1. Probing the Properties of the Quark-Gluon Plasma and Studying Strong-Field QCD in Heavy Ion Collisions @ RHIC and the LHC Prof. Brian A. Cole. Columbia University PHENIX and ATLAS

2. The “Big Picture” Heavy Ion (Au+Au) collision as seen by the STAR time- projection chamber. Why???

3. Fundamental Interactions Matter usually studied in the lab has properties determined by EM interactions. How would non-Abelian matter be different?

4. The Big Picture We have a fundamental theory of strong interactions exhibits asymptotic freedom at large momentum transfer. What about other limits of QCD? –High temperature –High field strength

5. QCD Thermodynamics (on Lattice) Rapid cross-over from “hadronic matter” to “Quark-Gluon Plasma” at T  170 MeV  Energy density,  ~ 1 GeV/fm 3. Only fundamental “phase transition” that can be studied in the laboratory. –Is the QGP weakly interacting?? Energy Density / T 4 Pressure / T 4

6. Relativistic Heavy Ion Collider  Run 1 (2000): Au-Au  S NN = 130 GeV  Run 2 (2001): Au-Au, p-p  S NN = 200 GeV  Run 3 (2003): d-Au, p-p  S NN = 200 GeV  Run 4 (2004): Au-Au  S NN = 200, 64 GeV, p-p  S NN = 200 GeV  Run 5 (2005): Cu-Cu  S NN = 200, 64 GeV, p-p  S NN = 200 GeV STAR

7. Heavy Ion Collision Time History t z RHIC collision space-time history in “parton cascade” model Initial particle production from strong fields Rapid thermalization “Hydrodynamic” evolution Hadronization (interesting but I won’t cover)

8. RHIC Initial Conditions Au+Au @ 200 GeV per nucleon,  = E/m  100. –Au diameter, d  14 fm, contracted d/   0.2 fm  Crossing time < 0.2 fm/c. Add quantum mechanics:  E  ħ c /  t –Fluctuations with  E > 1 GeV are “on shell”  These are primarily gluons (~ 200/collision)  RHIC is a gluon collider! (10 GeV/fm 3 )

9. “Saturation” @ low x @ High energy nuclei are highly Lorentz contracted –Except for soft gluons –Which overlap longitudinally –And recombine producing broadened k T distribution  Generates a new scale: Q s  Typical k T of gluons If Q s >>  QCD, perturbative calculations possible.  Large occupation #s for k T <Q s  classcial fields Saturation is a result of unitarity in QCD

10. QCD: Evolution Quarks radiate copiously  Evolution of proton (e.g.) parton distribution functions  Growth of gluon distribution @ low x @ high gluon density recombination starts to limit growth. Q s - resolution scale where recombination starts to dominate Limiting density  Q s 2 /  s –~ Classical field

11. Saturation @ HERA? Measurements of DIS cross-section vs x, Q 2 for x < 0.01. Plotted vs All x dependence in the saturation scale. –“Geometric scaling” Precursor to saturation in PDF evolution Golec-Biernat and Wusthoff (GBW) Saturation Model (empirical)

12. RHIC Particle Multiplicities Multiplicity @ RHIC on low end of predicted range Slow growth with impact parameter (N part ) –Inconsistent with factorized mini-jet production –Best described by saturation model Multiplicity per colliding nucleon pair

13. But, Have We Created “Matter” ? “Pressure” converts spatial anisotropy to momentum anisotropy. Requires early thermalization. Unique to heavy ion collisions Answer: yes  dN/d  x y z

14. “Elliptic Flow” Parameterize  variation by “v 2 ” parameter – Compare to “eccentricity”: Data consistent w/ hydrodynamic calculations

15. (Ideal) Hydrodynamics in one slide

16. Estimating the (Shear) Viscosity Relevant parameter for determining collective motion of quark-gluon plasma –viscosity to entropy ratio:  /s. Finite viscosity leads to dependence of flow strength on p T. –Correction  (  /s) p T 2 From data shown to right, obtain estimate: –  /s ~ 0.1 –Very small!  s is “sound attenuation length”  mean free path

17. Comparison to “Typical” Vicosities  /s ~ 0.1 Thus the statement: –QGP is most perfect fluid every created

18. Lattice QCD Estimate of  /s Nakamura & Sakai, hep-lat/0510100 T/T c   /s pQCD AdS/CFT Shear viscosity in quenched QCD

19. “Casual” Viscous Hydrodynamics Causal fix introduces a new scale,  , relaxation time. Uncertainty in   weakens  /s constraint –Concludes  /s < 0.5, but elliptic flow? P. Romatschke nucl-th/0701032 Comparison of viscous hydro results to meson spectra from PHENIX

20. Thermalization via Plasma Instabilities? p T vs p z anisotropy –Generates strong local chromo-magnetic fields –Lorentz forces produce rapid isotropization. Pressure from macro- scopic color fields?! Energy density

21. Use self-generated quarks/gluons/photons as probes of the medium (classic physics technique!) Penetrating Probes of Created Matter z t Collisions between partons

22. How to directly probe medium ? Use quarks & gluons from high-Q 2 scattering –“Created” at very early times (~ 0.1 fm). –Propagate through earliest, highest  matter. (QCD) Energy loss of (color) charged particle –~ Entirely due to radiation –Virtual gluon(s) of quark multiply scatter. e.g. GLV (Gyulassy, Levai, Vitev) formalism Experimentally measure using:  (Leading) high-p  hadrons  Di-jet correlations

23. Perturbative quantum chromo-dynamics Factorization: separation of  into –Short-distance physics: – calculable using perturbation theory ** –Long-distance physics:  ’s – universal, measured separately. Valid @ large momentum transfer – high p T particles p-p di-jet Event STAR From Collins, Soper, Sterman Phys. Lett. B438:184-192, 1998

24. pQCD – Single Hadron Production Add fragmentation to hadrons D(z) – fractional momentum distribution of particles in “jet” KKP Kretzer data vs pQCD Phys. Rev. Lett. 91, 241803 (2003)

25. PHENIX Au-Au  0 Spectra Calculations with no energy loss Calculations with energy loss Observe 20% of expected yield @ high p T  Deduce energy density  ~15 Gev/fm 3  Compare  crit ~ 1 GeV/fm 3  100 x normal nucleus energy density! p T spectrum Expected R AA  Observed/Expected Using p-p data as baseline

26. PHENIX: Au-Au High-p T  0 Suppression

27.  0 Suppression: dE/dx Comparisons Quark & gluon dE/dx analysis: Turbide et al (McGill) –Essentially an ab initio calculation –Compared to precision (relatively) data

28. Prompt Photon Production Prompt photons provide an independent control measurement for jet quenching. –Produced in hard scattering processes –But, no final-state effects (???)

29. Au-Au Prompt Photon Production Photon control measurement shows no quenching pQCD calculations OK, quenching a final-state effect

30. High-p T Single Particle Summary  5 violation of factorization up to 20 GeV/c –In hadron production (jets), but not prompt   Hard scatterings occur at expected rates  Suppression from final-state energy loss To explain data: Unscreened color charge dn/dy~1000 Energy density ~15 GeV/fm 3 >  10 “critical” energy density

31. Analysis of Single Hadron Data: BDMS-Z-SW “Thick medium” energy loss calculation Central 200 GeV Au+Au Transport coefficient: for radiated gluon Baier [ Nucl. Phys. A715, 209 (2003) ]: –C = 2 expected for ideal QGP –14 GeV/fm 2  c = 8-10!!  Strong coupling [ Eskola et al, Nucl. Phys. A747, 511 (2005)]

32. STAR Experiment: “Jet” Observations Number of pairs Angle between high energy particles 0º0º180º proton-proton jet event  In Au-Au collisions we see only one “jet” at a time !  How can this happen ?  Jet quenching! q q Analyze by measuring (azimuthal) angle between pairs of particles

33. Di-jet Distortion vs “Impact Parameter”

34. (di)Jet Angular Correlations (PHENIX) PHENIX (nucl-ex/0507004): moderate p T

35. Origin of di-jet Distortion? Mach cone? Jets may travel faster than the speed of sound in the medium. While depositing energy via gluon radiation. QCD “sonic boom”

36. Mach Cone (2) Ideal QGP, c s 2 = 1/3 Cos  M = c s   M = 55º Detailed calculation taking into account evolving speed of (gluon) sound from hydrodynamics. – But, other possible mechanisms proposed.

37. What I Didn’t Show You Charm quarks also are quenched –And show rapid thermalization! Large charm quark elliptic flow signal –Can only be established at the quark level. Large baryon excess for 2 < p T < 5 GeV/c – Hadron formation by quark recombination We see final state particle flavor distributions consistent with “freeze-out” from chemically equilibrated system. –We are rapidly approaching stage where QGP is ONLY viable interpretation of data

38. RHIC Physics Since start of RHIC, substantial progress on development of a rigorous foundation for understanding stages of a heavy ion collision: –Particle production from strong gluon fields –Thermalization (ideas but not yet understood) –Hydrodynamic evolution –Hadronization With jets as calibrated probe –But jet quenching is still not completely understood We are probing the properties of the QGP – with surprising results –Strong coupling – why? –Speed of sound?

39. Comparison to “Typical” Vicosities But what is this “viscosity bound”? –Calculation of viscosity using string theory –Huh????  /s ~ 0.1

40. AdS/CFT Correspondence Main idea Duality between string theory in anti-DeSitter space and conformal field theories. –Weakly coupled string theory  strongly coupled CFT Example conformal theory: –N=4 supersymmetric Yang-Mills –Which is not QCD (e.g. no running of  s ) –But similar enough?? AdS/CFT now being applied to many apsects of RHIC physics –Viscosity,  /s. –Jet quenching –“Sound” waves

41. Why Heavy Ions @ LHC? Low x – Gluon production from saturated initial state Energy density – ~ 50 GeV/fm 3 (?) Rate – “copious” jet production above 100 GeV Jets – Full jet reconstruction Detector – necessary detector “for free”!

42. Heavy Ion Initial Conditions: Modern At LHC we (think we) will be able to study “classical” gluon fields in nuclei –And their quantum evolution

43. A+A Multiplicity vs Energy LHC measurements will provide an essential test of whether we understand the mechanism responsible for bulk particle production. –e.g. does saturation correctly extrapolate? RHIC 200 GeV Saturation? Something else?

44. Saturation: Geometric Scaling to A-A? Extension of GBW analysis to NMC nuclear targets Using k T factorization calculate mult. (parton-hadron duality) Compare to PHOBOS data Armesto, Salgado, Wiedemann Phys. Rev. Lett. 94 :022002,2005 Why should it work here?

45. Elliptic Flow @ LHC LHC data will provide an essential test of our understanding of elliptic flow data @ RHIC –And test whether QGP is still strongly coupled –Extremely high priority given the possible relevance of AdS/CFT. Large ATLAS acceptance a big advantage ?? Can change horizontal scale by x2 @ LHC

46. Why Jets @ LHC? Rate @ High p T Can access jet energies in excess of 100 GeV Complete jet measurements  greater precision in use of jet tomography as a probe 80 GeV Jet in Pb+Pb

47. Jets as Color Antennas Studies of modified jets in heavy ion collisions may shed light on a “fundamental” problem in (particle) physcs A high-energy quark/gluon acts like a “color antenna” In vacuum, radiation strongly affected by quantum interference. But, in medium thermal gluons “regulate” radiation.

48. LHC Physics Opportunity Create & study quark-gluon plasma at T = 0.8~GeV Study particle production from strong gluon fields. New program with w/ new discoveries ~ guaranteed –If RHIC is any guide … p T reach, rates, detector capabilities at LHC allow for qualitatively different (better!) measurements. Overlap w/ many other sub-fields of physics  Particle physics  Plasma physics  Fluid/hydro dynamics  Thermal field theory, lattice & non-lattice  String theory (!?) – AdS-CFT correspondence  General relativity (gluon production as Unruh radiation?)

49. PHENIX: Cu-Cu  0 R AA R AA

50. PHENIX p-p Prompt  Production Absolute comparison, no fudge factors. pQCD very well reproduces prompt  cross- section. Points: PHENIX Curve: PQCD

51. “Centrality” Dependence of Suppression Measure yield above 4.5 GeV/c. Find suppression relative to p-p. Plot vs nuclear overlap. –N part = number of “participating” nucleons Test against “best” energy loss model –GLV = Gyulassy, Levai, Vitev Good agreement

52. PHENIX: High-p T  0 v 2 (Reaction Plane) Clear observation of decreasing v 2 @ high p T From parallel session talk by D. Winter

53. V 2 (p T ): Energy Loss Calculations v2v2 PQM: Dainese, Loizides, Paic, Eur. Phys. J. C38:461 2005

54. PHENIX: Reaction Plane Angle Dependence(2) For PHENIX reaction plane resolution & chosen bin sizes,  trig bin 4 has smallest flow effects. Even without subtracting flow contribution, a dip is seen for central collisions. Look in bin #4 PHENIX Preliminary

55. PHENIX: Reaction Plane Angle Dependence Study (di)jet correlations vs angle of trigger hadron relative to reaction plane –J. Bielcikova et al, Phys. Rev. C69:021901, 2004 –  trig =  trig -  –6 bins from 0 to  /2. Flow systematics change completely vs  trig Can study dependence of distortion on geometry.  Shoulder and dip seen in all  trig bins.  trig ? From Poster by J. Jia

56. Jet Conversion Photons There is a new source of “hard” photons in QGP –High p T quarks/gluons convert into photons in medium This extra contribution must be present –@ large enough t, incident jet sees unscreened partons What about at low-t ? –In principle, pole in the t channel produces “large” But medium screens @ low-t & regulates pole. –Jet-conversion  rate sensitive to screening mass. –And potentially also to quark/gluon thermal masses.

57. Jet Quenching: Photon Bremstrahlung For light quarks (and gluons??), in-medium energy loss dominated by radiation. –Interference between vacuum & induced radiation. –For large parton p T (> ~10 GeV/c) coherence crucial. Unfortunately, we can’t measure the gluons. But we could measure photon bremstrahlung!  Direct measurement of medium properties.

58. Put it all together … Extremely rich mixture of physics contributing to the photon spectrum in ~ 4-10 GeV/c range. How to unravel all of the different pieces? Shamelessly stolen from Simon’s talk.

59. PHENIX Measuring the Initial  ?? Bjorken Hydrodynamics: For  0 = 0.2 fm (k t ~ 1 GeV) –  Bj = 20 GeV/fm 3 !!! – dN g /dA ~ 6/fm 2 But, estimate too model dependent. Need experimental probe of initial state … ~ 150 fm 2 Formation time

60. Quark-Gluon Thermodynamics Lattice QCD Sudden change in # DOF in strongly interacting matter Critical temperature (Karsch et al) –T c = 150 – 170 MeV Energy density: –  = 0.3 – 1.3 GeV / fm 3 –Large uncertainty due to T 4 dependence. –But accessible in heavy ion collisions Karsch, hep-lat/0106019 T/T c  /T 4 Quark-Gluon Plasma

61. Hard high-Q 2 processes are abundant at collider energy Production of hard partons is a standard candle, unaffected by medium Hard partons interact with medium during propagation