Review of Structures in the Energy Dependence of Hadronic Observables Christoph BlumeInt. Workshop on Critical Point and Onset of Deconfinement Florence, July 3-6, 2006

Christoph Blume Florence, July Introduction Exploring the QCD Phase Diagram Cross over Critical point Lattice calculations: Fodor and Katz Bielefeld-Swansea group Hadron gas fits ( ): J. Manninen et al. 1st order Chemical freeze-out points approach phase boundary at SPS energies Transition to QGP likely to happen in this region E beam = AGeV (  s NN = GeV)

Christoph Blume Florence, July Introduction Energy Dependence Any evidence for a phase transition (or the even critical point) in hadronic observables seen ? Look for “non-smooth” behaviour in the energy dependencies Prominent examples: “horn”, “kink”, “step” Any other structures? How significant are they? Comparison to hadronic models Transport models (UrQMD + HSD) Statistical models Identify “trivial” structures Baseline comparison

Christoph Blume Florence, July Introduction Hadronic Scenery at SPS J. Cleymans, H. Oeschler, K. Redlich, and S. Wheaton, hep-ph/ Transition from baryon dominated to meson dominated system Statistical model: Transition at  s NN  8 GeV Maximum of strangeness prod. Evidences for structures beyond this?

Christoph Blume Florence, July Introduction ”Horn” / “Kink” / “Step”  K +  +   /  N w  HORN KINK STEP

Christoph Blume Florence, July Introduction Experiments AGS SPS RHIC ExperimentsE beam (A GeV)  s nn (GeV)SystemParticles AGS E802, E866, E877, E891, E895, E Au+Au , K, p,  SPS NA45, NA49, NA57, (NA44, WA98) Pb+Pb , K, p, , , , ,... RHIC STAR, PHENIX, BRAHMS, PHOBOS Au+Au , K, p, , , , ,...

Christoph Blume Florence, July Introduction Observables Particle yields Pions Strangeness Transverse mass spectra Radial flow  EOS Elliptic flow Initial pressure Bose-Einstein correlations System size and lifetime Not discussed here: Fluctuations

Christoph Blume Florence, July Particle Yields Energy Dependence of Particle Ratios  K +  /  +   K -  /  -   /   /   -  /   - +  +  /  UrQMD + HSD E.L. Bratkovskaya et al., PRC 69 (2004), Statistical hadron gas: P. Braun-Munzinger, J. Cleymans, H. Oeschler, and K. Redlich Nucl. Phys. A697 (2002) 902  s = 1 Full chem. equilibrium baseline

Christoph Blume Florence, July Particle Yields Comparison to Statistical Model (data – model)/  (data) Statistical hadron gas: P. Braun-Munzinger, J. Cleymans, H. Oeschler, and K. Redlich Nucl. Phys. A697 (2002) 902 Kaons and  deviate from stat. model for  s NN  7-8GeV ? ? Different situation for hyperons  s = 1

Christoph Blume Florence, July Particle Yields Position of Maxima Ratio Maximum at  s NN (GeV) K+/+K+/ // 5.1 -/+-/ -/+-/ Statistical model prediction: J. Cleymans, H. Oeschler, K. Redlich, and S. Wheaton, hep-ph/

Christoph Blume Florence, July Particle Yields Local Slope of Energy Dependence:  and K No significant structure for pions Indications for sudden changes in kaon e.-dependence (?)

Christoph Blume Florence, July Particle Yields Comparison s- and s-Carriers s-quark carriers: K -, K 0 (1)  (incl.  0 )  0,-,  - (2)  ± (3) s-quark carriers: K +, K 0 (1)  (incl.  0 )  0,+,  + (2)  ± (3) (1)  K 0    K + ,  K 0    K -  by isospin symmetry (2) Taken from hadron gas fit by Becattini et al., if not measured. (3) Empirical factor (    +  ) /  = 1.6 assumed. Data: E802, E866, E895, E917, NA49  1.5 (  +  +  -  ) Sudden change of strangeness production at  s NN = 7-8GeV ?

Christoph Blume Florence, July Particle Yields Local Slope of Energy Dep.: s/s-Quarks Local slope seems to change quite fast for strangeness at  s NN = 7-8GeV Smoother dependence for pions

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

Christoph Blume Florence, July Transverse Mass Spectra Energy Dependence of  m t  -m 0 Energy dependence of transverse activity seems to change around  s NN = 7-8GeV General feature for pion, kaons and protons Quite robust observation  negatively charged

Christoph Blume Florence, July Transverse Mass Spectra Local Slope of Energy Dependence:  m t  -m 0 Significant change of local slope for pions and kaons around  s NN = 7 GeV Similar for protons

Christoph Blume Florence, July Elliptic Flow Energy Dependence of v 2 for Pions Initial spatial anisotropy  different pressure gradients  momentum anisotropy v 2 Mid-rapidity data, p t integrated Energy dependence changes in SPS region

Christoph Blume Florence, July Elliptic Flow Model Comparison of v 2 for Pions H. Petersen, Hot Quarks06 Squeeze-out at lower energies not described w/o nuclear potential Energy dependence of v 2 not described by UrQMD At higher energies: lack of inital pressure! Indication for onset of partonic flow at SPS?

Christoph Blume Florence, July Elliptic Flow v 2 for Protons at 40A GeV ? NA49 PRC 68 (2003) Disappearance of proton flow? Evidence for 1 st order phase transition H. Stöcker, nucl-th/ Standard method different to cumulant method at mid-rapidity Larger systematic error Systematic study with higher precision needed Challenge for future experiments!

Christoph Blume Florence, July Bose-Einstein Correlations Energy Dependence of Radius Parameters

Christoph Blume Florence, July Bose-Einstein Correlations Energy Dependence of Radius Parameters k t  0.2GeV/c No indication for strong energy dependence between AGS and RHIC Structures? But: Unresolved discrepancies between SPS experiments!

Christoph Blume Florence, July Bose-Einstein Correlations Model Comparison: UrQMD NA49 data 20A – 158A GeV Reasonable description by transport model (R 2 out -R 2 side ) 1/2 slightly larger in model M. Bleicher, GRC06 QingFeng Li, Frankfurt

Christoph Blume Florence, July Bose-Einstein Correlations Model Comparison: UrQMD No structure in energy dependence in data and transport model  Data M. Bleicher, GRC06 QingFeng Li, Frankfurt

Christoph Blume Florence, July Summary Evidences for structures in hadronic exciation functions Around  s NN = 7-8GeV Particle Yields Qualitatively close to to statistical model expectations Clear deviations seen for kaons and  Maxima in X/  ratios as in stat. model ? Indication for sudden change in strangeness e.-dep. Transverse mass spectra Sudden change of  m t  Change of radial flow  EOS ? Elliptic flow No clear evidence, higher presision data needed Bose-Einstein correlations No evidence for structure High precision data mandatory!

Christoph Blume Florence, July Thanks!

Christoph Blume Florence, July High p t Energy Dependence of R CP for Pions and h - ? R pA Strongest drop of R CP between  s = 17.3GeV and  s = 62.4GeV Any onset at low energies? SPS

Christoph Blume Florence, July Particle Yields Energy Dependence of K + /  + Central Pb+Pb/Au+Au Mid-rapidity ratios Same structure as for 4 

Christoph Blume Florence, July Particle Yields Energy Dependence of 4  Yields AGSNA49BRAHMS Central Au+Au, Pb+Pb Access to the energy dependence of identified particle yields in the range  s NN = 2.5 – 200 GeV

Christoph Blume Florence, July Transverse Mass Spectra Inverse Slope Parameters of Kaons Feature cannot be described by transport models Y. Hama et al. Braz. J. Phys. 34 (2004), 322, hep-ph/ Hydro calculation with assumption of 1st order phase transition  Change of EOS seen?

Christoph Blume Florence, July 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

Christoph Blume Florence, July Transverse Mass Spectra “Hydro” - Model Basic 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 Florence, July Transverse Mass Spectra “Hydro” – Model Fits E895: nucl-ex/ NA49: Phys. Rev. C66 (2002) , nucl-ex/ PHENIX: Phys. Rev. C69 (2004) , nucl-ex/ Convave  Resonances ExponentialShoulder  Radial flow -- K - p

Christoph Blume Florence, July 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 Florence, July Transverse Mass Spectra Blast Wave Fits Good description of all particle species at SPS energies Blast wave implementation: F. Retiere and M. Lisa nucl-th/ Fit parameters:

Christoph Blume Florence, July Bose-Einstein Correlations Blast Wave Model Fits Combined fit to HBT radii and transverse mass spectra Good fit to the data slight deviations in R side at high k t Blast wave implementationn: M. Lisa, F. Retiere, nucl-th/ Emission function: Fit parameters:

Christoph Blume Florence, July Bose-Einstein Correlations Thermal Freeze-Out Parameters T chem J. Cleymans, K. Redlich, Phys. Rev. C60, (1999) Slightly increasing temperature with beam energy Approx. constant transverse geometrical Radii (R box  2R gauss ) Finite emission duration at SPS energies

Christoph Blume Florence, July Bose-Einstein Correlations Energy Dependence of Freeze-Out Volume D. Adamová et al. (CERES collaboration), Phys. Rev. Lett. 90 (2003) Minimum in freeze-out volume in SPS region Possible explanation: Constant mean free path freeze-out condition Transition baryon  meson dominated But: Unresolved inconsistencies between SPS experiments!

Christoph Blume Florence, July Bose-Einstein Correlations Energy Dependence of Freeze-Out Volume k t  0.15GeV/c

Christoph Blume Florence, July Particle Yields Antilambda-Antiproton Ratio Increase above 1 towards lower energies consistent with recent NA49 data Models predict ratio < 1 Hadron Gas 1: J. Manninen et al. Hadron Gas 2: K. Redlich et al. Hadron Gas 3: J. Rafelski et al.

Christoph Blume Florence, July Particle Yields Antibaryon-Baryon Ratio Strong increase of B/B ratio in SPS energy range Energy dependence weakens with increasing strangeness content Lines: Statistical hadron gas model J. Manninen et al. Fit to 4  data! NA49 preliminary No indications for structures in energy dependence