1. Introduction to Heavy Ion Collisions Rainer J. Fries Texas A&M University SERC School, VECC, Kolkata January 7-11, 2013

2. I.Quark Gluon Plasma 1.Quantum Chromodynamics 2.Basic Properties of QCD 3.Free the Quarks! 4.The Cosmic Connection II.Ultra-Relativistic Heavy Ion Collisions – An Introduction 1.Preliminaries: Kinematics, Geometry and all that 2.Basic Observations 3.Modeling the Fireball 4.Outlook III.Hard Probes 1.Hard Processes 2.Nuclear Modifications 3.Energy Loss IV.Quark Recombination V.Electromagnetic Probes VI.Heavy Flavor Probes Rainer Fries 2SERC 2013 Overview

3. Some Books used:  YHM = Yagi, Hatsuda and Miake, Quark Gluon Plasma (Cambridge 2005)  LR = Letessier and Rafelski, Hadrons and Quark Gluon Plasma (Cambridge, 2002) Many other excellent literature available Rainer Fries 3SERC 2013 Literature

4. Introduction to Heavy Ion Collisions Part I: Quark Gluon Plasma

5. Rainer Fries 5SERC 2013 I.1 Quantum Chromodynamics

6. Rainer Fries 6SERC 2013 Start with Electrodynamics Maxwell: Field strength: Vector potential: Covariant derivative: U(1) gauge invariance: Lagrangian: Gauge group determined by Commutator!

7. SERC 2013 7 A Strange New Electrodynamics C N Yang & R L Mills (1954) worked out the math for a generalization to “gauge fields” with more cimplicates symmetry groups.  Most important example: SU ( N ) = unitary N x N matrices with determinant 1. From now on where is a function that takes values in the space of N x N matrices. Rainer Fries

8. 8SERC 2013 SU(N) Yang-Mills Fields Maxwell: Field strength: Vector potential: Covariant derivative: U(1) gauge invariance: Lagrangian: Yang-Mills: Field strength: Vector potential: Covariant derivative: SU ( N ) gauge invariance: Lagrangian:

9. Rainer Fries 9SERC 2013 SU(N) Yang-Mills Fields Yang-Mills: Field strength: Vector potential: Covariant derivative: SU ( N ) gauge invariance: Lagrangian: All fields A and F and the current J are now N x N matrices. g = coupling constant of the theory. Non-abelian symmetry group  “non-abelian gauge field” One immediate consequence: quadratic and cubic terms in the equations of motion! The field theory is non-linear.

10. 1940 only 5 elementary particles were known: proton, neutron, electron, muon and positron. With the advent of accelerators at the end of the decade a big zoo of hadrons (hundreds!) was discovered. Who ordered that? Gell-Mann & Zweig (1964): the zoo of hadrons could be understood if hadrons consisted of combinations of more fundamental spin-1/2 fermions with SU( N f ) flavor symmetry. Gell-Mann called them quarks. A crazy idea at the time! Rainer Fries 10SERC 2013 Hadron Zoology Gell-Mann: ‘Such particles [quarks] presumably are not real but we may use them in our field theory anyway.’

11. An new Rutherford experiment at higher energy:  See lecture by P. Mathews Cross section for inelastic e+p scattering: extract two “structure functions” F 1 and F 2.  Simply given by leading order (one-photon exchange) QED and Lorentz invariance. Two independent kinematic variables:  is the virtuality of the exchanged photon  x is the momentum fraction of the object inside the proton struck by the photon (elastic scattering: x = 1)  They can be related to the observables: the deflection angle and the energy loss of the electron. Rainer Fries 11SERC 2013 Dissecting Hadrons  pepe pepe q

12. Different predictions had been made. Suppose the proton consists of point-like spin-½ fermions (as in the quark model). Then:  F 1, F 2 don’t depend on Q 2 (Bjorken scaling)  F 1, F 2 are not independent: (Callan-Gross relation) SLAC, 1968 (Friedman, Kendall and Taylor): Quarks it is! Rainer Fries 12SERC 2013 Quarks Bjorken scaling (shown here for HERA data) Callan-Gross

13. The complete quark family: What are their interactions? e+e- collisions: each quark comes in triplicate! New quantum number: color! Rainer Fries 13SERC 2013 Quarks

14. Fritsch, Gell-Mann, Leutwyler (1972): Quarks couple to a SU( N c ) Yang- Mills field. N c = number of colors.  Quanta of the Yang-Mills/gauge field: gluons  Color plays the role of the “charge” of the quark field. Quantum chromodynamics is born! QCD Lagrangian:  q = N f quark fields of masses m f. F = gluon field strength. Quantization: non-linearity  self-interaction of the gluon field  Gluon itself carries N c 2 -1 colors.  3-gluon vertex  4-gluon vertex Rainer Fries 14SERC 2013 Quantum Chromodynamics

15. Rainer Fries 15SERC 2013 I.2 Basic Properties of QCD

16. Analytically: No! Numerically: Yes, in certain situations  Lattice QCD.  Discretize space-time and use euclidean time.  Extremely costly in terms of CPU time, very smart algorithms needed.  See lectures by R. Gavai Perturbation theory: only works at large energy scales / short distances (see asymptotic freedom below).  Lectures by P. Pal, S. Mallik, A. Srivastava Effective theories: Based on certain approximations of QCD or general principles and symmetries of QCD (e.g. chiral perturbation theory, Nambu- Jona Lasinio (NJL) model, classical QCD etc.)  Lectures by A. Srivastava, R. Venugopalan Rainer Fries 16SERC 2013 Can We Solve QCD? QCDOC at Brookhaven National Lab

17. Running coupling in perturbative QCD (pQCD):  Perturbative  -function known up to 4 loops. Leading term in pQCD   For any reasonable number of active flavors N f = 3 … 6.  E.g. from pQCD “potential” (cf. Handbook of Perturbative QCD) In QED: Rainer Fries 17SERC 2013 Asymptotic Freedom  -function QED: e larger at higher energies/smaller distances: screening through electron-positron cloud QCD: g smaller at higher energies/smaller distances: anti-screening through gluon loops

18. Leading order running of the coupling:   QCD here: integration constant; “typical scale of QCD”   QCD  200 MeV Vanishing coupling at large energies = Asymptotic Freedom  This permits, e.g., the application of pQCD in DIS.  Large coupling at small energy scales = “infrared slavery”  Bound states can not be treated perturbatively Rainer Fries 18SERC 2013 Asymptotic Freedom Gross, Wilczek, Politzer (1974)

19. Experimental fact: no free quarks or fractional charges found. Confinement property of QCD:  Only color singlet configurations allowed to propagate over large distances.  Energy required to remove a quark larger than 2-particle creation threshold. Heuristic picture:  At large distances the Coulomb-like gluon field between quarks becomes a flux tube with string-like properties.  String breaks once enough work is done for pair creation.  Flux tubes can be understood as gluon flux expelled from the QCD vacuum. Rainer Fries 19SERC 2013 Confinement Confinement is non-perturbative. It has not yet been fully understood. It has been named one of the outstanding mathematical problems of our time. The Clay Foundation will pay you $1,000,000 if you solve it! http://www.claymath.org/

20. Why gluon flux tubes?  Anti-screening of color charges from perturbative running coupling: Dielectric constant of QCD vacuum  < 0.  Dual Meissner Effect:   0 for long distances, expelling (color) electric flux lines.  Usual Meissner Effect in superconductors: perfect diamagnetism expels magnetic flux. Potential between (heavy) quarks can be modeled successfully with a Coulomb plus linear term:  String tension K  0.9 GeV/fm.  Successful in quarkonium spectroscopy.  Can be calculated in lattice QCD (later). Rainer Fries 20SERC 2013 Confinement

21. Classical QCD has several gobal symmetries. Chiral symmetry SU( N f ) L  SU( N f ) R :  acting on 2 N f -tuple of left/right-handed quarks  Obvious when QCD Lagrangian rewritten with right/left-handed quarks :  Chiral symmetry slightly broken explicitly by finite quark masses of a few MeV. Scale invariance: massless classical QCD does not have a dimensionful parameter. Both symmetries are broken:  Chiral symmetry is spontanteously broken in the ground state of QCD by a chiral condensate.  Quantum effects break scale invariance:  QCD is scale intrinsic to QCD. Rainer Fries 21SERC 2013 Global Symmetries

22. Pions are the Goldstone bosons from the spontaneous breaking of chiral symmetry. Gell-Man-Oaks-Renner relation: Infer value of chiral condensate at T =0:  Chiral perturbation theory: decreasing with increasing temperature. There is also a gluon condensate in the QCD vacuum Dilation current   from scale invariance:  Conserved for scale-invariant QCD (Noether Theorem).  Through quantum effects:  Gluon condensate implies a non-vanishing energy momentum tensor of the QCD vacuum! Rainer Fries 22SERC 2013 QCD Vacuum

23. Assuming for vacuum from Lorentz invariance. Energy density of the vacuum: This is also called the Bag Constant for a successful model for hadrons: vacuum exerts a positive pressure P = B onto a cavity with quark modes. Summary: QCD vacuum is an ideal (color) dielectric medium with quark and gluon condensates, enforcing confinement for all but color singlet configurations. Rainer Fries 23SERC 2013 QCD Vacuum

24. Collins and Perry, 1975: Due to asymptotic Freedom coupling becomes arbitrarily weak for large energies i.e. also for large temperatures. Therefore quarks and gluons should be asymptotically free at very large temperatures T. This hypothetical state without confinement at high T would be called Quark Gluon Plasma (QGP). Expect vacuum condensates to melt as well  chiral symmetry restoration at large T. How can confinement be broken? Rainer Fries 24SERC 2013 Why Quark Gluon Plasma?

25. Rainer Fries 25SERC 2013 I.3 Free the Quarks!

26. Hadronic states cease to exist due to percolation. Density of massless free pion gas from Bose distribution growing like T 3. Pions will start to overlap at some temperature! Free pion volume with R   0.65 fm Closest packing of pions corresponds to ~ 260 MeV, percolation at which corresponds to T c = 186 MeV. Consequences:  Individual hadrons no longer well defined.  Percolation would allow quarks to propagate over large distances avoiding the QCD vacuum, confinement broken. A very simple model (massless free pions!),which gives a fair estimate of T c. Rainer Fries 26SERC 2013 End Of Confinement: Percolation

27. Hadronic physics breaks down at some temperature due to the “Hagedorn Catastrophe”. Above T  100 MeV thermal excitations of hadrons besides pions are important.  Many resonances contribute, each suppressed by factor at large mass M. Hadron spectrum at large mass:  Let be the number of resonances in a mass interval dM.  Fit to hadron spectrum: exponential increase in states parameterized as Total density of hadrons diverges for T > T 0. Hadron thermodynamics stops above T 0  150 … 200 MeV. Rainer Fries 27SERC 2013 End of Confinement: Hagedorn From YHM; originally: Gerber and Leutwyler; pions: chiral perturbation theory

28. Start with relativistic free gas of massless pions; degeneracy d  = 3 (isospin)  E.g. P and  from distributions fcts. f via energy momentum tensor:  Entropy s from thermodynamic relation Ts =  + P.  Note, speed of sound.  Corrections through interactions: cf. YHM, ch. 3.6 QGP:  Bag constant B : measure relative to vacuum.  Degeneracy:  d QGP = 37 for two light flavors, d QGP = 47.5 for three light flavors. Massive increase in degrees of freedom from hadron gas to QGP. Rainer Fries 28SERC 2013 QGP as a Relativistic Free Gas

29. Assume free pion gas and free quark gluon gas as two phases.  Low T : P  > P QGP due to bag constant  pion gas preferred state  High T : P  < P QGP due to larger degeneracy in QGP  QGP preferred state Phase transition: phase equilibrium requires P  = P QGP With B =(220 MeV) 4 and N f =2: T c  160 MeV. While P is continuous,  and s exhibit a jump at T c  first order phase transition. Latent heat. So far zero baryon chemical potential  = 0 (i.e. equal numbers of quark and antiquarks in equilibrium). Rainer Fries 29SERC 2013 A Simple Equation of State From YHM

30. Currently best method to determine the QCD equation of state: lattice QCD  See lectures by R. Gavai.  Have to test against experiment + hydrodynamic simulations. Transition as a function of quark masses (“Columbia plot”)  Pure Yang-Mills ( N f =0 or all masses   ): 1 st order, T c  260 MeV.  For realistic N f = “2+1” (light u,d, medium heavy s): crossover for  = 0. Chiral condensate = order parameter for chiral phase transition. Transition temperature for chiral phase transition:  T c = 154  9 MeV [RBC-Bielefeld]  T c = 151 MeV [Wuppertal-Bielefeld] Static heavy quark potential: QCD strings melt Rainer Fries 30SERC 2013 QGP: Survey of Lattice QCD Results Static quark potential (Karsch et al.) HotQCD, chiral condensate

31. Phase diagram of QCD in T -  plane: away from  =0 very little known. Sign problem for  ≠ 0 in lattice QCD.  Need innovative techniques: reweighting, Taylor expansion, imaginary , … Probably a critical point (endpoint of 1 st order phase transition line) located close to T = T c and  ~ 200-400 MeV. Rainer Fries 31SERC 2013 QGP: Survey of Lattice QCD Results [Fodor, Katz, JHEP 04, 050 (2004)]

32. Lattice equation of state (EOS)  Predictions closing in on realistic quark masses.  Here m  ~ 200 MeV. Interaction measure Compatible with HRG below ~ 160 MeV. Agreement with pQCD above 2-3 T c.  See Thermal Field Theory lectures by S. Mallik  First hint that QGP near T c is not a free gas! Rainer Fries 32SERC 2013 QGP: Survey of Lattice QCD Results HotQCD (2012) RBRC-Bielefeld (2008)

33. Rainer Fries 33SERC 2013 I.4 The Cosmic Connection

34. Rainer Fries 34SERC 2013 Matter In The Early Universe [www.nasa.gov] The history of luminous matter. Expansion + cooling; clumping and local reheating for the past ~ 13 billion years. Governed by gravity, dark matter, dark energy, … The tiny first second of the universe: strong and electroweak forces are important! And maybe much more exotic stuff …

35. Thermodynamic history: succession of phase transitions and freeze-outs. Rapid decrease in degrees of freedom. QCD transition @ ~ few  s Rainer Fries 35SERC 2013 The First Second Nuclear Physics: Strong Force/QCD time [D.J. Schwarz, Ann. Phys. 12, 220 (2003)] HEP: new particles? Atoms Galaxies … 10 9 K 10 12 K 10 15 K

36. Bulk properties (thermodynamic, transport, …) of QCD played an important role in the early universe.  Order of the QCD phase transition, latent heat, speed of sound, … Enduring cosmic effects?  Initial conditions for nucleo-synthesis and beyond.  Mass generation for luminous matter.  Relics? How can QGP be studied experimentally today? Rainer Fries 36SERC 2013 The QCD Transition in the Cosmos u u d u d u  s d u d g g g p ++ ~ 10 12 K

37. How can we study the QCD transition today?  Impacting cosmic rays (nuclear component!) – impractical  Nuclei in particle accelerators! Problem: extremely short life times ~ 10 -23 s for the fireball ~ typical time scales of QCD. Rainer Fries 37SERC 2013 Let’s Create a ‘Little Bang’ LHC: s NN = 14(7) TeV (p+p) s NN = 5.5(2.76) TeV (Pb+Pb) s tot = 1.1(0.55) PeV (Pb+Pb) T max ~ 800 MeV RHIC: s NN = 500 GeV (p+p) s NN = 200, 130, … 7.7 GeV (Au+Au) s tot,max = 40 TeV (Au+Au) T max ~ 400 MeV

38. 1. What is the gauge transformation for a quark field q ? Show that the derivative   q does not transform the same way but the covariant derivative D  q does. 2. Calculate the ratio of cross sections in e + e - from p. 13. 3. Familiarize yourself with the integrals over Boltzmann, Bose and Fermi functions. You can look at exercise 3.4 in YHM and ch. 10.4 in LR for guidance. For Boltzmann integrals the following representation of the McDonald (modified Bessel) functions is useful: What is the energy density of a free Boltzmann gas of particles of mass m and temperature T ? Rainer Fries 38SERC 2013 Homework Suggestions I

39. Introduction to Heavy Ion Collisions Part II: Ultra-relativistic heavy ion collisions

40. Rainer Fries 40SERC 2013 II.1 Preliminaries

41. Thousands of particles created. Directed kinetic energy of beams  mass (particle) production + thermal motion + collective motion Rainer Fries 41SERC 2013 High Energy Heavy Ion Collisions (HICs) RIKEN/BNL Research Center

42. Lorentz contraction of the nuclei L ~ R /   0. Approximate boost-invariance in beam direction a la Bjorken (later) Fireball: Longitudinal (~ boost invariant expansion) throughout time evolution  Not much altered through pressure gradients. Pressure in transverse expansion: collective transverse acceleration and expansion For arbitrary impact parameter b : elliptic overlap shape in transverse plane (“almond shape”)  For non-spherial nuclei (e.g. U+U) many more geometrical degrees of freedom. Rainer Fries 42SERC 2013 Basic Geometry x y z

43. 1.Initial condition: nuclear wave functions 2.After nuclear overlap: no immediate thermalization of matter  Probably strong gluon fields/glasma. 3.Approx. thermal and chemical equilibrium reached after ~ 0.2 – 1.0 fm/c  Around midrapidity, checked through applicability of hydrodynamics. 4.QGP phase: initial temperatures up to ~400/600 MeV (RHIC/LHC)  Transverse expansion and cooling of the fireball 5.Hadronization around T c and subsequent hot hadron gas phase  HRG may fall out of chemical equilibrium at “chemical freeze-out”. 6.Decoupling of hadrons (“kinetic freeze-out”) and free streaming of hadrons to detectors. Rainer Fries 43SERC 2013 Time Evolution 12456

44. For near boost-invariant system replace t and z coord. by longitudinal proper time  and space time rapidity .  Transverse plane = perp. to beam axis For some purposes light cone coordinates are used: Corr. in momentum space: rapidity such that the Lorentz-invariant phase space element is Experimentally preferred: pseudo-rapidity Relation: Rainer Fries 44SERC 2013 Kinematics From LR

45. Basic idea: Nuclei with ~ speed of light go through each other. Produced particles or fluid cells separate by velocity, i.e. z ~ v z. Definition for any observable O : (  = Lorentz boost)  In momentum space observables independent of y.  In hydro picture: quantities only depend on difference  - y. Breaking through finite nuclear velocities.  Cutoff at beam rapidity. Boost invariance is a good approximation around midrapidity y =0. Time evolution again drawn in Minkowski diagram for boost-invariant system: Rainer Fries 45SERC 2013 Boost Invariance From LR

46. Bjorken scenario: nuclei go through each other. Nuclei = bulk of net baryon number! Energy is deposited between the receding nuclei. BRAHMS baryon number at top RHIC energy:  dy = 2.0  0.4  Nucleon: 100 GeV  27 GeV With a field+QGP model (Kapusta, Mishustin) model from deceleration of the nuclei Rainer Fries 46SERC 2013 What Happens to the Nuclei? From LR Bjorken Landau

47. Not all particles are thermalized  Fireball lifetimes of 10-15 fm/c are too short. Soft particles ( P T 99%, “bulk” fireball  Thermalization  Quark Gluon Plasma  hydrodynamic expansion and cooling Hard particles ( P T > 1 -2GeV): <1%, rare “hard” probes  No or insufficient thermalization. Hard particles usually come from QCD jets. Prediction:  energy loss or fast partons and hadrons (“jet quenching”)  Can measure properties of QGP via transport coefficients. See Chapter 3. Rainer Fries 47SERC 2013 Hard Probes Soft Hard 99% 1% Some particles accelerated much more: fast probes. Fireball

48. Electromagnetic (EM) probes = penetrating probes  Photon/lepton mean free path in QGP ~ 100  quark/gluon mfp.  Neglect any final state interactions.  Photons: e.g. temperature measurements from thermal radiation  Dileptons: e.g. in-medium modifications of vector mesons Heavy Flavor Probes: hadrons with charm or bottom quarks.  < 1% of particle content, not in chemical equilibrium  Thermalization time delayed by ~ m / T, larger than lifetime of fireball  Degree of thermalization  strength of interactions in QGP  Quarkonia: melting order  thermometer Generally:  Bulk hadrons = snap shot at T = T fo.  Hard, electromagnetic and heavy flavor probes: integrals over time evolution. Possibly information from early times! Rainer Fries 48SERC 2013 Other Probes

49. Find QGP  Classical QGP signatures:  Strangeness enhancement.  Quarkonium melting.  Thermal QGP radiation Measure “text book” properties of QGP:  Phase diagram and equation of state  Transport coefficients like viscosities  New phenomena: color glass, chiral magnetic effect, etc. Rainer Fries 49SERC 2013 What to Measure?

50. Rainer Fries 50SERC 2013 II.2 Basic Observations

51. So easy to measure in experiment, so hard to calculate in theory! dN / dy per participant: slow growth with  s and centrality. LHC predictions: no model does very well in both shape and normalization! Rainer Fries 51SERC 2013 Multiplicities [Andronic et al, arXiv:1210.7724] More on color glass [Albacete et al., Kharzeev et al.] later and in lectures by R. Venugopalan

52. Hadrons are found in chemical equilibrium.  Compare to prediction from  Chemical freeze-out temperature T chem ~ 160-170 MeV  T chem independent of  s at large energies  Very small  B, compatible with dN B / dy measurements. Enough time to chemically equilibrate!  But inelastic processes (e.g. K+p   +  ) shut off below T chem ; elastic processes needed for kinetic equilibrium! Rainer Fries 52SERC 2013 Chemical Equilibrium [Andronic et al, arXiv:1210.7724] [Braun-Munzinger, Stachel, arXiv:1101.3167]

53. Another important test for equilibration: thermal transverse spectra of hadrons. However: thermal source is not at rest: collective transverse expansion.  Boltzmann with flow velocity u  :  At low p T : typical “flow shoulder” for heavier hadrons.  At high low p T : blue shift of temperature Rainer Fries 53SERC 2013 Thermal Equilibrium and Flow Collective flow can also be observed in the average transverse momenta of different particles as a function of mass.

54. Bulk hadron data for p T < 2 GeV can be fit well by “blast wave shape” = thermal distribution + flow.  Temperature in the fit = kinetic freeze-out temperature, typically ~100 MeV.  Typical average velocities 0.5-0.7 c for central RHIC and LHC. Kinetic equilibrium below T chem is maintained by elastic scattering. Realistically: Not all particles decouple at the same temperature.  Furthermore: decoupling is not a sudden process but a gradual shut off of the interaction rate. This can be seen in higher freeze-out temperatures for multi-strange hadrons,e.g. , ,  (“sequential freeze-out)  Small cross sections of these particles in a HRG. Rainer Fries 54SERC 2013 Flow and Freeze-out

55. Initial spatial eccentricity in transverse plane at finite b  final momentum space anisotropy of produced particles. Mechanism for bulk particles: anisotropy in pressure gradients. Analysis of final particle anisotropy in terms of harmonics:  v 2 = elliptic flow Excellent test for hydro and transport models. v 2 data requires short equilibration times ~ 0.2–1 fm/c. Rainer Fries 55SERC 2013 Elliptic Flow x y z

56. Spatial eccentricity self quenches.  Plot: Spatial and momentum space anisotropies in ideal hydro with two EOS for b=7 fm Au+Au at RHIC (Kolb and Heinz) v 2 as function of p T : mass ordering Excellent test for hydro and transport models. v 2 data requires short equilibration times ~ 0.2–1 fm/c. Rainer Fries 56SERC 2013 Elliptic Flow [Ideal hydro, RHIC: P. Huovinen et al., Phys. Lett. B 503, 58 (2003)] [Viscous hydro, LHC: C. Shen et al., arxiv:1105.3226]

57. Rainer Fries 57SERC 2013 II.3 Modeling the Fireball

58. Simple estimate for average energy density, boost-invariant longitudinal expansion only (Bjorken):  A = transverse area,  0 = formation time.  PHENIX: ~ 5.4 GeV/fm 3 in central Au+Au collisions at RHIC.  Well above ~ 1 GeV/fm 3 for the critical energy density. Blast-wave models: an attempt to parameterize the flow field at the time of kinetic freeze-out.  Flow rapidity:   0,  2 = radial and elliptic flow parameters  Reduced radius  Flow angle given by  The flow field u  ( r,  s ) given by ,  b has to be used in distribution.  Decent description of bulk spectra and elliptic flow. Rainer Fries 58SERC 2013 Two Simple Models [BW by Retiere and Lisa, PRC 70 (2004)]

59. Nuclear collision = collisions of nucleons moving on eikonal lines. Given a N-N cross section compute density of binary N-N collisions n coll and density of participants n part in the transverse plane. Here: n coll briefly, more details in tutorials by P. Shukla.  Let f 1 (r), f 2 (r) be the transverse area densities of nucleons.  Collision density: Example: head-on ( b =0) collision of Pb nuclei at 2.76 TeV.  Total number of binary collisions: Rainer Fries 59SERC 2013 Glauber Model

60. Previous example: “optical” Glauber with hard sphere nuclei; better: Monte Carlo implementation with realistic nucleon distribution. Glauber allows an identification    Exp. centrality  Typical Glauber table (here ALICE) Common model assumption: Large-x/hard processes resolve individual nucleons, their yield scales like N coll.  Confirmed (later)! Soft processes/bulk multiplicities come from coherent interactions and yield scales with N part.  More refined: hydro Glauber initial conditions often modeled as linear combination  This is an assumption, there is no first principle connection between the Glauber model and a hydro energy density! Rainer Fries 60SERC 2013 Glauber Model

61. From optical Glauber: N coll ~ A 4/3, N part ~ A scaling with nuclear size. Recent evidence (later) suggests the importance of getting initial fluctuations right. Fluctuations in Glauber Monte Carlo important:  Codes publicly available, e.g. PHOBOS Glauber MC, GLISSANDO etc. Important properties of initial state fluctuations:  Event plane can rotate from obvious reaction plane (given by beam axis and impact vector).  Odd eccentricities (triangularity  3,  5, …) no longer vanish.  Modifications to the size of  2 and v 2, e.g. for most central collisions. Rainer Fries 61SERC 2013 Glauber: Initial Fluctuations

62. Most promising idea for describing early times in HICs: color glass condensate. See lectures by R. Venugopalan. Nuclei/hadrons at asymptotically high energy:  Saturated gluon density ~ Q s -2  scale Q s >>  QCD  Probes interact with many quarks + gluons coherently.  Large occupation numbers  quasi-classical fields.  Large nuclei are better: Q s ~ A 1/3 Effective Theory a la McLerran & Venugopalan  For intersecting light cone currents J 1, J 2 (given by SU(3) charge distributions  1,  2 ) solve Yang-Mills equations for gluon field A  (  1,  2 ).  Calculate any observable O(  1,  2 ) from the gluon field.  Compute expectation value of O by averaging over  1,  2. since those are arbitrary frozen fluctuations of a color-neutral object. Rainer Fries 62SERC 2013 Color Glass [L. McLerran, R. Venugopalan] [A. Kovner, L. McLerran, H. Weigert] …

63. First step: calculate field of an SU(3) (color) capacitor expanding with the speed of light! Before the collision: color glass = pulse of strictly transverse (color) electric and magnetic fields, mutually orthogonal, with random color orientations, in each nucleus. Rainer Fries 63SERC 2013 Color Glass

64. First step: calculate field of an SU(3) (color) capacitor expanding with the speed of light! Before the collision: color glass = pulse of strictly transverse (color) electric and magnetic fields, mutually orthogonal, with random color orientations, in each nucleus. Immediately after overlap (forward light cone,   0): strong longitudinal electric & magnetic fields. Rainer Fries 64SERC 2013 Initial Gluon Fields E0E0 B0B0 [L. McLerran, T. Lappi] [RJF, J.I. Kapusta, Y. Li] …

65. First step: calculate field of an SU(3) (color) capacitor expanding with the speed of light! Before the collision: color glass = pulse of strictly transverse (color) electric and magnetic fields, mutually orthogonal, with random color orientations, in each nucleus. Immediately after overlap (forward light cone,   0): strong longitudinal electric & magnetic fields. Transverse E, B fields start linearly in time  Rainer Fries 65SERC 2013 Initial Gluon Fields [RJF, J.I. Kapusta, Y. Li] [T. Lappi]

66. Initial structure of the energy-momentum tensor Equilibration: pressure isotropization hydrodynamics! Mechanism of fast kinetic equilibration not well understood (for CGC, see lecture by R. Venugopalan) Rainer Fries 66SERC 2013 Energy-Momentum Tensor Later: Ideal plasma (local rest frame)  p T L Transverse pressure P T =  0 Longitudinal pressure P L = –  0 Gauge fields: Particle distributions f : [Lappi] [RJF, Kapusta, Li] [Fujii, Fukushima, Hidaka]

67. Once the system is at (close to) kinetic equilbrium hydrodynamics can be applied to simulate expansion and cooling, see lectures by T. Hirano Hydrodynamics = universal long wave length dynamics of fluids in or close to thermal equilibrium. Ideal relativistic hydrodynamics = energy-momentum conservation + current conservation for all conserved charges + equation of state Corrections to the shape of EM tensor when slightly off equilibrium:  ,   and W  and V  are bulk stress, shear stress, energy flow and particle flow. Rainer Fries 67SERC 2013 Hydrodynamics

68. In 1 st order viscous hydrodynamics viscous stress comes from gradients of the velocity field, e.g. (Navier-Stokes) where ,  are the bulk and shear viscosity. 2 nd order viscous hydrodynamics: need this order to avoid acausalities in 1 st order relativistic theory, introduce relaxation of bulk and shear stress to Navier-Stokes values. One central result of viscous hydro: v 2 breaks down at larger p T  bounds on shear viscosity over entropy density  / s from experiment Rainer Fries 68SERC 2013 Hydrodynamics [T. Hirano] [Romatschke 2 ]

69. State of the art hydro: include fluctuations in initial conditions and run hydro event-by-event to get all anisotropy coefficients v 2, v 3, v 4, … Freeze-out: pure hydro = sudden freeze-out from fluid cells into particles on hypersurface defined by T = T fo. State-of-the-art: switch to hadronic transport model like URQMD between T c and T fo., advantage: microscopic modeling of dissipative effects, realistic freeze-out. More on hydro and transport in lectures by T. Hirano, S.Bass and V. Greco Rainer Fries 69SERC 2013 Hydrodynamics [M. Lisa using AZHYDRO] [Schenke, Jeon and Gale]

70. Rainer Fries 70SERC 2013 II.3 Outlook

71. Viscosity and sQGP  Lectures by T. Hirano, S. Bass, V. Greco Transport models  Lectures by S. Bass,V. Greco Mapping the phase diagram, beam energy scan  S. Bass (?) Hard probes and jets(?)  chapter 4 Photons and dileptons(?)  chapter 6 Quark recombination  chapter 5 Heavy flavors physics  chapter 7 (?), lecture by S. Bass Rainer Fries 71SERC 2013 What is Missing Here?

72. 1. Derive the relation between rapidity and pseudorapidity as shown on p.44 2. Reproduce basic features of the spectra and elliptic flow measured in heavy ion collisions qualitatively using the blast wave model from p. 58, assuming reasonable parameters. 3. In the Glauber model, calculate the total number of binary collision for a Au+Au collision at 200 GeV with an impact parameter of 7 fm. 4. Solve the equations of ideal hydrodynamics analytically for a boost- invariant system that is isotropic and translationally invariant in the transverse plane (a so-called 1+1 dimensional hydro). Assume a simple free relativistic gas equation of state  = 3 P. How does the energy density behave as a function of proper time  ? Rainer Fries 72SERC 2013 Homework Suggestions II

73. Introduction to Heavy Ion Collisions Part III: Hard Probes

74. Rainer Fries 74SERC 2013 III.1 Hard Processes

75. High momentum quarks/gluons produced  QCD jets Confinement  single partons have to create collimated sprays of hadrons.  First seen in e + e - collisions. Possible measurements: Find jets in the calorimeter and measure their energies.  Only recently possible in HICs. Find modifications. Measure high momentum hadrons inside jets (but w/o identifying jets) Rainer Fries 75SERC 2013 QCD Jets Jets in p+p

76. Spectra (jets or high- p T hadrons) are best measured against the p+p reference. Introduce nuclear modification factor Collision scaling for hard processes confirmed by  R AA for photons/Z/W = 1  R AA for hadrons  1 for rising impact parameter b. Basic conclusion from hadron R AA data  Suppression = “jet quenching”  This originates from energy loss of partons in the surrounding QGP medium. Rainer Fries 76SERC 2013 Nuclear Modification Factors

77. Production of high momentum partons in collisions (p+p, A+A) still involves bound states which are non-perturbative. Reason we can apply pQCD: factorization theorems Basic scheme of “collinear factorization” for A+B  C+X  A,B,C = hadrons (A,B could also be nuclei) What is the meaning? The leading contribution (“leading twist”) to A+B  C+X consists of one parton each from A,B,C, called a,b,c undergoing a hard scattering a+b  c+x. Contributions with more partons are suppressed by powers of 1/Q(“higher twist”), Q = single hard momentum scale in the process. Rainer Fries 77SERC 2013 Factorization PDF Parton cross section PDF FF FF= fragmentation function (parton  hadrons) Expect modifications in nucleus- nucleus here. PDF= parton distribution function

78. Leading twist contribution in a diagram: “Hard part” of the process: the partonic cross section a+b  c+x, calculable in perturbation theory. “Soft part”: parton distributions, fragmentation functions dealing with long- distance dynamics of QCD. Not calculable in pQCD but universal! Rainer Fries 78SERC 2013 Factorization

79. Large momentum transfer ensures small coupling. Perturbative expansion of the parton cross section possible: Leading order cross sections have long been calculated, see Owens, Rev. Mod. Phys. 59, 465 (1984).  One example: q+q’  q+q’ (one of many channels at LO).  s, t, u = Mandelstam variables. Next-to-leading order: includes first radiative corrections; codes available, e.g. PHOX family Rainer Fries 79SERC 2013 Parton Cross Sections q q’

80. Parton distribution function = probability to find a parton a in a hadron H with a momentum fraction  (0 <  < 1).   and  here are the same variables as x and Q in deep-inelastic scattering. Definition in terms of operators (light cone gauge). Scale dependence (on  ) vanishes at leading order (called the naïve parton model) and is weak (logarithmic) if radiative corrections are calculated (this is the same as the near Q-independence of F 1, F 2 in DIS!)  Diagrams for leading and next-to-leading order quark PDFs: Rainer Fries 80SERC 2013 PDFs and Fragmentation Fcts.

81. Radiative corrections leads to the famous DGLAP equations which determine the dependence of every f on .  E.g. quark splitting function: Important: Universality! PDFs are independent of the process. PDFs for a hadron can be measured in DIS and used to calculate jet production at the LHC.  Proton PDFs well known down to  ~10 -5 (CTEQ, MSTW etc.)  PDFs for nuclei have large uncertainties! Fragmentation function: probability to find a hadron H with momentum fraction z (0< z <1) in a jet created by a parton a (here a quark). Analogous to PDFs in many ways. Rainer Fries 81SERC 2013 PDFs and Fragmentation Fcts.

82. Here: assume LO cross sections. For more see [Fries and Nonaka, Prog. Part. Nucl. Phys. 66 (2011)] Best starting point: A+B  two jets (represented by partons c,d); again A,B are protons or nuclei; y a, y b = jet rapidities, p T = shared transverse momentum.  Parton momentum fractions fixed by energy and momentum conservation: Example: single hadron production as a function of hadron P T and rapidity y from a collision A+B (protons or nuclei). Rainer Fries 82SERC 2013 Handy Factorization Formulas

83. Rainer Fries 83SERC 2013 III.2 Nuclear Modifications

84. How do hard processes in A+A differ from p+p. First initial state effects. nPDFs: Much less known than proton PDFs, in particular gluons.  Big problem for LHC baseline calculations. Usual ansatz:  Isospin mixing  In addition: shadowing and EMC effect encoded in modification factor R A. Rainer Fries 84SERC 2013 Nuclear Parton Distributions [Eskola et al., (1998, 2008)]

85. Higher twist = higher dimensional operators beyond parton distributions, suppressed by (  /Q) n. In very large nuclei A this twist expansion can be changed since some operators scale like. These operators (“nuclear enhanced higher twist”) usually correspond to multiple scattering. E.g.: leading and next-to-leading twist for Drell-Yan (dilepton production): The new operator describing a quark and a gluon in nucleus A is  Kinematically the gluon is restricted to be very soft here. This is a two-parton distribution function that encodes correlations between quarks and gluons. Rainer Fries 85SERC 2013 Higher Twist in Nuclei [For review: Fries and Nonaka, Prog. Part. Nucl. Phys. 66 (2011)]

86. N -parton (higher twist) distributions are universal and should be measured and parameterized just like (1-)parton distribution functions.  However very little is known besides approximate normalization of 2-parton functions.  Ansatz: Back to Drell-Yan example, leading and next-to-leading twist (LT/NLT):  where Rainer Fries 86SERC 2013 Higher Twist in Nuclei

87. Because of the derivative on the  -function this NLT does not contribute to the q T -integrated cross section. Calculate the average transverse momentum square of the dilepton pair: With the model from above for two equal nuclei Expect transverse momentum broadening in A+A collisions, increasing with nuclear size as A 1/3. Physical picture: multiple scattering in the initial state leads to a random walk in q T -space. Rainer Fries 87SERC 2013 Higher Twist in Nuclei

88. This enhancement of average transverse momentum is known as the Cronin effect. Cronin et al. (1975): Usual explanation: partons have to travel through (cold) nuclear matter and receive random soft kicks before undergoing the hard scattering.  Path length dependence typical for random walk. As a function of P T : particles are pushed away from P T = 0 but total yield is not changed. Higher twist corrections explain the effect within a strict pQCD framework! Rainer Fries 88SERC 2013 Cronin Effect

89. Rainer Fries 89SERC 2013 III.3 Parton Energy Loss

90. Dominant effect of final state effects on hadrons: energy loss (seen as a suppression of R AA ). Dominant process for light quarks/gluons: inducedsluon bremsstrahlung. Medium is usually characterized by a transport coefficient, the average squared momentum transfer per mean free path. Rainer Fries 90SERC 2013 Energy Loss Models 00 Medium Leading jet parton

91. Generic feature: Landau-Pomeranchuk-Migdal (LPM) effect. Consider formation time of radiation (transv. mom. k T, energy  ):  If mean free path > t f : incoherent scattering  If t f / ; interference effects.  Deeply coherent regime: t f > L (length of the medium) In the LPM region the energy loss per unit length is, i.e. total energy loss is quadratic in path length L. Several calculations for single particle energy loss on the market:  Will focus on one here as an example. Rainer Fries 91SERC 2013 Energy Loss Models AMY BDMPS ASW GLV DGLV Higher Twist AMY Perturbative plasma in the high temperature limit Extrapolated from DIS off large nuclei (e+A  h+X)

92. Consider energy loss in cold nuclear matter, here semi-inclusive DIS on nucleus A, i.e. a hadron from the quark scattered by the photon is measured. [X. F. Guo and X. N. Wang, PRL 85 (2000)] Cross section can be written as  “Hadronic tensor W  ” describes the process  * + A  H + X Leading twist, LO (2) and NLO (2’) in the coupling constant: Rainer Fries 92SERC 2013 Higher Twist Formalim

93. Next-to-leading twist correction to diagrams 2’ (two examples): scatter off additional parton from the nucleus. Two poles (indicated by circles) contribute with alternating signs  destructive interference, the origin of the LPM effect in this approach.  The T ag/A are quark-gluon distribution functions similar to before. Rainer Fries 93SERC 2013 Higher Twist Formalism

94. The NLT correction can be written in the same form as the leading twist with a modified fragmentation function which obeys the evolution equation with an additional term in the splitting function Simultaneous fitting of D and T not possible. Need to model them: , note interference term.  First iteration for fragmentation function: Rainer Fries 94SERC 2013 Higher Twist Formalism

95. Can calculate average energy loss of parton through the modification of the splitting function: So, LPM effect recovered. These results do well with data on semi-inclusive DIS on nuclei (e.g. HERMES). [Wang andWang] Conjecture: these results can be applied to the final state interactions of partons in QGP medium. E.g. simple ansatz for modified fragmentation function with momentum shift  z : Rainer Fries 95SERC 2013 Higher Twist: Energy Loss

96. Energy loss models fit or analogous parameter to R AA data and Comparative study by Bass et al. on RHIC data Most models underpredict v 2 data: v 2 at high p T is created by different path length in and out of plane. Consensus: is roughly a few GeV 2 /fm around the formation time of QGP, about 15 times larger than for cold nuclear matter. Rainer Fries 96SERC 2013 Phenomenology [Armesto et al., arxiv:0907.0667] [Wang and Wang]

97. Rainer Fries 97SERC 2013 III.4 Some Backup Topics

98. New ways to extract information: changes in chemical composition of jets. Jet particles couple to QGP  chemical gradients  changing hadro- chemistry for jets  Additional photons; quark  gluon conversions  Results are sensitive to the mean free path in the medium. Predictions (RHIC high P T )  enhanced strangeness yield  reduced strangeness v 2. No enhancement for strangeness at LHC, no enhancement for charm+bottom. Rainer Fries 98SERC 2013 Jet Chemistry q, g photon q, g s [W. Liu, RJF, PRC 77, 054902 (2008)] [W. Liu, RJF, PRC 78, 037902 (2008)] [RJF et al., PRL 90, 132301 (2003)] [C.M. Ko et al., JIMP E 16, 1930 (2007)] STAR preliminary

99. Why tomography? Is it possible? Access to certain correlation observables  R measures average initial spatial fluctuations.  Relation to energy loss: Potential signatures in experimental data: Rainer Fries 99SERC 2013 Tomography Of The Little Bang density of jets emerging density of QGP average correction due to fluctuations [R. Rodriguez, RJF, E. Ramirez, Phys. Lett. B 693 (2010)]

100. JET = Jet and Electromagnetic Tomography of Extreme Phases of Matter  http://jet.lbl.gov/ http://jet.lbl.gov/  DOE Topical Center in Nuclear Theory, ~2.4 M$  Columbia, Duke, LANL, LBNL, LLNL, McGill, Ohio State, Purdue, Texas A&M  PIs at Texas A&M: RJF and Che-Ming Ko Goal: Improve our understanding of hard probes in heavy ion collisions and develop a tool set that allows a quantitative characterization of hard probes in quark gluon plasma. Rainer Fries 100SERC 2013 Advertisement: JET Collaboration

101. Introduction to Heavy Ion Collisions Part IV: Quark Recombination

102. Hadronization = difficult, non-perturbative problem We are often saved by applying two limits:  Universality at large momentum  fragmentation functions, can be measured.  Thermalization at low momenta  equation of state, can be calculated on the lattice. What happens in other cases? Important to know in heavy ion phenomenology. In practice in HICs: intermediate P T range between 2 and 6 GeV/c described neither by hydrodynamics nor pQCD. New phenomena observed! Rainer Fries 102SERC 2013 Why Quark Recombination?

103. RHIC+LHC: strong quenching of high- P T pions and kaons.  As we now know: parton energy loss. No jet quenching for baryons? ( R AA, R CP ~ 1)  Seen for P T ~ 1.5 … 5 GeV/c.  “Baryon Anomaly” at intermediate P T. Rainer Fries 103SERC 2013 Baryon Puzzle PHENIX

104. Proton/pion ratio > 1 at P T ~ 4 GeV in Au+Au collisions. Expectation from parton fragmentation: p/  ~ 0.1 … 0.3  As measured in p+p and e + +e - Rainer Fries 104SERC 2013 Baryon Puzzle PHENIX

105. General baryon/meson pattern: p, , ,  versus K, , , K*,  Rainer Fries 105SERC 2013 Baryon vs Meson

106. Scaling first found experimentally  n = number of valence quarks Very much unlike (ideal) hydrodynamics Rainer Fries 106SERC 2013 Elliptic Flow Scaling

107. In addition at low P T : scaling with kinetic energy  Inspired (but not precisely described) by hydrodynamics. Scaling of both KE T and n close to perfect up to KE T /n ~ 1.0 GeV. KE T scaling is not a recombination effect but can be explained by flow and sequential freeze-out. Rainer Fries 107SERC 2013 Elliptic Flow Scaling [He, Fries and Rapp, PRC (2010)]

108. Simplest realization of a recombination model  Recombine valence quarks of hadrons  Dressed quarks, no gluons Instantaneous projection of quark states (density matrix  ) on hadronic states with momentum P: Effectively: 2  1, 3  1 processes  Big caveat: projection conserves only 3 components of 4-momentum. Rainer Fries 108SERC 2013 Instantaneous Coalescence Model

109. Hadron spectra can be written as a convolution of Wigner functions W,   Replace Wigner function by classical phase space distribution “Master formula” for all classical instantaneous reco models One further approximation: collinear limit  Similar to light cone formalism with k T >> P Rainer Fries 109SERC 2013 Instantaneous Coalescence Quark Wigner function Meson Wigner function Production hypersurface [Greco, Ko & Levai] [RJF, Müller, Nonaka & Bass] [Hwa & Yang] [Rapp & Shuryak] Can be modeled with hard exclusive light cone wave functions

110. Thermal parton spectra yield thermal hadron spectra.  For instant. recombination (collinear case):  Should also hold in the transport approach.  Automatically delivers N B ~ N M if mass effects are suppressed Details of hadron structure do not seem to be relevant for thermal recombination at intermediate and high momentum.  Wave function can be integrated out.  Important for elliptic flow scaling.  Also seen numerically in full 6-D phase space coalescence. Rainer Fries 110SERC 2013 The Thermal Case

111. Comparison of different scenarios Power law parton spectrum  Recombination is suppressed  Good: QCD factorization should hold at least for asymptotically large momentum Exponential parton spectrum  Recombination more effective  Even larger effect for baryons Rainer Fries 111SERC 2013 Exponential and Power Law Spectra Exponential: Power law: for mesons

112. Recombination of thermal partons dominates up to 4 GeV/c for mesons, 6 GeV/c for baryons at RHIC; maybe slightly higher at LHC. Rainer Fries 112SERC 2013 Phenomenology [Greco, Ko & Levai] [RJF, Müller, Nonaka & Bass]

113. Assume universal elliptic flow v 2 p of the partons before the phase transition Recombination prediction  Factorization of momentum and position space (!) Recover scaling law for infinitely narrow wave functions  Scaling holds numerically also for less special choices. Rainer Fries 113SERC 2013 Elliptic Flow Scaling Momentum shared: fractions x and 1-x

114. Scaling law potentially receives uncertainties from:  Hadron wave function (higher Fock states, shape)  Non-trivial space-momentum correlations  Resonance decays, hadronic phase (pions!) Experimentally: small deviations confirmed Rainer Fries 114SERC 2013 Deviations From Scaling

115. Resonance Recombination Model: Boltzmann approach applied to ensemble of quarks and antiquarks Mesons = resonances created through quark-antiquark scattering  Breit-Wigner cross sections: In the equilibrium limit: Properties:  Conserves energy and momentum, leads to finite hadronization times.  Is consistent with kinetic equilibrium (checked explicitly).  Baryons: difficult, need to implement diquarks. Rainer Fries 115SERC 2013 Alternatives: Transport Approach [Ravagli & Rapp PLB 655 (2007)] [Ravagli, van Hees & Rapp, PRC 79 (2009)]

116. Introduction to Heavy Ion Collisions Part V: Electromagnetic Probes

117. Identify all important sources and develop a strategy to measure them individually. Transverse momentum spectra of single direct photons  Hierarchy in momentum  Reflects hierarchy in average momentum transfer (or temperature) in a cooling and diluting system) More sophisticated strategies:  Elliptic Flow  Correlations of photons with hadrons and jets Most things here also applicable to dileptons. Rainer Fries 117SERC 2013 Classifying Photon Sources EE Hadron Gas Thermal T f QGP Thermal T i “Pre-Equilibrium”? Jet Re-interaction √(T i x√s) Hard prompt

118. Prompt photons from initial hard scattering of partons in the nuclei. Calculable in factorized QCD perturbation theory, p+p collisions: important baseline to understand prompt photons in heavy ion collisions despite somewhat different initial state. Rainer Fries 118SERC 2013 Prompt Hard Photons Compton Annihilation PDF Parton cross section PDF Parton processes at leading order:

119. Parton process: PDF Parton cross section PDF FF Photons can also fragment off jets created in initial collisions (Bremsstrahlung)  Described by photon fragmentation function  Factorization: At NLO, prompt hard and fragmentation photons can be treated consistently. Possible problem in nuclear matter:  Final state suppression for fragmenting photons but not for prompt photons?  Induces uncertainty in direct photon baseline. Rainer Fries 119SERC 2013 Fragmentation Photons

120. Photon world data @ hadron colliders [Aurenche et al., PRD (2006)] Direct photons in p+p = prompt hard photons and fragmentation photons. Direct photon data in p+p well described by NLO pQCD calculations. This seems like a safe baseline! In A+A: the usual cold nuclear matter effects in the initial state:  Nuclear PDFs  Cronin effect Rainer Fries 120SERC 2013 Photon Baseline

121. Annihilation, Compton and bremsstrahlung processes also occur between thermalized partons in a QGP. Hope to measure the temperature T (or its time-average), confirm existence of deconfined quark-gluon phase Resummation program (hard thermal loop) + collinear radiation (AMY) A hot hadron gas shines as well.  Annihilation, creation and Compton-like processes with pions  + vector mesons, baryons … Rainer Fries 121SERC 2013 Thermal Radiation [Arnold, Moore & Yaffe, JHEP (2001, 2002)] [Kapusta, Lichard & Seibert (1991)] [Baier et al. (1996)] [Aurenche et al. (1996, 1998)] [Kapusta, Lichard & Seibert (1991); …]

122. Thermal + hard photons Sufficient to give a decent description of RHIC data. Rainer Fries 122SERC 2013 Summary so Far [Turbide, Rapp & Gale, PRC (2004)] [d’Enterria & Peressounko (2006)]

123. The assumption f thermal + hard photons in the basis of the PHENIX and ALICE temperature measurements. Rainer Fries 123SERC 2013 Temperature Records Exponential fit for p T < 2.2 GeV/c inv. slope T = 304±51 MeV for 0–40% Pb–Pb at √s 2.76 TeV PHENIX: T = 221±19±19 MeV for 0–20% Au–Au at √s 200 GeV [Safarik, QM12]

124. Any process that radiates gluons should be able to radiate real and virtual photons. Final state interactions of jets can give us additional photons. Compton, annihilation and Bremsstrahlung processes can also occur between a fast parton in a jet and a medium parton. Rainer Fries 124SERC 2013 There Must Be More

125. Elastic conversion cross sections peak forward and backward.  Yield from these jet-to-photon conversions:  They can also be understood as “back-scattering” photons Induced photon bremsstrahlung Rainer Fries 125SERC 2013 Photons from Jet-Medium Interactions  jet  jet   [Zakharov, JETP Lett. (2004)] [RJF, Müller & Srivastava, PRL (2002)]

126. Features:  Spedtrum sensitive to leading jet particle distrubtions at intermediate times.  Strongly dependent on temperature.  An independent thermometer? How bright is this new source?  Can be as important as initial hard photons at intermediate p T ! Rainer Fries 126SERC 2013 Back-Scattering Photons 126 FMS PRL 90 (2003)

127. Complete phenomenological analysis including simultaneous fit of pion quenching  Extended AMY (+ hadronic gas); hydro fireball; initial state effects Good description of RHIC single inclusive direct photon spectra. But: little sensitivity to individual sources. How strong are jet-medium photons? Rainer Fries 127SERC 2013 Adding Jet-Medium Photons to the Mix [Turbide, Gale, Frodermann & Heinz (2007)] [Qin, Ruppert, Gale, Jeon & Moore (2009)]

128. Azimuthal anisotropy for finite impact parameter. Three different mechanisms: Rainer Fries 128SERC 2013 Elliptic Flow Revisited Initial anisotropy Final anisotropy Elliptic flow v 2 Bulkpressure gradient collective flowv 2 > 0 saturated hard probe path lengthquenchingv 2 > 0 rare hard P T probe path lengthadditional production v 2 < 0 [Turbide, Gale & RJF, PRL 96 (2006)]

129. Have to add other photon sources with vanishing or positive v 2.  Almost perfect cancellation, |v 2 | small Large negative v 2 excluded by experiment (intermediate P T ) Next best hope: correlations of photons with jets. At low P T : PHENIX photon v 2 puzzle: too big! Rainer Fries 129SERC 2013 Photon Elliptic Flow [Liu & RJF, PRC (2006)] [Turbide, Gale & RJF (2006)] [Chatterjee, Frodermann, Heinz, Srivastava; …] [S. De, RJF (2012)]

130. Rainer Fries 130SERC 2013 Thank You For Your Attention