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Diffusion and local deconfinement in relativistic systems

Explore Relativistic Diffusion Model for baryon interactions, indicating local deconfinement and QGP formation at RHIC energies. Analysis of transverse energy and rapidity distributions at various collision energies.

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Diffusion and local deconfinement in relativistic systems

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

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

  3. 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. 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 pT, or ET -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. Linear RDM - For m=1,q=2-n=1 and a linear drift function J(y) = (yeq-y)/y the mean value becomes • The rapidity relaxation time y determines the peak positions • The rapidity diffusion coefficient Dy is calculated from y and the equilibrium temperature T in the weak-coupling limit and the variance is with

  6. 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. Transverse energy spectra: SPS • RDM-prediction @SPS energies, pL=157.7 A GeV • SNN= 17.3 GeV • NA 49 data scaled to 4 acceptance • Calorimeter data, integrated over all particle species

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

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

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

  12. 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 ymax= 5.36 GW, Phys. Rev. C 69, 024906 (2004)

  13. 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. 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. Central Au-Au @ RHIC vs. SPS • BRAHMS data at SNN=200GeV 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. Central Au-Au at RHIC • BRAHMS data at SNN=200GeV 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. Au-Au at RHIC RDM-prediction for 62.4 GeV (the lower RHIC energy measured by BRAHMS; data analysis is underway)

  18. 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 tint/y determines how fast the net-baryon system equilibrates in rapidity space. The effective rapidity diffusion coefficient is Dyeff, the longitudinal expansion velocity vcoll. *At 62.4 GeV, Dyeff will need adjustement to forthcoming data.

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

  20. d-Au 200 GeV net protons 40 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) 30 dn/dy 20 10 0 -6 -4 -2 0 2 4 6 y

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

  22. Produced particles in the 3 sources RDM: Charged-hadron (pseudo-) rapidity distributions PHOBOS data at SNN=130, 200GeV for charged hadrons Central 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 M. Biyajima et al., Prog. Theor. Phys.Suppl. 153, 344 (2004)

  23. 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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