Heavy Ion Phenomenlogy and Hydrodynamic Models

1. Heavy Ion Phenomenlogy and Hydrodynamic Models Hydrodynamic models of heavy-ion collisions are only useful to the extent that they tell us something about the matter created in collisions Paul Sorensen Brookhaven National Laboratory

2. Three Lectures • Heavy-ion collisions & motivation for hydro • Concept of flow • Introduction to observables • Model comparisons • Uncertainties • Deviations from ideal hydro • Viscosity and Knudsen number • Questions of validity

3. QGP on the QCD phase diagram QGP

4. energy density or pressure temperature, T QGP and QCD theory Quark Gluon Plasma established theoretically Lattice calculations indicate a rapid crossover accompanied by an increase in the number of degrees of freedom scaled pressure, p/ F.~Karsch, arXiv:0711.0656 [hep-lat] energy density, ()1/4 [GeV/fm3]1/4 How can QGP be studied in the lab? Hydrodynamic models MAY help

5. Heavy ion collisions beam axis Approach of Lorentz Contracted Au Nuclei

6. Heavy ion collisions beam axis Approach of Lorentz Contracted Au Nuclei

7. Heavy ion collisions y beam axis z x transverse plane

8. y z x Heavy ion collisions expanding fireball spectators reaction plane beam axis spectators transverse plane

9. y z x Heavy ion collisions expanding fireball spectators reaction plane beam axis spectators transverse plane

10. y z x We can estimate the initial energy density in a slice of the fireball For RHIC: ~4x larger than lattice critical energy transverse plane measured estimated Heavy ion collisions expanding fireball spectators on plane beam axis spectators transverse plane

11. Heavy ion collisions transverse plane spectators spectators reaction plane beam axis

12. Heavy ion collisions transverse plane spectators spectators reaction plane beam axis

13. Longitudinal Projection of one event 1000’s of produced particles streaming into the detector

14. Transverse Projection of one event 1000’s of produced particles streaming into the detector

15. Models of Heavy-ion Collisions • RQMD • UrQMD • AMPT • EPOS • MPC • VENUS • Hydrodynamic models • Hydro+Cascade • Blastwave

16. What can we get from hydro Information about the space-time evolution and T and energy density etc.

17. What can we get from hydro Sensitivity to the Equation of State scaled pressure, p/ F.~Karsch, arXiv:0711.0656 [hep-lat] energy density, ()1/4 [GeV/fm3]1/4

20. out-of-plane   in-plane off-axis (non-central) Au+Au collision Experimental observables pz, y • We can study how various particles are distributed in momentum space • [-E, px, py, pz] or [-E, pT, , y] • correlations and fluctuations of these variables pT colliding beams  • We can vary • the collision energy (snn) • the system size (different nuclei) • deformation of the collision zone

21. Triple momentum-space distribution Most of what we do is count how many (at what angle, what momentum and with what mass) In A+A collisions, azimuthal symmetry is broken by the almond shape of the overlap region. Instead of integrating over  we use a Fourier series for the  dependence

22. Correlations After characterizing the single particle distributions, we study various correlations Typically, the density of pairs is measured and compared to the product of the single particle density Ex. of 2 correlation measures with different normalizations: correlated particles per pair, correlated particles per particle

23. Rlong qside x1 qout Rside qlong x2 Rout Femptoscopy (HBT) x p1 p2 y Peak at small relative momentum yields information about the size of the homogeneity region through interference notice the p(dot)x space-momentum correlation

24. How to relate data to hydro • Salient features of hydrodynamic models are • Space-momentum correlations; x maps to p • Collective motion; matter moves with a common flow • In hydro models, these features arise via pressure gradients in the overlap zone • Pressure gradients give rise to fluid velocity

25. How to relate data to hydro • Salient features of hydrodynamic models are • Space-momentum correlations; x maps to p • Collective motion; matter moves with a common flow • In hydro models, these features arise via pressure gradients in the overlap zone • Hydro models make continuum assumption: • density, pressure, temperature, and velocity • are well-defined at infinitesimally small points • A thermodynamic Equation of State is used to complete the set of conservation equations (assumes thermodynamic equilibrium)(for more discussion ask the other Paul)

26. Checking assumptions Hydrodynamic models of heavy-ion collisions are only useful to the extent that they tell us something about the matter created in collisions We collide nuclei at high energy in an attempt to study nuclear matter at finite temperature How do we verify that hydro models (assumptions) make sense for our system Keeping in mind: assumptions are not predictions. Disproving an assumption calls into question the prediction but may not completely invalidate the result

27. (1/pT)(dN/dpT) pT Effect of collective motion on pT spectra Treat particles as emitted from a locally equilibrated region Each region is boosted according to the flow velocity More massive particles get a bigger pT boost (p=mv) (1/pT)(dN/dpT) M m pT

28. Hadron Spectra from RHICp+p and Au+Au collisions at 200 GeV ud central peripheral

29. Hadron Spectra (centrality) RCP = (Central/Peripheral)(1/Nbin) Massive baryons spectra bulge out more in central But, what about massive mesons? Why are they different? J.Phys.G31:S889-S896,2005: nucl-ex/0412003

30. Effect of collective motion on azimuthal distributions The pressure would be highest at the center and zero in vacuum. So the pressure gradient is largest in the x-direction Would lead to a bigger boost in x than y

31. Effect of collective motion on azimuthal distributions

32. Why do they call it “perfect” 0 mean-free-path limit Ballistic expansion particle density

33. But… Sensitivity to an EoS? particle density

34. Analogy with fermi gasses 100 s 2000 s Observation of a Strongly Interacting Degenerate Fermi Gas of Atoms K. M. O'Hara 1, S. L. Hemmer 1, M. E. Gehm 1, S. R. Granade 1, J. E. Thomas 1

35. Elliptic Flow v2 Do heavy ion collisions convert spatial anisotropy to momentum anisotropy according to the equations of ideal hydrodynamics? Low pT (soft): Mass ordering indicative of a common velocity Consistent with a 1) strong x-p correlations 2) emmision from a source with a common boost but also meson/baryon grouping at intermediate pT for v2. PRL 92 (2004) 052302; PRL 91 (2003) 182301 intermediate pT low pT

36. flow v(r) slow  fast  R(r) r mT(r) r R(mT) r mT Effect of collective motion on homogeneity regions hubble expansion geometry the flow ansatz mT increases with r R decreases with r R decreases with r

37. slow  fast  R (fm) R(mT) mT (GeV/c) mT Effect of collective motion on homogeneity regions

38. elliptic flow J.Phys.G31:S889-S896,2005: nucl-ex/0412003 transverse momentum pT (GeV/c) Uncertainties in the initial conditions of the QGP phase preclude better characterization of the matter formed Early times (<1 fm): under intense theoretical investigation We need experimental probes of the early time dynamics colliding nuclei: sheets of CGC initial singularity Glasma: unstable longitudinal fields growth of instabilities quantum fluctuations seed instabilities transverse magnetic fields turbulance? jet quenching QGP phase anamolous viscosity? hadronization hadronic rescattering freezeout detectors energy loss and jet quenching jets and heavy quarks form quarkonium melts; flow develops 0 fm 0.1 fm 1 fm 10 fm 1015 fm time scale 1 fm ≈ 3x10-24 sec

39. Summary • So far, I presented what I think are the salient features of hydrodynamic models • And I showed some of the data that seems to be consistent with those expectations • The next lecture will be more critical • There are some reasons to question the hydrodynamic paradigm and I’ll try to give a snapshot of the whole landscape

40. Heavy Ion Phenomenlogy and Hydrodynamic Models Hydrodynamic models of heavy-ion collisions are only useful to the extent that they tell us something about the matter created in collisions Paul Sorensen Brookhaven National Laboratory

41. Lecture 2 • Comparing to hydrodynamic models • Does the comparison make sense? • Uncertainties in models • Do data require hydrodynamic flow?

42. Some Uncertainty • What are the initial conditions • At what time, if ever, does hydro become applicable (0) • What is the viscosity during a “fluid” phase? • When does the fluid phase end? • How does one go from fluid to particles? • Maybe some others…

43. What do we want to learn from hydro Can we talk about a locally thermalized matter at some point in the evolution? If so, what is the Equation of State? What are the properties of the matter? scaled pressure, p/ F.~Karsch, arXiv:0711.0656 [hep-lat] energy density, ()1/4 [GeV/fm3]1/4

44. Does hydro make sense to try? hydro data

45. Spectra show possible “flow”

46. Elliptic Flow v2 Do heavy ion collisions convert spatial anisotropy to momentum anisotropy according to the equations of ideal hydrodynamics? PRL 92 (2004) 052302; PRL 91 (2003) 182301 Low pT (soft): Mass ordering indicative of a common velocity Consistent with 1) strong space-momentum correlations 2) emmision from a source with a common boost intermediate pT low pT

47. v2 and the EoS

48. But… Sensitivity to an EoS? particle density

49. v2 mass ordering and the EoS One “classic” signature: mass dependence of v2(pT) If the matters expansion is described by a hydrodynamic model can we learn something about the EOS needed to describe the data? Kolb, Heinz, nucl-ex/0204061 Fitting the heavy particle spectra leads to a failure to describe the splitting

50. Fitting spectra and v2