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Christoph Blume University of Heidelberg

International School on: Quark-Gluon Plasma and Heavy Ion Collisions: Past, Present, Future Villa Gualino, Turino, Italy Soft Probes III. Christoph Blume University of Heidelberg. Observables. Temperature. Strangeness Resonances. Femtoscopy Fluctuations. Kinetic Freeze-Out.

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Christoph Blume University of Heidelberg

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  1. International School on:Quark-Gluon Plasma and Heavy Ion Collisions:Past, Present, FutureVilla Gualino, Turino, ItalySoft Probes III Christoph Blume University of Heidelberg

  2. Observables Temperature Strangeness Resonances Femtoscopy Fluctuations Kinetic Freeze-Out Chemical Freeze-Out Flow Jets + Heavy Flavor Photons

  3. Fluctuations

  4. The Early Universe ...

  5. Fluctuations in Cosmology WMAP Only 1 Event Fluctuations on the level of < 10-4

  6. Fluctuations in Heavy Ion Physics Probe the medium response (susceptibilities) Study hadronization properties Might be sensitive to QGP phase Hadron gas reacts differently than QGP Different number of degrees of freedom Nature of the phase transition Order of the transition (cross over ⇔ 1st order) Existence of critical point ⇒ sudden increase of fluctuations Quark number susceptibility from lattice QCD (Bielefeld group)

  7. Fluctuations Measures (I): Basics Basic event-by-event observables: Multiplicities Average transverse momenta 〈pT〉 Particle ratios (e.g. K/π) Conserved quantities (charge Q, strangeness S, baryon number B ) Fluctuations usually characterized by second moments ⇒ variance Higher moments (kurtosis) recently investigated Two averages: inside a given event and over all events Large and uniform detector acceptance is helpful Need to separate simple statistical fluctuations from dynamical ones Large effect in heavy ion physics: volume (impact parameter) fluctuations

  8. Example: 〈pT〉 Fluctuations

  9. Fluctuation Measures (II): Means and Variances Observable x (e.g. pT ) for a single particle i ⇒ mean in a given event of multiplicity Nj : Mean over all events of a quantity Xj, which characterizes each event : The weighting factor is wj = 1 for quantities such as the event-wise multiplicity (i.e. ). In the case (e.g. average pT) we have The variance of Xj is : see also: NPA727, 97 (2003)

  10. Fluctuation Measures (III): Means and Variances Mean over all particles i and events j of the single particle observable xi : Corresponding variance : Mean over all events j of the event-wise mean Mx (e.g. average pT): Variance of Mx:

  11. Example: Multiplicity Fluctuations NA49: PRC75, 064904 (2007)

  12. Fluctuation Measures (IV): Φx Properties: Φx = 0 for independent particle emission (no interparticle correlations) Φx(A+A) = Φx(p+p) if A+A was a simple superposition of p+p M. Gazdzicki and S. Mrowczynski, ZPC54, 127 (1992) Not a dimensionless quantity 〈...〉 : averaging over events

  13. Example: 〈pT〉 Fluctuations central Pb+Pb @ √sNN = 17.3 GeV NA49: PLB459, 679 (1999)

  14. Example: 〈pT〉 Fluctuations NA49: PRC70, 034902 (2004)

  15. Fluctuation Measures (V): σdyn Definition : S. Voloshin, V. Koch, H.G. Ritter, PRC60, 024901 (1999) If only statistical fluctuations are present ⇒ Normalized dynamical fluctuation: NA45: NPA727, 97 (2003) Normalization removes energy dependencies, e.g. due to increase of 〈pT〉

  16. Example: 〈pT〉 Fluctuations NA45: NPA727, 97 (2003)

  17. Fluctuation Measures (VI): Particle Ratios A/B Mixed events as reference PRC79, 044910 (2009) Poisson statistics as reference: C. Pruneau, S. Gavin, and S. Voloshin, PRC66, 044904 (2002) Negative values imply dominating correlations between A and B

  18. Example: K/π Fluctuations STAR: arXiv:0901.1795

  19. Example: K/π Fluctuations Comparison of energy and system size dependence of νdyn STAR: arXiv:0901.1795

  20. Example: K/p and p/π Fluctuations S/B fluctuation as QGP signal V. Koch, A. Majumder, and J. Randrup, PRL95, 182301 (2005) T < Tc: S and B can be unrelated (Kaons: S = -1, B = 0) T > Tc: S and B are correlated (s-Quark: S = -1, B = 1/3) K/p p/π Dominated by resonance decays

  21. Fluctuation Measures (VII): pT Correlations Covariance of transverse momenta of different particles STAR: PRC72, 044902 (2005) with Independent of detection efficiencies Influence of other effects (e.g. Coulomb interaction or Bose-Einstein corr.) can more easily be studied

  22. Example: pT Correlations STAR: PRC72, 044902 (2005)

  23. Example: Net-Charge Fluctuations Hadron Gas: Charge unit = 1 Quark Gluon Plasma: Charge unit = 1/3 ⇒ Charge fluctuations should be reduced in QGP relative to hadron gas S. Jeon and V. Koch, PRL85, 2076 (2000) M. Asakawa, U. Heinz and B. Müller, PRL85, 2072 (2000)

  24. Example: Net-Charge Fluctuations Charge Conservation Limit HIJING QGP Au+Au, √sNN = 130 GeV Signal obscured by resonance decays Strongly acceptance dependent STAR: PRC68 044905 (2003)

  25. Balance Function ⇒ Sensitive to hadronization time in an expanding system

  26. Balance Function With, e.g., being the density of pairs inside a given relative pseudo-rapidity range Analysis done as a function of S. Bass, P. Danielewicz, and S. Pratt, PRL85, 2689 (2000)

  27. Balance Function Shuffled: randomly shuffle charges inside a given event ⇒ largest possible BF-width Possible evidence for delayed hadronization STAR: PRC82, 024905 (2010)

  28. Fluctuations Fluctuations observed on the level of 1 - 10% Many “trivial” effects Volume fluctuations Resonance decays Acceptance effects Short range correlations (Bose-Einstein) Conservation laws (Mini-)jets Elliptic flow ... But clear evidence for dynamical fluctuations with non-trivial energy or system size dependencies

  29. QCD Critical Point

  30. The QCD Phase Diagram

  31. Analogy: Phase Diagram of Water Cross over Critical point 1st order phase boundary

  32. The QCD Phase Diagram K. Rajagopal, CPOD Conference 09

  33. Critical Point Predictions Lattice QCD calculation at finite μB Z. Fodor and S. Katz JHEP 0404, 050 (2004) But current predictions scatter quite a lot The CP might even not exist at all ... P. de Forcrand and O. Philipsen, JHEP01, 077 (2007) M. Stephanov, CPOD conference 09

  34. Critical Point Predictions Focusing effect Proximity of critical point might influence isentropic trajectories M. Askawa et al., PRL101, 122302 (2008) Larger critical area possible Y. Hatta and T. Ikeda, PRD67, 014028 (2003)

  35. First Attempts • Multiplicity fluctuations as a function of B Amplitude of Fluctuations: M. Stephanov et al. Phys. Rev. D60, 114028 (1999) Width of crit. region: Y. Hatta and T. Ikeda, Phys. Rev. D67, 014028 (2003) Position of crit. point: Z. Fodor and S. Katz JHEP 0404, 050 (2004) B from stat. model fit: F. Becattini et al., Phys. Rev. C73, 044905 (2006) NA49 data: Phys. Rev. C79, 044904 (2009)

  36. Strategy: Energy Scan STAR at RHIC NA61 at the SPS CBM at FAIR Observables: Fluctuations Flow Spectra Overview: arXiv:1007.2613

  37. The QCD Phase Diagram

  38. Critical Endpoint from Lattice QCD

  39. Order of the Phase Transition

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