Christoph Blume University of Frankfurt Winter Workshop on Nuclear Dynamics, 2010, Ochos Rios, Jamaica Particle Production at the SPS and the QCD Phase Diagram Christoph Blume University of Frankfurt 26 th Winter Workshop on Nuclear Dynamics Ocho Rios, Jamaica January 2010

Outline Christoph Blume WWND 2010, Ocho Rios, Jamaica 1 How to probe different regions of the QCD phase diagram? Variation of center-of-mass energy Way of scanning different freeze-out parameters T and μ B Variation of system size How do T and μ B depend on system size Core corona approach Critical point search Systematic study of multiplicity fluctuations Other observables How to probe different regions of the QCD phase diagram? Variation of center-of-mass energy Way of scanning different freeze-out parameters T and μ B Variation of system size How do T and μ B depend on system size Core corona approach Critical point search Systematic study of multiplicity fluctuations Other observables

QCD Phase Diagram Christoph Blume WWND 2010, Ocho Rios, Jamaica 2 A. Andronic et al., arXiv: L. McLarren and R.D. Pisarski, Nucl. Phys. A796, 83 (2007).

Christoph Blume WWND 2010, Ocho Rios, Jamaica 3 QCD Phase Diagram Experimental Access High energies (RHIC/LHC)  B small System reaches QGP phase Low energies (AGS)  B large System stays in hadronic phase In between (SPS/FAIR) Variation of  B by changing  s NN Possible to localize critical point? Other control parameters (e.g. system size)?

Christoph Blume WWND 2010, Ocho Rios, Jamaica 4 Significant change of shape at SPS energies Peak  dip structure Rapid change of net-baryon density at y = 0  Strong variation of  B Significant change of shape at SPS energies Peak  dip structure Rapid change of net-baryon density at y = 0  Strong variation of  B Energy Dependence Net-Baryon Distributions BRAHMS Phys. Rev. Lett. 93 (2004), A GeV Phys. Rev. Lett. 82 (1999), 2471 E802 Phys. Rev. C 60 (1999), NA49 preliminary Central Pb+Pb/Au+Au

5 Energy Dependence Example:  /π- and  /π-Ratios NA49 data Phys. Rev. C78, (2008) Statistical models Generally good description at all energies Fixes parameters T and μ B NA49 data Phys. Rev. C78, (2008) Statistical models Generally good description at all energies Fixes parameters T and μ B |y| < 0.4 |y| < 0.5 SHM(B): A. Andronic et al. Nucl. Phys. A 772, 167 (2006). UrQMD: M. Bleicher et al., J. Phys. G 25, 1856 (1999) and private communication HSD: E. Bratkovskaya et al., Phys. Rev. C69, (2004) // // − -/-/ +/+/ −  = 1.5 (  + +  - ) Christoph Blume WWND 2010, Ocho Rios, Jamaica

6 Results from different beam energies Analysis of particle yields with statistical models Freeze-out points reach QGP phase boundary at top SPS energies Caveat: Disagreement between different LQCD results on T C Results from different beam energies Analysis of particle yields with statistical models Freeze-out points reach QGP phase boundary at top SPS energies Caveat: Disagreement between different LQCD results on T C QCD Phase Diagram Data Points F. Becattini et al., Phys Rev. C69, (2004).

System Size Dependence Freeze-out Parameter Christoph Blume WWND 2010, Ocho Rios, Jamaica 7 How do freeze-out parameters depend on system size ? Statistical model fits result in different T Central reactions Way to move around in phase diagram? How do freeze-out parameters depend on system size ? Statistical model fits result in different T Central reactions Way to move around in phase diagram? F. Becattini et al., Phys. Rev. C73, (2005)

Christoph Blume WWND 2010, Ocho Rios, Jamaica 8 System Size Dependence (Anti-)Proton y-Spectra Preliminary data by NA49 Minimum bias Pb+Pb at 158A GeV Preliminary data by NA49 Minimum bias Pb+Pb at 158A GeV NA49 preliminary NA49 preliminary p p H. Ströbele et al. arXiv:

Christoph Blume WWND 2010, Ocho Rios, Jamaica 9 System Size Dependence Net-Protons NA49 preliminary p - p Cen. Per. No strong system size dependence observed No strong system size dependence observed Peripheral spectrum slightly more pronounced y-dependence than central one Beam rapidity not measured! In measured rapdity range similar shape like p+p data ⇒ System size has no big influence on μ B p+p Data: M. Aguilar-Benitz et al., Z. Phys. C 50 (1991), 405. NA49 preliminary central per. p+p

10 System Size Dependence Enhancement factors of , , and  Enhancement factor p+p data: NA49 Early saturation  N w  > 60 Core Corona Model f (N W ) = fraction of nucleons that scatter more than once F. Becattini and J. Manninen, J. Phys. G35, (2008) K. Werner, Phys. Rev. Lett. 98, (2007) J. Aichelin and K. Werner, arXiv: Enhancement factor p+p data: NA49 Early saturation  N w  > 60 Core Corona Model f (N W ) = fraction of nucleons that scatter more than once F. Becattini and J. Manninen, J. Phys. G35, (2008) K. Werner, Phys. Rev. Lett. 98, (2007) J. Aichelin and K. Werner, arXiv: C+C 158A GeV Si+Si Pb+Pb Christoph Blume WWND 2010, Ocho Rios, Jamaica

11 System Size Dependence Average Transverse Mass:  m t  -m 0 Similar dependence as for multiplicities observed Early saturation  N w  > 60 Core Corona model f(N W ) = fraction of nucleons, that scatter more than once F. Becattini and J. Manninen, J. Phys. G35, (2008) K. Werner, Phys. Rev. Lett. 98, (2007) J. Aichelin and K. Werner, arXiv: NA49 data: Phys. Rev. C80 (2009), Similar dependence as for multiplicities observed Early saturation  N w  > 60 Core Corona model f(N W ) = fraction of nucleons, that scatter more than once F. Becattini and J. Manninen, J. Phys. G35, (2008) K. Werner, Phys. Rev. Lett. 98, (2007) J. Aichelin and K. Werner, arXiv: NA49 data: Phys. Rev. C80 (2009), |y| < 0.4 (0.5) Christoph Blume WWND 2010, Ocho Rios, Jamaica

System Size Dependence Core-Corona: Central ↔ Peripheral Christoph Blume WWND 2010, Ocho Rios, Jamaica 12 Core Corona model f(N part ) = fraction of nucleons, that scatter more than once Centrality dependence Stronger for smaller systems Central reactions Still clear change of f max with system size Compare f max (Pb+Pb) ≈ 0.9 and f max (C+C) ≈ 0.65 ⇒ apparent change of T + μ B Not real, just different mixture of core and corona Thanks to K. Reygers for providing the Glauber code Core Corona model f(N part ) = fraction of nucleons, that scatter more than once Centrality dependence Stronger for smaller systems Central reactions Still clear change of f max with system size Compare f max (Pb+Pb) ≈ 0.9 and f max (C+C) ≈ 0.65 ⇒ apparent change of T + μ B Not real, just different mixture of core and corona Thanks to K. Reygers for providing the Glauber code System size is not a good control parameter to move around in QCD phase diagram System size is not a good control parameter to move around in QCD phase diagram

System Size Dependence Core-Corona: Asymmetric Systems Christoph Blume WWND 2010, Ocho Rios, Jamaica 13 Core Corona model f(N part ) = fraction of nucleons, that scatter more than once Centrality dependence Peculiar shape for small projectiles (e.g. C, O, Si, S) Core Corona model f(N part ) = fraction of nucleons, that scatter more than once Centrality dependence Peculiar shape for small projectiles (e.g. C, O, Si, S) Limiting case: p + A f(N part ) = 1 / N part Model applicable in p+A? First attempt in T. Šuša et al., Nucl. Phys. A698 (2002) 491c

Christoph Blume WWND 2010, Ocho Rios, Jamaica 14 Critical Point Theoretical Predictions M. Stephanov, CPOD conference 09 Lattice QCD difficult for  B > 0 Sign problem in Fermion-determinant Progress in recent years (e.g. Fodor and Katz) Results strongly divergent Typically  B > 200 MeV Perhaps no critical point at all for  B < 500 MeV (de Forcrand and Philipsen) Lattice QCD difficult for  B > 0 Sign problem in Fermion-determinant Progress in recent years (e.g. Fodor and Katz) Results strongly divergent Typically  B > 200 MeV Perhaps no critical point at all for  B < 500 MeV (de Forcrand and Philipsen)

Critical Point Observables Christoph Blume WWND 2010, Ocho Rios, Jamaica 15 Elliptic flow v 2 R. A. Lacey et al., arXiv: : η/s versus T and μ B. E. Shuryak, arXiv:hep-ph/ : Decrease (increase) of baryon (meson) flow. Higher experimental precision required. m t -Spectra of baryons and anti-baryons Asakawa et al., Phys. Rev. Lett. 101 (2008) Higher experimental precision required. Di-pion (sigma) intermittency study T. Anticic et al., arXiv No unambiguous signal seen yet Fluctuations: multiplicity and/or 〈 p t 〉 Stephanov, Rajagopal, Shuryak, Phys. Rev. D60 (1999), Elliptic flow v 2 R. A. Lacey et al., arXiv: : η/s versus T and μ B. E. Shuryak, arXiv:hep-ph/ : Decrease (increase) of baryon (meson) flow. Higher experimental precision required. m t -Spectra of baryons and anti-baryons Asakawa et al., Phys. Rev. Lett. 101 (2008) Higher experimental precision required. Di-pion (sigma) intermittency study T. Anticic et al., arXiv No unambiguous signal seen yet Fluctuations: multiplicity and/or 〈 p t 〉 Stephanov, Rajagopal, Shuryak, Phys. Rev. D60 (1999),

Christoph Blume WWND 2010, Ocho Rios, Jamaica 16 Critical Point Multiplicity Fluctuations Pb+Pb, 158A GeV 1 < y < y beam Charged multiplicity n Extensive quantity  tight centrality selection (1%) to reduce volume fluctuations Scaled variance  Energy dependence of  Data narrower than Poisson (  < 1) Trend reproduced by UrQMD Charged multiplicity n Extensive quantity  tight centrality selection (1%) to reduce volume fluctuations Scaled variance  Energy dependence of  Data narrower than Poisson (  < 1) Trend reproduced by UrQMD

Christoph Blume WWND 2010, Ocho Rios, Jamaica 17 Critical Point Multiplicity Fluctuations n-Fluctuations as a function of  B NA49 data: Phys. Rev. C79, (2009)  B from stat. model fit: F. Becattini et al., Phys. Rev. C73, (2006) Amplitude of Fluctuations: M. Stephanov et al. Phys. Rev. D60, (1999) Width of crit. region: Y. Hatta and T. Ikeda, Phys. Rev. D67, (2003) Position of crit. point: Z. Fodor and S. Katz JHEP 0404, 050 (2004)

Critical Point Elliptic Flow v 2 Christoph Blume WWND 2010, Ocho Rios, Jamaica 18 Energy dependence of v 2 of protons and pions Large systematic effects Especially for proton v 2 ! Clearly needs improvements on the experimental side Energy dependence of v 2 of protons and pions Large systematic effects Especially for proton v 2 ! Clearly needs improvements on the experimental side

Christoph Blume WWND 2010, Ocho Rios, Jamaica 19 Critical region Larger area in T -  B plane Focusing effect Proximity of critical point might influence isentropic trajectories (n B /s = const.) Critical region Larger area in T -  B plane Focusing effect Proximity of critical point might influence isentropic trajectories (n B /s = const.) Critical Point Theoretical Predictions Y. Hatta and T. Ikeda, Phys. Rev. D67, (2003) Askawa et al., Phys. Rev. Lett. 101, (2008)

Critical Point m t -Spectra of Baryons and Antibaryons Christoph Blume WWND 2010, Ocho Rios, Jamaica 20 Expectation: B/B ratio should fall with m t Askawa et al., PRL. 101, (2008) Expectation: B/B ratio should fall with m t Askawa et al., PRL. 101, (2008) No significant energy dependence of slope a observed K. Grebieszkov et al., Nucl. Phys. A830 (2009), 547c

Summary Christoph Blume WWND 2010, Ocho Rios, Jamaica 21 How to probe different regions of the QCD phase diagram ? Variation of center-of-mass energy Good control parameter to move around in phase diagram Variation of system size Changes only relative contribution of core and pp-like corona (if core-corona ansatz holds) Change in T only apparent, μ B = const. Search for critical point First results from multiplicity fluctuations negative Need for better observables Multi-dimensional (scale and p t -dependent) fluctuation studies How to probe different regions of the QCD phase diagram ? Variation of center-of-mass energy Good control parameter to move around in phase diagram Variation of system size Changes only relative contribution of core and pp-like corona (if core-corona ansatz holds) Change in T only apparent, μ B = const. Search for critical point First results from multiplicity fluctuations negative Need for better observables Multi-dimensional (scale and p t -dependent) fluctuation studies

22 Backup

System Size Dependence p+A Collisions Christoph Blume WWND 2010, Ocho Rios, Jamaica 23 No clear evidence for decrease with N part Significant decrease visible only for anti-lambda Data not fully consistent NA57: F. Antinori et al., J. Phys. G32 (2006) 427 NA49: T. Šuša et al., Nucl. Phys. A698 (2002) 491c No clear evidence for decrease with N part Significant decrease visible only for anti-lambda Data not fully consistent NA57: F. Antinori et al., J. Phys. G32 (2006) 427 NA49: T. Šuša et al., Nucl. Phys. A698 (2002) 491c

Critical Point Di-Pion (Sigma) Intermittency Christoph Blume WWND 2010, Ocho Rios, Jamaica 24 π + π - Pairs above di-pion threshold Factorial moments F 2 (M) M: Number of bins in transverse momentum space Subtract mixed event background ⇒ ΔF 2 (M) Search for power law behavior ΔF 2 (M) ∼ (M 2 ) Φ2 Φ 2 : critical exponent Φ 2 > 0 for Si+Si Coulomb effects become an issue for larger systems π + π - Pairs above di-pion threshold Factorial moments F 2 (M) M: Number of bins in transverse momentum space Subtract mixed event background ⇒ ΔF 2 (M) Search for power law behavior ΔF 2 (M) ∼ (M 2 ) Φ2 Φ 2 : critical exponent Φ 2 > 0 for Si+Si Coulomb effects become an issue for larger systems p+p, C+C, Si+Si at 158A GeV T. Anticic et al. arXiv N.G. Antoniou, F.K. Diakonos, and G. Mavromanolakis

Christoph Blume WWND 2010, Ocho Rios, Jamaica 25 Critical Point  p t  -Fluctuations Measure of  p t  -fluctuations Energy dependence of  pt No significant variation with  s NN for central collisions Trend reproduced by UrQMD Measure of  p t  -fluctuations Energy dependence of  pt No significant variation with  s NN for central collisions Trend reproduced by UrQMD

Christoph Blume WWND 2010, Ocho Rios, Jamaica 26 Critical Point  p t  -Fluctuations  p t  -Fluctuations as a function of  B NA49 data: Phys. Rev. C79, (2009)  B from stat. model fit: F. Becattini et al., Phys. Rev. C73, (2006) Amplitude of fluctuations: M. Stephanov et al. Phys. Rev. D60, (1999) Width of crit. region: Y. Hatta and T. Ikeda, Phys. Rev. D67, (2003) Position of crit. point: Z. Fodor and S. Katz JHEP 0404, 050 (2004)

Christoph Blume WWND 2010, Ocho Rios, Jamaica 27 Stronger n-Fluctuations seen in smaller systems Hypothetic critical point (CP 2 ) at T = 178 MeV and  B = 250 MeV Stronger n-Fluctuations seen in smaller systems Hypothetic critical point (CP 2 ) at T = 178 MeV and  B = 250 MeV Critical Point System Size Dependence of n-Fluctuations F. Becattini et al., Phys. Rev. C73, (2006)

28 System Size Dependence dN/dy at Mid-rapidity for Λ, Ξ, and Ω Transport models OK for  Slightly below  Too low for  UrQMD: H. Petersen et al. arXiv: HSD: W. Cassing and E. Bratkovskaya, Phys. Rep. 308, 65 (1999) and private communication Core Corona model OK for  and  F. Becattini and J. Manninen, Phys. Lett. B673, 19 (2009) J. Aichelin and K. Werner, arXiv: Transport models OK for  Slightly below  Too low for  UrQMD: H. Petersen et al. arXiv: HSD: W. Cassing and E. Bratkovskaya, Phys. Rep. 308, 65 (1999) and private communication Core Corona model OK for  and  F. Becattini and J. Manninen, Phys. Lett. B673, 19 (2009) J. Aichelin and K. Werner, arXiv: − Christoph Blume WWND 2010, Ocho Rios, Jamaica

29 Energy Dependence Total Multiplicities AGSNA49RHIC Central A+A collisions Only total multiplicities (4  ) shown Chemical freeze-out Experimental points in T-  B plane Analysis with statistical models Baryons (stopping)   B Strange particles  T (+  B ) Phase boundary reached ? Central A+A collisions Only total multiplicities (4  ) shown Chemical freeze-out Experimental points in T-  B plane Analysis with statistical models Baryons (stopping)   B Strange particles  T (+  B ) Phase boundary reached ?

Christoph Blume WWND 2010, Ocho Rios, Jamaica 30 Lattice QCD General consensus: cross over for  B = 0 Critical Temperature T c Depends on order parameter e.g. chiral condensate: or s-quark susceptibility  s Significant differences between collaborations (Budapest-Wuppertal, Riken-Bielefeld-Columbia “hotQCD”) Lattice QCD General consensus: cross over for  B = 0 Critical Temperature T c Depends on order parameter e.g. chiral condensate: or s-quark susceptibility  s Significant differences between collaborations (Budapest-Wuppertal, Riken-Bielefeld-Columbia “hotQCD”) QCD Phase Diagram Phase Boundary for  B = 0 Figs. and table: Budapest-Wuppertal-Group, Y. Aoki et al., arXiv:

Christoph Blume WWND 2010, Ocho Rios, Jamaica 31 QCD Phase Diagram K. Rajagopal, MIT CPOD conference 09

Christoph Blume WWND 2010, Ocho Rios, Jamaica 32 Strangeness in Heavy Ion Reactions Statistical Models F. Becattini et al., Phys. Rev. C69, (2004) A. Andronic, P. Braun-Munzinger, and J. Stachel, arXiv: Assumption: Multiplicities are determined by statistical weights (chemical equilibrium) Grand-canonical partition function: Parameters: V, T,  B, (  s ) Allows in general excellent fits to measured multiplicities Limits of applicability ?  Rare particles and low energies Assumption: Multiplicities are determined by statistical weights (chemical equilibrium) Grand-canonical partition function: Parameters: V, T,  B, (  s ) Allows in general excellent fits to measured multiplicities Limits of applicability ?  Rare particles and low energies

33 Energy Dependence K + /π + and  /π - -Ratios Extended statistical model Higher mass resonances included (up to 3 GeV)  Improved description of pions and thus of the K + /  + -ratio Limiting temperature reached in SPS energy region Equilibration due to proximity of phase boundary? Extended statistical model Higher mass resonances included (up to 3 GeV)  Improved description of pions and thus of the K + /  + -ratio Limiting temperature reached in SPS energy region Equilibration due to proximity of phase boundary? A. Andronic, P. Braun-Munzinger and J. Stachel, arXiv: Christoph Blume WWND 2010, Ocho Rios, Jamaica

Energy Dependence K + /π + -Ratio: Comparison to STAR Data Christoph Blume WWND 2010, Ocho Rios, Jamaica 34 STAR measurements at lower energies √s NN = GeV Good agreement with NA49 data STAR measurements at lower energies √s NN = GeV Good agreement with NA49 data STAR: L. Kumar et al., SQM2008 arXiv: