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Energy Dependence of Soft Hadron Production

Christoph Blume. 2nd International Workshop on the Critical Point and Onset of Deconfinement Bergen Mar. 30 - Apr. 3, 2005. Energy Dependence of Soft Hadron Production. Critical point. 1st order transition.  B = 0 : cross over transition at T  170 MeV. Cross over line

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Energy Dependence of Soft Hadron Production

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  1. Christoph Blume 2nd International Workshop on the Critical Point and Onset of Deconfinement Bergen Mar. 30 - Apr. 3, 2005 Energy Dependence of Soft Hadron Production

  2. Critical point 1st order transition B = 0: cross over transition at T  170 MeV Cross over line from lattice QCD T = 0: 1st order transition Lattice calculations: Fodor and Katz Bielefeld-Swansea group The QCD Phase DiagramThe Simplified Version Phase boundary separating QGP and hadronic world Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  3. High energies (RHIC/LHC) B low QGP phase (most likely) reached Lower energies (AGS) B high System remains in hadronic phase Intermediate energies Vary B by studying nuclear collisions at different s Possible to locate where the phase boundary is reached? The QCD Phase DiagramHeavy Ion Reactions Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  4. SPS AGS RHIC The QCD Phase DiagramExperimental Observables • SPS energy regime allows to explore an essential part of the phase diagram • Transition to QGP is likely to happen at SPS energies • Ebeam = 20 - 158 AGeV (sNN = 6.3 - 17.3 GeV) • Use hadronic observables to pin down phase transition • Systematic studies:  Energy dependence of central A+A reactions Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  5. OutlineSoft Hadron Production • Soft physics regime • pt < 2 GeV/c • Bulk properties of particle production • Rapidity Spectra • Longitudinal expansion • Particle Yields • Strangeness • Chemical freeze-out conditions • Transverse Mass Spectra • Transverse expansion ( EOS?) • Thermal freeze-out conditions • Fluctuations • K/ (p/) fluctuations Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  6. Rapidity Spectra Central Pb+Pb 7% (20-80) 5/10% (158) NA49 Change of shape only for L Others: ~ Gaussians Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  7. Rapidity SpectraPions Central Pb+Pb/Au+Au Comparison AGS, SPS, and RHIC Single Gaussians! Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  8. Rapidity SpectraEnergy Dependence of Widths Pion widths are close to Landau prediction, but not perfectly But: Perfect agreement to linear dependence on ybeam Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  9. Rapidity SpectraEnergy Dependence of Widths Linear dependence on ybeam Clear hierarchy for Gaussian-like particles at SPS (p, ,  excluded):  > K+ > K-,  >  Seems to break down at AGS Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  10. Rapidity SpectraMass Dependence of Widths  negatives Approx. linear dependence on particle mass Similar slope at all SPS energies  Thermal component of longitudinal flow Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  11. Rapidity SpectraDependence on Strangeness Content Central Pb+Pb, 158 AGeV NA49 Net protons: 3 valence quarks (uud ) Net s: 2 valence (ud ) + 1 produced quark (s ) Net s: 1 valence (d ) + 2 produced quarks (ss ) Omegas: 3 produced quarks (sss ) Net protons difficult to reconcile with pure Landau ! Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  12. Particle Yields AGS NA49 BRAHMS Central Au+Au, Pb+Pb 4 multiplicities only! Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  13. Particle YieldsStatistical Hadron Gas Model Becattini et al., Phys. Ref. C69 (2004) 024905 Assumption of chemical equilibrium at the freeze-out point  Particle production can be described with a few parameters: V, T, B, s Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  14. Particle YieldsPhase Diagram (II): Chemical Freeze-Out Chemical freeze-out points approach phase boundary at top SPS energies Does the system cross the phase boundary ? And if yes, where ? Freeze-out curve at E /N = 1GeV Cleymans and Redlich PRL 81 (1998) 5284 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  15. / K+/+ -/ K-/- / -++/ Particle YieldsEnergy Dependence Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  16. UrQMD HSD E.L. Bratkovskaya et al., PRC 69 (2004), 054907 / K+/+ -/ K-/- / -++/ Particle YieldsEnergy Dependence Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  17. Statistical hadron gas model: s = 1 P. Braun-Munzinger, J. Cleymans, H. Oeschler, and K. Redlich Nucl. Phys. A697 (2002) 902 / K+/+ -/ K-/- / -++/ Particle YieldsEnergy Dependence Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  18. Statistical hadron gas model: s free F. Becattini, M. Gazdzicki, A. Keränen, J. Manninen, R. Stock PRC 69 (2004), 024905 / K+/+ -/ K-/- / -++/ Particle YieldsEnergy Dependence Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  19. s-quark carriers: K-, K0(1)  (incl. 0) 0,-, - (2) ±(3) s-quark carriers: K+, K0(1)  (incl. 0) 0,+, + (2) ±(3) (1)K0  K+, K0  K- by isospin symmetry (2)Taken from hadron gas fit by F. Becattini et al., if not measured. (3)Empirical factor ( + ) /  = 1.6 assumed. Energy dependence of strangeness production changes at  30 AGeV Particle YieldsComparison s- and s-Carriers Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  20. Maximum in strangeness/pion ratio Same for s and s quarks Particle Yields(Anti-)Strangeness to Pion Ratio Difficult to model Solid line: Statistical hadron gas model with s = 1 K. Redlich, priv. comm. Predicted as signal for the onset of deconfinement M. Gazdzicki and M.I. Gorenstein, Acta Phys. Polon. B30 (1999), 2705 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  21. Transverse Mass Spectra Central (7%) Pb+Pb NA49 Radial flow fit (“Blast Wave”) 20 AGeV 30 AGeV Here: tindependent of r Schnedermann, Sollfrank, and Heinz, Phys. Rev. C46 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  22. Transverse Mass Spectra p - K- Model: U. Wiedemann and U. Heinz, Phys. Rev. C56 (1997) 3265 B. Tomasik, nucl-th/0304079 Data: E895: nucl-ex/0306033 NA49: Phys. Rev. C66 (2002) 054902, nucl-ex/0403023 PHENIX: Phys. Rev. C69 (2004) 024904, nucl-ex/0307022 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  23. Transverse Mass SpectraEnergy Dependence of Fit Parameter Fit to -, K- and p Tch Box-shaped source profile and linear velocity profile Fit range 0.1 < mt-m0 < 0.8 GeV Energy dependence of Tf seems to change around 30 AGeV Thermal and chemical freeze-out different? Single freeze-out model? Continous increase of T Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  24. Transverse Mass SpectraPhase Diagram (III): Thermal Freeze-Out Thermal freeze-out seems to be at lower temperature than chemical freeze-out from top AGS energies on Strongly model dependent ! Single freeze-out models ? Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  25. Transverse Mass SpectraInverse Slope Parameters of Kaons Step in energy dependence Seems to be absent in p+p How about other particle types? p+p compilation from: M. Kliemant, B. Lungwitz, and M. Gazdzicki, PRC 69 (2004) 044903 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  26. Transverse Mass SpectraEnergy Dependence of mt-m0  negatively charged Energy dependence of transverse activity seems to change around 30 AGeV. General feature for pion, kaons and protons Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  27. Transverse Mass SpectraInverse Slope Parameters of Kaons Feature cannot be described by transport models Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  28. Transverse Mass SpectraInverse Slope Parameters of Kaons Hydro calculation Y. Hama et al. Braz. J. Phys. 34 (2004), 322, hep-ph/0309192 Assuming 1st order phase transition Initial conditions from NeXus  Change of EOS seen? Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  29. Elliptic FlowEnergy Dependence Initial spatial anisotropy  different pressure gradients  momentum anisotropy v2 Mid-rapidity data, pt integrated Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  30. 30 AGeV Elliptic FlowEnergy Dependence + Transport Model Data show saturation of scaled v2 Points to an initial QGP pressure from 30 AGeV on ! M. Bleicher, SQM04 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  31. FluctuationsThe Critical Point Endpoint of the first order phase transition line  crossover on left side Position quite uncertain But recent lattice calculations by Fodor and Katz predicts position at B = 360 MeV using physical quark masses It might be accessible in the SPS energy range Observables:Event-by-event fluctuations Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  32. 160 GeV preliminary 20 GeV preliminary s= RMS/Mean * 100 [%] s2dynamic = s2data - s2mix FluctuationsParticle Ratios Event-by-event fluctuations of e.g. K/ • Compare to mixed event • reference • Resolution • Finite number statistics NA49  Extraction of dynamical fluctuations NA49 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  33. FluctuationsEnergy Dependence of K/p Fluctuations Data wider than mixed events reference Clear energy dependence of K/p fluctuations observed  Decrease with energy Fluctuation from UrQMD independent of energy Non-zero value due to energy and strangeness conservation preliminary Promising, but no clear evidence for critical point yet Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  34. FluctuationsEnergy Dependence of p/p Fluctuations • Data narrower than reference • Can be caused by resonances Clear energy dependence of p/p fluctuations observed  Increase with energy preliminary • Similar trend seen in UrQMD • Resonance contribution changes with beam energy Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  35. Summary • Systematic study of energy dependence (still ongoing) • Rapidity and transverse mass spectra • Particle Yields • Fluctuations • A variety of interesting features have been revealed: • Mass dependence of rapidity widths, seemingly independent of beam energy at SPS • Clear change of the energy dependence of mt-spectra at 30 AGeV  Evidence for a change of EOS? • Maximum in the strangeness to pion ratio at 30 AGeV  Evidence for deconfinement? • Outlook: Search for critical point • No clear evidence yet (K/ fluctuations)  dedicated search with future projects (SPS, FAIR) Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  36. The End Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  37. Particle YieldsEnergy Dependence Central Pb+Pb/Au+Au Mid-rapidity ratios Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  38. Transverse Mass SpectraBlast Wave Model • Basic blast wave model: • Common freeze-out of all particle types • Boost invariant longitudinal expansion • Transverse expansion is modelled by a velocity profile • “Standard” version: Schnedermann, Sollfrank, and Heinz, Phys. Rev. C46 • Extended version: • Resonance contribution included • Baryonic resonances introduce dependence on B • Chemical freeze-out: Tch and B taken from freeze-out curve • Thermal freeze-out: System cools down, therefore assume: • Conservation of entropy • Conservation of effective particle numbers U. Wiedemann and U. Heinz, Phys. Rev. C56 (1997) 3265 B. Tomasik, nucl-th/0304079 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  39. Rapidity DistributionsLandau Scenario in p+p Pion production ~ Entropy Isentropic expansion Description of the pion gas as a 3D relativistic fluid L. D. Landau, Izv. Akad. Nauk. SSSR 17 (1953) 52 P. Carruthers and M. Duong-Van, Phys. Ref. D8 (1973) 859 Prediction: dN/dy is Gaussian of a width  = 2L given by: (simplified model) Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  40. Rapidity SpectraKaons Single Gaussian works reasonably well for K- Does not really work for K+ at lower SPS energies  Use RMS Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  41. / K+/+ -/ K-/- / -++/ Particle YieldsEnergy Dependence Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  42. (*) M.I. Gorenstein, K. A. Bugaev and M. Gazdzicki, PRL. 88 (2002), 132301. B1 linear 90 0.5 Fit to K, p, ,  B2 linear 170 0.2 Fit to J/ and ’ (*) Transverse Mass SpectraThe Omega Evidence for early freeze-out of the Omega from blast wave fits? NA49 publication: C. Alt et al., nucl-ex/0409004 Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  43. yP yT yP yT y y y y y’T y’P y0 y0 Rapidity SpectraRapidty Shift y Baryon number distributions at lower energies: higher energies: How does the rapidity shift y evolve with beam energy? Determines the energy available in the produced fireball Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  44. Energy loss E : RHIC (sNN = 200 GeV): E/Nucleon = 73 ± 6 GeV Rapidity SpectraEnergy Dependence of y  BRAHMS, I.G. Bearden et al. PRL 93 (2004), 102301 Rapidity shift: Seems to increase linearly at AGS and SPS: y /ybeam  0.27 But: Weaker increase to RHIC energies! Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  45. Rapidity SpectraEnergy Dependence ofNet-Protons BRAHMS, I.G. Bearden et al. PRL 93 (2004), 102301 The shape of the distributions changes dramatically with energy AGS: baryonic system  RHIC: mesonic system  Large implications in the hadronic sector Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

  46. Transverse Mass SpectraInverse Slope Parameters of Kaons Model comparisons M. Bleicher, SQM04 Additional resonances? UrQMD 2.1 Initial QGP pressure? Christoph Blume Bergen Workshop, Mar.30-Apr.3 2005

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