1. RHIC Phenomenology: Quantum Chromo-Dynamics with relativistic heavy ions D. Kharzeev BNL School on Heavy Ion Phenomenology, Bielefeld, September 2005

2. 1/2 of all “elementary” particles of the Standard Model are not observable; they are confined within hadrons by “color” interactions Quarks and the Standard Model

3. “The red-haired man” by Daniil Kharms (1905-1942) from “Blue Notebook No.10” Once there was a red-haired man who had no eyes or ears. Neither did he have any hair, … Therefore there’s no knowing whom we are even talking about. In fact we better not say anything about him... so he was called “red-haired” only theoretically Theoretical notion of color:

4. Outline Quantum Chromo-Dynamics - the theory of strong interactions Classical dynamics and quantum anomalies QCD phase diagram A glimpse of RHIC data New facets of QCD at RHIC and LHC: o Color Glass Condensate o (strongly coupled) Quark-Gluon Plasma o links between General Relativity and QCD

5. What is QCD? QCD = Quark Model + Gauge Invariance.i local gauge transformation:

6. QCD and the origin of mass.i Invariant under scale () and chiral transformations in the limit of massless quarks Experiment: u,d quarks are almost massless… … but then… all hadrons must be massless as well! Where does the “dark mass” of the proton come from? Left Right gluons quarks

7. QCD and quantum anomalies trace of the energy- momentum tensor Classical scale invariance is broken by quantum effects: scale anomaly Hadrons get masses coupling runs with the distance “beta-function”; describes the dependence of coupling on momentum

8. Asymptotic Freedom At short distances, the strong force becomes weak (anti-screening) - one can access the “asymptotically free” regime in hard processes and in super-dense matter (inter-particle distances ~ 1/T) number of colors number of flavors

9. Asymptotic freedom and Landau levels of 2D parton gasB The effective potential: sum over 2D Landau levels 1. The lowest level n=0 of radius is unstable! 2. Strong fields Short distances Paramagnetic response of the vacuum: H V

10. QCD and the classical limit.i Classical dynamics applies when the action is large in units of the Planck constant (Bohr-Sommerfeld quantization) => Need weak coupling and strong fields weak field strong field (equivalent to setting )

11. Building up strong color fields: small x (high energy) and large A (heavy nuclei) Bjorken x : the fraction of hadron’s momentum carried by a parton; high energies s open access to small x = Q 2 /s Because the probability to emit an extra gluon is ~  s ln(1/x) ~ 1, the number of gluons at small x grows; the transverse area is limited transverse density becomes large Large x the boundary of non-linear regime: partons of size 1/Q > 1/Q s overlap small x

12. Strong color fields in heavy nuclei At small Bjorken x, hard processes develop over.large longitudinal distances All partons contribute coherently => at sufficiently small x and/or.large A strong fields, weak coupling! Density of partons in the transverse plane as a new dimensionful parameter Q s (“saturation scale”)

13. Non-linear QCD evolution and population growth T. Malthus (1798) r - rate of maximum population growth timerapidity Unlimited growth! Linear evolution: Color glass condensate

14. Resolving the gluon cloud at small x and short distances ~ 1/Q 2 number of gluons “jets”: high momentum partons

15. Population growth in a limited environment Pierre Verhulst (1845) Stable population: K - maximum sustainable population; define “logistic equation” x t The limit is universal (no dependence on the initial condition)

16. Population growth in a limited environment: a (short) path to chaos “logistic map” Discrete version: bifurcations leading to chaos Fixed points Rate of growth (the value of ) ( limit of the popu- lation) John von Neumann High energy evolution starts here.

17. Semi-classical QCD: experimental tests

18. Hadron multiplicities: the effect of parton coherence

19. Semi-classical QCD and total multiplicities in heavy ion collisions Expect very simple dependence of multiplicity.on atomic number A / N part : N part :

20. Classical QCD in action

21. Classical QCD dynamics in action The data on hadron multiplicities in Au-Au and d-Au collisions support the quasi-classical picture Kharzeev & Levin, Phys. Lett. B523 (2001) 79

22. Gluon multiplication in a limited (nuclear) environment At large rapidity y (small angle) expect suppression of hard particles! The ratio of pA and pp cross sections transverse momentum DK, Levin, McLerran; DK, Kovchegov,Tuchin; Albacete,Armesto, Kovner,Wiedemann; …

23. Quantum regime at short distances: the effect of the classical background 1) Small x evolution leads to anomalous dimension 2) Q s is the only relevant dimensionful parameter in the CGC;.thus everything scales in the ratio 3) SinceTthe A-dependence is changed Expect high p T suppression at sufficiently small x

24. Phase diagram of high energy QCD

25. Model predictions I. Vitev nucl-th/0302002 v2 D. Kharzeev, Yu. Kovchegov and K. Tuchin, hep-ph/0307037 CGC at y=0 Y=0 Y=3 Y=-3 Very high energy As y grows R. Debbe, BRAHMS Coll., Talk at DNP Meeting, Tucson, November 2003

26. R.Debbe, BRAHMS, QM’04 Nuclear Modification of Hard Parton Scattering

27. Color Glass Condensate: confronting the data DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045 BRAHMS data,  

28. Color Glass Condensate: confronting the data DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045 BRAHMS data, R CP  

29. Confronting the RHIC data hadrons charm DK & K.Tuchin STAR Collaboration

30. Centrality dependence R.Debbe, BRAHMS, QM’04

31. d Au Phenix Preliminary

32. d Au Phenix Preliminary

33. d Au Color Glass? Shadowing? Cronin effect & anti-shadowing? Phenix Preliminary

34. Newly Found State of Matter Could Yield Insights Into Basic Laws of Nature By JAMES GLANZ Published: January 13, 2004 OAKLAND, Calif., Jan. 12 — A fleeting, ultradense state of matter, comparable in some respects to a bizarre kind of subatomic pudding, has been discovered deep within the core of ordinary gold atoms, scientists from Brookhaven National Laboratory said at a conference here Monday… Shattered Glass Seeking the densest matter: the color glass condensate By David Appell April 19, 2004

35. How dense is the produced matter? The initial energy density achieved: mean transverse momentum of produced gluons gluon formation time the density of the gluons in the transverse plane and in rapidity about 100 times nuclear density !

36. What happens at such energy densities? Phase transitions: deconfinement Chiral symmetry restoration U A (1) restoration Data from lattice QCD simulations F. Karsch et al critical temperature ~ 10 12 K; cf temperature inside the Sun ~ 10 7 K

37. Strongly coupled QCD plasma C. Bernard, T.Blum, ‘97 Bielefeld Interactions are important! (strongly coupled Quark-Gluon Plasma)

38. Coulomb potential in QCD Spectral representation in the t-channel: If physical particles can be produced (positive spectral density), then unitarity implies screening Gluons Quarks (transverse)

39. Coulomb potential in QCD - II Missing non-Abelian effect: instantaneous Coulomb exchange dressed by (zero modes of) transverse gluons Negative sign (the shift of the ground level due to perturbations - unstable vacuum! ): Anti-screening

40. Screening in Quark-Gluon Plasma These diagrams are enhanced at finite temperature: (scattering off thermal gluons and quarks) This diagram is not: => At high enough T, screening wins

41. Screening in the QGP F.Karsch’s lecture; F.Zantow’s talk T-dependence of the running coupling develops in the non-perturbative region at T < 3 T c Strong force is screened by the presence of thermal gluons and quarks

42. sQGP Lecture by F.Karsch

43. Percolation deconfinement, CGC? Lecture by H. Satz

44. A.Nakamura and S.Sakai, hep-lat/0406009 Perfect fluid sQGP: more fluid than water? KSS bound: strongly coupled SUSY QCD = classical supergravity

45. Charge fluctuations in sQGP Lecture by F.Karsch Hadron resonance gas Dynamical quarks QQ bound states S.Ejiri, F.Karsch and K.Redlich, 05

46. Do we see the QCD matter at RHIC ? I. Collective flow => Lectures by J.-Y. Ollitrault Au-Au collisions at RHIC produce strongly interacting matter shear viscosity - to - entropy ratio hydrodynamics: QCD liquid is more fluid than water, SUSY Yang-Mills (AdS-CFT corr.) : Hydro limit STAR PHOBOS Hydro limit STAR PHOBOS

47. v2v2v2v2 Azimuthal anisotropy as a measure of the interaction strength

48. Azimuthal anisotropy defined

49. Do we see the QCD matter at RHIC? II. Suppression of high p T particles => Lectures by U.Wiedemann consistent with the predicted parton energy loss from induced gluon radiation in dense QCD matter R J/Y suppression -> F.Fleuret, H.Satz

50. Jets (high momentum partons) - I Jet d’Eau Geneva 3-jet event, LEP Geneva

51. Jets -II Niagara Falls Au-Au collision event, RHIC

52. Geometry of jet suppression Away-side suppression is larger out-of-plane compared to in-plane STAR Collaboration

53. Di-jet correlations ‘Mono-Jets’ from Au + Au at 200 GeV Di-Jets from p + p at 200 GeV STAR Coll., PRL90(2002) 082302

54. The emerging picture Big question: How does the produced matter thermalize so fast? Perturbation theory + Kinetic equations: Thermalization time too long (?)

55. Recent idea: Quantum Black Holes and Relativistic Heavy Ions ? DK & K.Tuchin, hep-ph/0501234

56. Outline What is a black hole? Why black holes decay Why black holes cannot be produced at RHIC Why black holes may anyway teach us about the properties of QCD matter produced at RHIC

57. What is a black hole? Rev. John Michell (1724-1793) If the semi-diameter of a sphere of the same density as the Sun in the proportion of five hundred to one, and by supposing light to be attracted by the same force in proportion to its [mass] with other bodies, all light emitted from such a body would be made to return towards it, by its own proper gravity. Letter to the Royal Society, 1783:

58. Who was John Michell? Rev. John Michell (1724-1793) John Michell is a little short Man, of a black Complexion, and fat; but having no Acquaintance with him, can say little of him… from a contemporary diary

59. What is a black hole? Pierre-Simon LaPlace (1749-1827) "...[It] is therefore possible that the largest luminous bodies in the universe may, through this cause, be invisible." -- Le Système du Monde, 1796 “What we know is not much. What we do not know is immense.”

60. What is a black hole? A. Einstein, 1915: energy- momentum tensor Einstein tensor: Ricci tensor K. Schwarzschild, 1916: A solution for a static isotropic gravitational field singularity at r = 2GM !

61. Scwarzschild radius The meaning of R = 2GM ? Consider the following Michell-like “derivation”: m M v if we could put v = c, would get R = 2GM (cannot do that!) But: it is the distance at which the energy in the gravitational field is ~ mc 2 … quantum effects?

62. Black holes radiate Black holes emit thermal radiation with temperature S.Hawking ‘74 acceleration of gravity at the surface, (4GM) -1

63. Do we see black holes in the Universe? Cygnus X-1 binary system: super-giant star orbiting around a black hole?

64. Can black holes be produced at RHIC? W. Busza, R.L. Jaffe, J. Sandweiss, F. Wilczek, hep-ph/9910333 RHIC: M < 10 4 GeV R > 10 -2 fm E = 200 GeV No role for classical or quantum gravity: < 10 -22 < 10 -34

65. Can black holes anyway help us to understand the physics at RHIC? One new idea: use a mathematical correspondence between a gauge theory and gravity in AdS space Gauge theory Gravity Anti de Sitter space - solution of Einstein’s equations with a negative cosmological constant  (de Sitter space - solution with a positive  inflation  Maldacena deconfinement - black hole formation in AdS 5 xS 3 xT space Witten; Polyakov; Gubser, Klebanov; Son, Starinets, Kovtun; Nastase; … boundary

66. What is the origin of gravitational effects? In the AdS/CFT correspondence, gravity as described in the Anti - de Sitter space emerges as a consequence of the conformal invariance of the gauge theory (e.g., N=4 SUSY Yang-Mills) Isometry group = SO(2,d-1) for AdS d for AdS 5 boundary is S 3 x Time; SO(2,4) maps the boundary on itself and acts as a conformal group in 3+1 dimensions - hence the gauge theory defined on the boundary is conformal (no asymptotic freedom, no confinement) Are gravitational-like effects possible in QCD?      

67. Black holes radiate Black holes emit thermal radiation with temperature S.Hawking ‘74 acceleration of gravity at the surface, (4GM) -1

68. Similar things happen in non-inertial frames Einstein’s Equivalence Principle: Gravity Acceleration in a non-inertial frame An observer moving with an acceleration a detects a thermal radiation with temperature W.Unruh ‘76

69. In both cases the radiation is due to the presence of event horizon Accelerated frame: part of space-time is hidden (causally disconnected) from an accelerating observer; Rindler metric Black hole: the interior is hidden from an outside observer; Schwarzschild metric

70. Pure and mixed states: the event horizons mixed state pure state

71. Thermal radiation can be understood as a consequence of tunneling through the event horizon Let us start with relativistic classical mechanics: velocity of a particle moving with an acceleration a classical action: it has an imaginary part in Euclidean space…

72. well, now we need some quantum mechanics, too: The rate of tunneling under the potential barrier: This is a Boltzmann factor with

73. Accelerating detector Positive frequency Green’s function (m=0): Along an inertial trajectory Along a uniformly accelerated trajectory Accelerated detector is effectively immersed into a heat bath at temperature T U =a/2  Unruh,76

74. An example: electric field The force:The acceleration: The rate: What is this? Schwinger formula for the rate of pair production; an exact non-perturbative QED result factor of 2: contribution from the field

75. The Schwinger formula e+e+ e-e- Dirac sea E ++ + …

76. The Schwinger formula Consider motion of a charged particle in a constant electric field E. Action is given by Equations of motion yield the trajectory where a=eE/m is the acceleration Classically forbidden trajectory

77. Action along the classical trajectory: In Quantum Mechanics S(t) is an analytical function of t Classically forbidden paths contribute to Vacuum decays with probability Note, this expression can not be expanded in powers of the coupling - non-perturbative QED! Sauter,31 Weisskopf,36 Schwinger,51

78. Pair production by a pulse Consider a time dependent field E t Constant field limit Short pulse limit a thermal spectrum with

79. Chromo-electric field: Wong equations Classical motion of a particle in the external non- Abelian field: The constant chromo-electric field is described by Solution: vector I 3 precesses about 3-axis with I 3 =const Effective Lagrangian: Brown, Duff, 75; Batalin, Matinian,Savvidy,77; Nayak, van Nieuwenhuizen, 2005

80. An accelerated observer consider an observer with internal degrees of freedom; for energy levels E 1 and E 2 the ratio of occupancy factors Bell, Leinaas: depolarization in accelerators? For the excitations with transverse momentum p T :

81. but this is all purely academic (?) Take g = 9.8 m/s 2 ; the temperature is only Can one study the Hawking radiation on Earth? Gravity?

82. Electric fields? Lasers? compilation by A.Ringwald

83. Condensed matter black holes? Unruh ‘81; e.g. T. Vachaspati, cond-mat/0404480 “slow light”?

84. Strong interactions? Consider a dissociation of a high energy hadron of mass m into a final hadronic state of mass M; The probability of transition: m Transition amplitude: In dual resonance model: Unitarity:   P(m  M)=const, b=1/2  universal slope limiting acceleration M Hagedorn temperature!

85. Fermi - Landau statistical model of multi-particle production Enrico Fermi 1901-1954 Lev D. Landau 1908-1968 Hadron production at high energies is driven by statistical mechanics; universal temperature

86. Where on Earth can one achieve the largest acceleration (deceleration) ? Relativistic heavy ion collisions! - stronger color fields: 

87. Hawking phenomenon in the parton language k The longitudinal frequency of gluon fields in the initial wave functions is typically very small: p Parton configurations are frozen, Gauge fields are flat in the longitudinal direction G +- = 0

88. But: quantum fluctuations (gluon radiation in the collision process) necessarily induce Gluons produced at mid-rapidity have large frequency (c.m.s.) => a pulse of strong chromo-electric field Production of gluons and quark pairs with 3D thermal spectrum 1/Q s

89. 1) Classical Yang-Mills equations for the Weizsacker-Williams fields are unstable in the longitudinal direction => the thermal seed will grow (a link to the instability-driven thermalization?) 2) Non-perturbative effect, despite the weak coupling (non-analytical dependence on g ) 3) Thermalization time cf “bottom-up” scenario c~1 (no powers of 1/g)

90. Deceleration-induced phase transitions? Consider Nambu-Jona-Lasinio model in Rindler space e.g.,Ohsaku,04 Commutation relations: Rindler space:

91. Gap equation in an accelerated frame Introduce the scalar and pseudo-scalar fields Effective action (at large N): Gap equation: where

92. Rapid deceleration induces phase transitions Nambu- Jona-Lasinio model (BCS - type) Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric

93. Black holes A link between General Relativity and QCD? solution to some of the RHIC puzzles? RHIC collisions

94. Additional slides

95. Classical QCD in action

96. Do we see the QCD matter at RHIC? II. Suppression of high p T particles => consistent with the predicted parton energy loss from induced gluon radiation in dense QCD matter R

97. Strong color fields (Color Glass Condensate) as a necessary condition for the formation of Quark-Gluon Plasma The critical acceleration (or the Hagedorn temperature) can be exceeded only if the density of partonic states changes accordingly; this means that the average transverse momentum of partons should grow CGC QGP

98. A.Nakamura and S.Sakai, hep-lat/0406009 Perfect fluid sQGP: more fluid than water? KSS bound: strongly coupled SUSY QCD = classical supergravity

99. Kovtun, Son, Starinets, hep-th/0405231 sQGP: more fluid than water

100. RHIC: a dedicated QCD machine

101. Bogolyubov transformation Second quantization: where Equivalently: where Obviously: Therefore

102. Pair production by a pulse Consider a time dependent field E t Narozhnyj, Nikishov, 70 Constant filed limit Short pulse limit

103. Applications to heavy ions Consider breakdown of a high energy hadron of mass m into a final hadronic state of invariant mass M. Transition probability: Unruh effect: Using the dual resonance model, the density of hadronic states: where b is universal slope of Regge trajectories string tension:

104. Hagedorn temperature Probability conservation: Therefore, The string tension cannot create acceleration bigger than and, thus, produce pairs at temperature bigger than One needs stronger field to get larger temperature, e.g.

105. Pair production in GR The same problem of quantization in external field! In Schwartzschild metric (tortoise coordinate) Black hole emission rate: where  GM is acceleration of gravity at the surface of black hole, T=1/(8  GM) Hawking, 75 in out

106. What is a black hole? S. Chandrasekhar

107. At One Trillion Degrees, Even Gold Turns Into the Sloshiest Liquid By KENNETH CHANG KENNETH CHANG Published: April 19, 2005 It is about a trillion degrees hot and flows like water. Actually, it flows much better than water. Scientists at the Brookhaven National Laboratory on Long Island announced yesterday that experiments at its Relativistic Heavy Ion Collider - RHIC, … Picking apart the 'Big Bang' brings a big mystery By Dan Vergano, USA TODAY An atom-smashing fireball experiment has physicists puzzling over existing theories about the moments after the "Big Bang" that scientists say created the universe. Researchers conducted the experiment over the past three years at the Energy Department's Brookhaven National Laboratory in Long Island, New York.

108. Jets (high momentum partons) - I Jet d’Eau Geneva 3-jet event, LEP Geneva

109. Jets -II Niagara Falls Au-Au collision event, RHIC

110. Semi-classical QCD and total multiplicities in heavy ion collisions Expect very simple dependence of multiplicity.on atomic number A / N part : N part :

111. Quantization in external field Condier charged scalar field  coupled to external electric field E. Klein-Gordon equation: Let A   A  (t). Then the eigenstates are where Note,   in (x) are different from   out (x)

112. Recent idea: Quantum Black Holes and Relativistic Heavy Ions ? DK & K.Tuchin, hep-ph/0501234

113. Effective Lagrangian Effective Lagrangian in constant magnetic field: sum over Landau levels (generalization to E≠0 is straightforward): In weak fields: Heisenberg, Euler, 36 Note thatin all orders of this expansion. +++ …

114. Similar things happen in non-inertial frames Einstein’s Equivalence Principle: Gravity Acceleration in a non-inertial frame An observer moving with an acceleration a detects a thermal radiation with temperature W.Unruh ‘76

115. In both cases the radiation is due to the presence of event horizon Black hole: the interior is hidden from an outside observer; Schwarzschild metric Accelerated frame: part of space-time is hidden (causally disconnected) from an accelerating observer; Rindler metric

116. Thermal radiation can be understood as a consequence of tunneling through the event horizon Let us start with relativistic classical mechanics: velocity of a particle moving with an acceleration a classical action: it has an imaginary part…

117. well, now we need some quantum mechanics, too: The rate of tunneling under the potential barrier: This is a Boltzmann factor with

118. An example: electric field The force:The acceleration: The rate: What is this? Schwinger formula for the rate of pair production; an exact non-perturbative QED result factor of 2: contribution from the field

119. The Schwinger formula e+e+ e-e- Dirac sea E

120. A quantum observer consider an observer with internal degrees of freedom; for energy levels E 1 and E 2 the ratio of occupancy factors Bell, Leinaas: depolarization in accelerators? For the excitations with transverse momentum p T :

121. but this is all purely academic (?) Take g = 9.8 m/s 2 ; the temperature is only Where on Earth can one achieve the largest acceleration (deceleration) ? Relativistic heavy ion collisions!

122. Why not hadron collisions? Consider a dissociation of a high energy hadron of mass m into a final hadronic state of mass M; The probability of transition: m Transition amplitude: In dual resonance model: Unitarity:   P(m  M)=const, b=1/2  universal slope limiting acceleration Hagedorn temperature! M

123. Color Glass Condensate as a necessary condition for the formation of Quark-Gluon Plasma The critical acceleration (or the Hagedorn temperature) can be exceeded only if the density of partonic states changes accordingly; this means that the average transverse momentum of partons should grow CGC QGP

124. Quantum thermal radiation at RHIC The event horizon emerges due to the fast decceleration of the colliding nuclei in strong color fields; Tunneling through the event horizon leads to the thermal spectrum Rindler and Minkowski spaces

125. Fast thermalization Rindler coordinates: collision point QsQs horizons Gluons tunneling through the event horizons have thermal distribution. They get on mass-shell in  t=2  Q s (period of Euclidean motion)

126. Rapid deceleration induces phase transitions Nambu- Jona-Lasinio model (BCS - type) Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric

127. Hawking radiation New link between General Relativity and QCD; solution to some of the RHIC puzzles? RHIC event

128. Quark-Hadron phase transition Order of the deconfinement phase transition - Implications for baryosynthesis Topological fluctuations - primordial magnetic fields? P, CP violation ?

129. The future: experimental facilities LHC

130. PHENIX Collaboration 0.906<  <1.042 dN/dy = A (N coll )  induced gluon radiation should be suppressed for heavy quarks; is it?

131. Direct photons as a probe What is the origin of the “B/  puzzle”? 0-10% Central 200 GeV AuAu PHENIX Preliminary 1 + (  pQCD x N coll ) /  phenix backgrd Vogelsang NLO

132. Heavy quarkonium as a probe Talk by F. Karsch the link between the observables and the McLerran-Svetitsky confinement criterion

133. Heavy quark internal energy above T Talks by F.Karsch, P. Petreczky, K. Petrov, F. Zantow, O.Kaczmarek, S. Digal O.Kaczmarek, F. Karsch, P.Petreczky, F. Zantow, hep-lat/0309121

134. Summary 1. Quantum Chromo-Dynamics is an established and consistent field theory of strong interactions but it’s properties are far from being understood 2. High energy nuclear collisions test the predictions of strong field QCD and probe the properties of super-dense matter 3. New connections between field theory and General Relativity (black holes,…) All of this directly tested by experiment!

135. Additional slides

136. Classical QCD in action The data on hadron multiplicities in Au-Au and d-Au collisions support the semi-classical picture

137. Quantum regime at short distances: the effect of the classical background 1) Small x evolution leads to anomalous dimension 2) Q s is the only relevant dimensionful parameter in the CGC;.thus everything scales in the ratio 3) SinceTthe A-dependence is changed Expect high p T suppression at sufficiently small x