Energy Dependence of Soft Hadron Production Christoph Blume2nd International Workshop on the Critical Point and Onset of Deconfinement Bergen Mar Apr. 3, 2005

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

Christoph Blume Bergen Workshop, Mar.30-Apr The QCD Phase Diagram Heavy Ion Reactions 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?

Christoph Blume Bergen Workshop, Mar.30-Apr  SPS energy regime allows to explore an essential part of the phase diagram –Transition to QGP is likely to happen at SPS energies –E beam = AGeV (  s NN = GeV)  Use hadronic observables to pin down phase transition  Systematic studies:  Energy dependence of central A+A reactions The QCD Phase Diagram Experimental Observables AGS SPS RHIC

Christoph Blume Bergen Workshop, Mar.30-Apr Outline Soft Hadron Production  Soft physics regime –p t < 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 Rapidity Spectra Central Pb+Pb 7% (20-80) 5/10% (158) NA49 Change of shape only for  Others: ~ Gaussians

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

Christoph Blume Bergen Workshop, Mar.30-Apr Rapidity Spectra Energy Dependence of Widths Pion widths are close to Landau prediction, but not perfectly But: Perfect agreement to linear dependence on y beam

Christoph Blume Bergen Workshop, Mar.30-Apr Rapidity Spectra Energy Dependence of Widths Linear dependence on y beam 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 Rapidity Spectra Mass Dependence of Widths Approx. linear dependence on particle mass Similar slope at all SPS energies  Thermal component of longitudinal flow  negatives

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

Christoph Blume Bergen Workshop, Mar.30-Apr Particle Yields AGSNA49BRAHMS Central Au+Au, Pb+Pb 4  multiplicities only!

Christoph Blume Bergen Workshop, Mar.30-Apr Particle Yields Statistical Hadron Gas Model Becattini et al., Phys. Ref. C69 (2004) 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 Particle Yields Phase 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 Particle Yields Energy Dependence  K +  /  +   K -  /  -   /   /   -  /   - +  +  / 

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

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

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

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

Christoph Blume Bergen Workshop, Mar.30-Apr Particle Yields (Anti-)Strangeness to Pion Ratio Maximum in strangeness/pion ratio Same for s and s quarks 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 Transverse Mass Spectra 20 AGeV30 AGeV Central (7%) Pb+Pb NA49 Schnedermann, Sollfrank, and Heinz, Phys. Rev. C46 Radial flow fit (“Blast Wave”) Here:  t independent of r

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

Christoph Blume Bergen Workshop, Mar.30-Apr Transverse Mass Spectra Energy Dependence of Fit Parameter Fit to  -, K - and p Box-shaped source profile and linear velocity profile Fit range 0.1 < m t -m 0 < 0.8 GeV Energy dependence of T f seems to change around 30 AGeV Thermal and chemical freeze-out different? Single freeze-out model? Continous increase of  T  T ch

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

Christoph Blume Bergen Workshop, Mar.30-Apr Transverse Mass Spectra Energy Dependence of  m t  -m 0 Energy dependence of transverse activity seems to change around 30 AGeV. General feature for pion, kaons and protons  negatively charged

Christoph Blume Bergen Workshop, Mar.30-Apr Transverse Mass Spectra Inverse Slope Parameters of Kaons Feature cannot be described by transport models

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

Christoph Blume Bergen Workshop, Mar.30-Apr Elliptic Flow Energy Dependence Mid-rapidity data, p t integrated Initial spatial anisotropy  different pressure gradients  momentum anisotropy v 2

Christoph Blume Bergen Workshop, Mar.30-Apr Elliptic Flow Energy Dependence + Transport Model 30 AGeV Data show saturation of scaled v 2 M. Bleicher, SQM04 Points to an initial QGP pressure from 30 AGeV on !

Christoph Blume Bergen Workshop, Mar.30-Apr Fluctuations The 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 GeV preliminary Fluctuations Particle Ratios preliminary 160 GeV Compare to mixed event reference  Resolution  Finite number statistics  Extraction of dynamical fluctuations  2 dynamic =  2 data -  2 mix  = RMS/Mean * 100 [%] Event-by-event fluctuations of e.g. K/  NA49

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

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

Christoph Blume Bergen Workshop, Mar.30-Apr 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 m t -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 The End

Christoph Blume Bergen Workshop, Mar.30-Apr Particle Yields Energy Dependence Central Pb+Pb/Au+Au Mid-rapidity ratios

Christoph Blume Bergen Workshop, Mar.30-Apr Transverse Mass Spectra Blast 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: T ch 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/

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

Christoph Blume Bergen Workshop, Mar.30-Apr Rapidity Spectra Kaons 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 Particle Yields Energy Dependence  K +  /  +   K -  /  -   /   /   -  /   - +  +  / 

Christoph Blume Bergen Workshop, Mar.30-Apr Transverse Mass Spectra The Omega Evidence for early freeze-out of the Omega from blast wave fits? Blast Wave Model Velocity Profile T f (MeV)  t  Aconstant1250.5from fits shown before (*) M.I. Gorenstein, K. A. Bugaev and M. Gazdzicki, PRL. 88 (2002), Fit to K, p, ,  0.590linearB1 Fit to J/  and  ’ (*)0.2170linearB2 NA49 publication: C. Alt et al., nucl-ex/

Christoph Blume Bergen Workshop, Mar.30-Apr Rapidity Spectra Rapidty Shift  y yPyP yTyT y0y0 yy yy y0y0 yPyP yTyT yy yy y’ P y’ T How does the rapidity shift  y evolve with beam energy? Determines the energy available in the produced fireball Baryon number distributions at lower energies:higher energies:

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

Christoph Blume Bergen Workshop, Mar.30-Apr Rapidity Spectra Energy Dependence of Net-Protons BRAHMS, I.G. Bearden et al. PRL 93 (2004), 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 Transverse Mass Spectra Inverse Slope Parameters of Kaons Model comparisons M. Bleicher, SQM04 Additional resonances? UrQMD 2.1 Initial QGP pressure?