions at AGS, SPS Rapidity density distributions evolve from bell-shape to double-hump as the energy increases from AGS (4.9 GeV) to SPS (17.3 GeV) Diffusion-model solutions are shown for SPS energies

11 YITP2/0511 Net proton rapidity spectra Linear RDM-calculations @SPS and RHIC energies SPS: Pb-Pb,  S NN = 17.3 GeV; NA 49 data RHIC: Au-Au,  S NN = 200 GeV; BRAHMS data GW, Phys. Rev. C 69, 024906 (2004) see also GW, Eur. Phys. J. A5, 85 (1999). High midrap.yield

12 YITP2/0512 RDM-solutions for Au-Au Rapidity density distributions of net protons for various values of t/  y Approach to thermal equilibrium for t/  y >>1 Continuous evolution of the distribution functions with time GW, Phys. Rev. C 69, 024906 (2004) y max = 5.36

13 YITP2/0513 RDM for Au-Au @ RHIC Net protons in central collisions Linear (solid curves) and nonlinear RDM-results; weak-coupling solution is dotted Midrapidity data require transition to thermal equilibrium (dashed area) Nonlinear solution: GW, Phys. Lett. B 569, 67 (2003)

14 YITP2/0514 Discontinuous evolution for Au-Au Rapidity density distributions of net protons for various values of t/  y Disontinuous evolution of the distribution functions with time towards the local thermal equilibrium distribution (22 protons) Thermal equilibrium (expanding) GW, Phys. Rev. C 69, 024906 (2004)

15 YITP2/0515 Central Au-Au @ RHIC vs. SPS BRAHMS data at  S NN =200 GeV for net protons Central 10% of the cross section Relativistic Diffusion Model for the nonequilibrium contributions Discontinuous transition to local statistical equilibrium at midrapidity indicates deconfinement. GW, PLB 569, 67 (2003) and Phys. Rev. C 69 (2004)

16 YITP2/0516 Central Au-Au at RHIC BRAHMS data at  S NN =200 GeV for net protons Central 5% of the cross section Relativistic Diffusion Model for the nonequilibrium contributions, plus Local statistical equilibrium at midrapidity (expanding source) Calc. GW (2004); data P. Christiansen (BRAHMS), Priv. comm.

17 YITP2/0517 Au-Au at RHIC RDM-prediction for 62.4 GeV (the lower RHIC energy measured by BRAHMS; data analysis is underway)

18 YITP2/0518 Heavy Relativistic Systems Parameters for heavy relativistic systems at AGS, SPS and RHIC energies. The beam rapidity is expressed in the c.m. system. The ratio  int /  y determines how fast the net-baryon system equilibrates in rapidity space. The effective rapidity diffusion coefficient is D y eff, the longitudinal expansion velocity v coll. *At 62.4 GeV, D y eff will need adjustement to forthcoming data.

19 YITP2/0519 d-Au 200 GeV net protons RDM-schematic calculation for d-Au:  3 sources model  yeq=0  Net protons  D from Au-Au (overestimated) -6-4-2 0 246 y 10 20 30 40 0 dn/dy

20 YITP2/0520 d-Au 200 GeV net protons RDM-schematic calculation for d-Au:  3 sources model  yeq as in GW, Z.Phys. A355, 301 (1996)  Net protons  D from Au-Au (overestimated) -6-4-2 0 246 y 10 20 30 40 0 dn/dy

21 YITP2/0521 3 sources RDM: Charged-hadron (pseudo-) rapidity distributions BRAHMS data at  S NN =200 GeV for charged hadrons Central collisions Relativistic Diffusion Model for the non-equil. plus equilibrium contributions (»3 sources«) n=N/N ch ; N ch ≈ 4630, 0-5% M. Biyajima et al., Prog. Theor. Phys.Suppl. 153, 344 (2004))

22 YITP2/0522 Produced particles in the 3 sources RDM: Charged-hadron (pseudo-) rapidity distributions M. Biyajima et al., Prog. Theor. Phys.Suppl. 153, 344 (2004) PHOBOS data at  S NN =130, 200 GeV for charged hadronsCentral collisions (0-6%) Number of particles in the 3 “sources”: 448:3134:448 @ 130 GeV 551:3858:551 @ 200 GeV Most of the produced charged hadrons at RHIC are in the equilibrated midrapidity region

23 YITP2/0523 Summary The Relativistic Diffusion Model describes/predicts net baryon and charged hadron transverse energy and rapidity distributions from SIS to RHIC accurately At SPS energies, net-proton rapidity spectra (dN/dy) show no signals yet for QGP formation At RHIC energies, there are indications for QGP formation (»third source«) from dN/dy : - A fraction of ≈22 net protons (≈55 net baryons) reaches local thermal equilibrium. - This transition is discontinuous and most likely due to an intermediary deconfinement of the constituent partons (quarks and gluons). Both nonequilibrium and equilibrium fractions of the distribution show strong longitudinal collective expansion.

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