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

Phase Diagram (H2O) This knowledge is elemental to the phase 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

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

What Constitutes Soft Physics? Straw 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 99.5% soft “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

The many roles of Soft Physics? 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

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

Event Characterization? x y YRP 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

“Interrogative Role” of Soft Physics u Phases and Properties of QCD ? Flow Correlations Multiplicity & particle ratios “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

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

Multiplicity Measurements! pT = pL q = 45 (135) degrees h = ±0.88 pT>pL 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: pL>>pT 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

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

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

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

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

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

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! Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009 16

Extrapolation of dNch/dhmax vs s Soft physics at the LHC Extrapolation of dNch/dhmax vs 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 Central collisions Saturation model Armesto Salgado Wiedemann, PRL 94 (2005) 022002 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

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

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

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

Soft physics & Hadrochemisty Extracted T & µB values neutron stars Baryonic Potential B [MeV] early universe Chemical Temperature Tch [MeV] 200 250 150 100 50 400 600 800 1000 1200 AGS SIS SPS RHIC quark-gluon plasma hadron gas deconfinement chiral restauration Lattice QCD atomic nuclei 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

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

Robust Experimental Source Functions obtained from moments 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

Thermal model with Bjorken longitudinal expansion and transverse Flow 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

Why Flow Measurements? From ET Distributions Control Params. 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

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

Quark-Like Degrees of Freedom Evident KET – CQN Scaling It is often argued that Strong coupling is Incompatible with quark degrees of freedom Phys. Rev. Lett. 98, 162301 (2007) Mesons Baryons 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

Predicted Signal for hydrodynamic behavior -> local equilibrium Recombination P. Kolb et al Is there value added for v4 Measurements? Predicted Signal for hydrodynamic behavior -> local equilibrium Quark recombination models predict a specific relationship between the ratio v4/(v2)2 for hadrons and partons 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

KET and CQN Scaling for v4 Further Indication of strong coupling? 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

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

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

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

This provides a simple fitting ansatz for the data and 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

Use procedure to study simulated data Operational ansatz validated 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

10-15% larger than for fluid with η/s =1/4π in central events. 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

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

function of centrality etc. 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

Centrality dependent CQN scaled v2 η/s for quarks directly ? PHENIX Preliminary RAA out-of-plane is relative constant with centrality at low pT. η/s for quarks directly ? Roy A. Lacey, Stony Brook; Quark Matter 09, Knoxville, TN March 30 - April 4, 2009 Arkadij Taranenko, QM2009 2018/8/7 38 38

Transport Coefficient Estimates 2 X the conjectured lower bound 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

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

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