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- Soft Physics - Flow & Bulk Properties Roy A. Lacey Chemistry Dept. Stony Brook University

- Soft Physics - Flow & Bulk Properties Roy A. Lacey Chemistry Dept. Stony Brook University. Soft Physics is like an old friend - highly thought of, but often taken for granted. Phase Diagram (H 2 O). A fundamental understanding requires knowledge of:

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- Soft Physics - Flow & Bulk Properties Roy A. Lacey Chemistry Dept. Stony Brook University

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  1. - Soft Physics - Flow & Bulk Properties Roy A. Lacey Chemistry Dept. Stony Brook University Soft Physics is like an old friend - highly thought of, but often taken for granted Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  2. Phase Diagram (H2O) • A fundamental understanding requires knowledge of: • The location of the Critical End Point (CEP) • The location of phase coexistence lines • The properties of each phase This knowledge is elemental to the phase diagram of any substance ! Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  3. p Schematic Phase Diagram (QCD) A fundamental understanding Of the QCD phase diagram is still lacking A central goal of our field is to map out the QCD Phase diagram and to establish the properties of the different phases --LHC, RHIC, SPS, FAIR, etc Soft physics plays an essential role in studies of QCD phase diagram Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  4. Straw 99.5% soft What Constitutes Soft Physics? A Straw man definition of soft physics • “Hard physics” • Particle production characterized • by large momentum transfer • Interactions occur at the partonic level • Small coupling constants • Binary scaling • etc • “Soft physics” • Particle production characterized • by small momentum transfer • Large coupling constants • Participant scaling • etc • Phenomenological modeling Particle production is dominated by soft particles Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  5. Straw The many roles of Soft Physics? • “Interrogative Role” • Energy/entropy density? • Thermalization ? • Space-time extent? • transport coefficients – η/s? • Equation of state - cs • “Support Role” • Event Characterization • Event Plane determination • etc • Measurements • Multiplicity • Geometry • Event Anisotropy • – Reaction plane • Measurements • Multiplicity • Femtoscopy • Flow • etc Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  6. Event Characterization? Collision Centrality • Collisions are described as a superposition of elementary nucleon-nucleon collisions • (e.g. Glauber model) • The number of nucleon-nucleon collisions ( Ncoll ) and the number of participant nucleons ( Npart ) depend on the impact parameter • Each collision/participant contributes to particle production and consequently to multiplicity • Numerical calculations give Ncoll, Npart, ε, R, S, etc Soft physics plays a crucial role in the determination of important geometrical quantities routinely used in our field. Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  7. y YRP x Event Characterization? Reaction Plane • The reaction plane is the plane defined by the impact parameter and the beam direction • The orientation of the reaction plane can be estimated from the global event anisotropy • Anisotropic transverse flow is a correlation between the azimuth [=tan-1 (py/px)] of the produced particles and the reaction plane! • Unambiguous signature of collective behavior Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  8. u “Interrogative Role” of Soft Physics Femtoscopic Correlations Soft physics provide crucial information on reaction thermodynamics, dynamics, and provide constraints for the extraction of transport coefficients (η/s, cs, λ, etc) Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  9. Multiplicity Measurements! • Why ? • Multiplicity provides insights on: • The Entropy of the system created in the collision • How the initial energy is redistributed to produce particles in the final state • Energy density of the system • (via Bjorken formula) • Mechanisms of particle production • (hard vs. soft) • Thermalization • In central AuAu collisions at RHIC (s=200 GeV) about 5000 particles are created Multiplicities are commonly expressed as charged particle densities in a given range of polar angle Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  10. pT = pL q = 45 (135) degrees h = ±0.88 pT>pL pL>>pT pL>>pT Multiplicity Measurements! • Mid-rapidity region • Particles with pT>pL produced at q angles around 90° • Bjorken formula to estimate the energy density in case of a broad plateau at midrapidity invariant for Lorentz boosts: eBJ~ 5 - 15 GeV/fm3 ~ 35 – 100 ε0 • Fragmentation regions: • Particles with pL>>pT produced in the fragmentation of the colliding nuclei at q angles around 0° & 180° Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  11. Multiplicity Measurements! central central peripheral peripheral energy s Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  12. Scaling properties of Multiplicity Measurements! • Scaling variables: • Rationale • Simple test of the scaling with Npart • If particle production scales with Npart, these variables should not depend on the centrality of the collisions • Facilitates rudimentary comparison with pp collisions where Npart=2 total multiplicity normalized to the number of participant pairs particle density at mid-rapidity Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  13. Scaling properties of Multiplicity Measurements! • Scaling variables: • Rationale • Simple test of the scaling with Npart • If particle production scales with Npart, these variables should not depend on the centrality of the collisions • Facilitates rudimentary comparison with pp collisions where Npart=2 total multiplicity normalized to the number of participant pairs particle density at mid-rapidity Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  14. Scaling properties of Multiplicity Measurements! • Yield per participant pair increases by ≈ 25% from peripheral to central Au-Au collisions • Is this due to a contribution of the hard component of particle production? • The ratio 200 / 19.6 is independent of centrality • A two-component fit with dN/dh [ (1-x) Npart/2 + x Ncoll] gives compatible values of x (≈ 0.13) at the two energies • From Ratio: Factorization of centrality (geometry) and s (energy) dependence Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  15. Scaling properties of Multiplicity Measurements! • The dN/dh per participant pair at mid-rapidity in central heavy ion collisions increases with ln s from AGS to RHIC energies • The s dependence is different for pp and AA collisions Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  16. Scaling properties of Multiplicity Measurements! • Total multiplicity: • Nch scales with Npart • Nch per participant pair different from p-p, but compatible with e+e-, collisions at the same energy Simple scaling rules dominate! 16 Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  17. Soft physics at the LHC • Extrapolation of dNch/dhmaxvss • Fit to dN/dh  ln s • Saturation model (dN/dh  sl with l=0.288) • The first 10k events at the LHC could be decisive Saturation model Armesto Salgado Wiedemann, PRL 94 (2005) 022002 Central collisions Models prior to RHIC Extrapolation of dN/dhln s 5500 Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  18. Soft physics & Hadrochemisty Questions of Interest • At freeze-out; • is the fireball in thermal and chemical equilibrium? • what is the temperature Tch ? • what is the baryonic content of the fireball ? • find T and mB values that minimize the difference between model predicted and measured particle ratios • Analysis with a statistical hadronization ansatz • Chemical equilibrium assumed • One can calculate the multiplicity of various hadronic species • Model comparisons could then be made to data. • Free parameters of the model - µ and T. Riexp and Rimodel are the measured and predicted particle ratios si is the (statistical + systematic) error on experimental points Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  19. Soft physics & Hadrochemisty • A. Andronic et al., Nucl. Phys. A772 (2006) 167. Fit to measured particle ratios • PbPb - Ebeam=40 GeV/ nucleon - s=8.77 GeV • Minimum of c2 for: T=156±3 MeV mB=403±18 MeV c2 contour lines Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  20. Soft physics & Hadrochemisty • A. Andronic et al., Nucl. Phys. A772 (2006) 167. Fit to measured particle ratios • AuAu - s=130 GeV • Minimum of c2 for: T=166±5 MeV mB=38±11 MeV c2 contour lines Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  21. early universe 250 RHIC quark-gluon plasma 200 Lattice QCD SPS 150 AGS deconfinement chiral restauration Chemical Temperature Tch [MeV] 100 SIS hadron gas 50 neutron stars atomic nuclei 0 0 200 400 600 800 1000 1200 Baryonic Potential B [MeV] Soft physics & Hadrochemisty Extracted T & µB values For s >≈ 10 GeV chemical freeze-out very close to phase boundary Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  22. Expand R(q) and S(r) in Cartesian Harmonic basis (Danielewicz and Pratt nucl-th/0501003) Substitute (2) and (3) into (1) The 3D integral equation is reduced to a set of 1D relations for different l coefficients  moments Source Imaging Methodology (3D) 3D Koonin Pratt Eqn. Reliable measurement of the full Source Function in 3D ! Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  23. Correlation Moments PHENIX Data Robust Experimental Source Functions obtained from moments Contributions from l > 6 is negligible Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  24. Model Comparison • Therminator: • A.Kisiel et al. Comput.Phys.Commun.174, 669 (2006) • Thermal model with Bjorken longitudinal expansion and transverse Flow • Spectra & yields constrain thermal properties • Transverse radius ρmax : controls • transverse extent • Breakup time in fluid element rest frame, • : controls longitudinal extent • Emission duration : controls tails in • long and out directions • a controls x-t correlations Source Function Comparison to Models Give robust life time estimates  Consistent with Crossover transition Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  25. Why Flow Measurements? Control Params. From ET Distributions Expect Large Pressure Gradients  Hydro Flow Straightforward to make a variety of scaling tests Deviations of Elliptic & hexadecapole flow from ideal hydrodynamic expectations -> Constraints for thermalization, sound speed, viscosity, etc. Detailed integral and differential Measurements now available What do they tell us ? Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  26. Central Arms Recent Measurements New RXN detector RXN RXN BBC/MPC BBC/MPC PHENIX Preliminary Event planes Five separate measurements of v2 and v4 in the same experiment is decisive Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  27. Baryons Mesons Phys. Rev. Lett. 98, 162301 (2007) KET – CQN Scaling It is often argued that Strong coupling is Incompatible with quark degrees of freedom How strong is “strong”? Quark-Like Degrees of Freedom Evident As well as an Indication for strong coupling? Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  28. Recombination P. Kolb et al Is there value added for v4Measurements? Quark recombination models predict a specific relationship between the ratio v4/(v2)2 for hadrons and partons Predicted Signal for hydrodynamic behavior -> local equilibrium Ollitrault et al This gives the scaling relation between Baryons and Mesons These predictions can be in/validated Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  29. KET and CQN Scaling for v4 PHENIX Preliminary KET & nq2 scaling validated for v4 Further Indication of strong coupling? Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  30. Flow is universal PHENIX Preliminary V4 = k(v2)2 where k is the same for different particle species. Demonstrates the universal nature of vn Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  31. u Can we estimate the strength of the coupling and the degree of thermalization ? From First Rate Flow Data The extraction of a small value of η/s linked to a short mean free path λ, would lend decisive insight Viscous hydro Transport Several Hybrids of Hydro and Transport We now consider one hybrid approach Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  32. Hybrid Approach Operational Ansatz (Ollitrault) The Boltzmann equation reduces to hydrodynamics when the mean free path is small C. Marle, Annales Poincare Phys.Theor. 10,67 (1969). System characterized by two Dimensionless numbers The liquidity or dilution number (D) The Knudsen number (Kn) Applicability of Boltzmann D << 1 Hydrodynamics is the limit Kn << 1 One can then use transport to study and parameterize the approach to hydrodynamic behavior (local equilibrium) Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  33. Hybrid Approach Degree of local equilibrium Schematic calculation For a given value of D Functional form does not depend on D Determined from fit to calculations This provides a simple fitting ansatz for the data and Straightforward procedure for local equilibrium estimate “Any untaken shot is 100% missed ” Wayne Gretzky Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  34. An Operational Test Use procedure to study simulated data Operational ansatz validated Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  35. Data and Fits PHENIX Preliminary Within model ansatz straightforward to estimate degree of local equilibrium! 10-15% larger than for fluid with η/s =1/4π in central events. Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  36. Truth or Myth – Good fits to the data PHENIX Preliminary Hydro like Npart dependence for v4 Similar Conclusions Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  37. Data Fits Fits allow η/s estimate as function of centrality etc. λ = 0.3 – 0.35 Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  38. RAA out-of-plane is relative constant with centrality at low pT. Centrality dependent CQN scaled v2 PHENIX Preliminary η/s for quarks directly ? Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009 Arkadij Taranenko, QM2009 2019/10/24 38

  39. Transport Coefficient Estimates Lacey & Taranenko nucl-ex/0610029 2 X the conjectured lower bound Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  40. t t = -z/c t = z/c eBjorken~ 5 - 15 GeV/fm3 ~ 35 – 100 ε0 0 z:collision axis Gold nucleus Gold nucleus v~0.99c Particle ratio measurements “Thermalized” partonic Fluid! (s)QGP? Flow measurements Multiplicity measurements A “little Bang” occurs in RHIC collisions Emerging Picture Soft Physics plays a crucial role! Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

  41. End Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009

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