Turbulent nonabelian matter in high energy nuclear collisions A. - PowerPoint PPT Presentation

JINR, June 06, 2012 Turbulent nonabelian matter in high energy nuclear collisions A. Leonidov P.N. Lebedev Physical Institute, Moscow A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

◮ Elliptic flow in heavy ion collisions ◮ Emergence of Kolmogorov spectrum in glasma ◮ Emergence of Kolmogorov spectrum in the toy CGC model ◮ Emergence of Kolmogorov spectrum in QGP ◮ Turbulent instability in QED plasma A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Elliptic flow Y X Spectators Ψ RP b Spectators Definition of the reaction plane A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Elliptic flow Spatial asymmetry of the reaction zone ◮ � y 2 − x 2 � ǫ s , part = � y 2 + x 2 � ◮ � = 1 dxdy ( y 2 − x 2 ) dN p � y 2 − x 2 � N p dx dy Momentum asymmetry: elliptic flow ◮ � p 2 � X − p 2 Y v 2 ≡ p 2 X + p 2 Y ◮ 1 dN 1 dN = (1+ p T dydp T d φ 2 π p T dydp T 2 v 2 ( p T ) cos 2( φ − Ψ RP ) + . . . ) A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Elliptic flow Y � � � � X Hydrodynamic origin of the elliptic flow: anisotropic pressure converts spatial anisotropy is into momentum one A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Elliptic flow 0.08 2 v 0.06 0.04 0.02 ALICE STAR 0 PHOBOS PHENIX -0.02 NA49 CERES -0.04 E877 EOS -0.06 E895 FOPI -0.08 2 3 4 1 10 10 10 10 s (GeV) NN Average elliptic flow as a function of √ s A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Elliptic flow ALICE at p T = 1.7GeV/c at p T = 0.7GeV/c 10 3 10 4 Differential elliptic flow as a function of √ s A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Elliptic flow ε / 2 0.25 HYDRO limits v 0.2 0.15 0.1 E /A=11.8 GeV, E877 lab E /A=40 GeV, NA49 lab 0.05 E /A=158 GeV, NA49 lab s =130 GeV, STAR NN s =200 GeV, STAR Prelim. NN 0 0 5 10 15 20 25 30 35 (1/S) dN /dy ch Hydro limit for ideal liquid for v 2 reached at RHIC A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Elliptic flow Glauber 25 STAR non-flow corrected (est.) -4 η /s=10 STAR event-plane 20 η /s=0.08 v 2 (percent) 15 η /s=0.16 10 5 0 0 1 2 3 4 p T [GeV] CGC -4 η /s=10 25 STAR non-flow corrected (est). η /s=0.08 STAR event-plane 20 v 2 (percent) 15 η /s=0.16 10 5 η /s=0.24 0 0 1 2 3 4 p T [GeV] Dependence of v 2 on viscosity for Glauber and CGC initial conditions A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Initial conditions Initial transverse energy density for AuAu collisions at √ s = 200 GeV A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Little Bang: collision stages t freeze out hadrons in eq. hydrodynamics gluons & quarks in eq. gluons & quarks out of eq. kinetic theory strong fields classical EOMs z (beam axis) A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Little Bang: before the collision Initial state at t < 0 A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Nuclei before collision: degrees of freedom fields sources k + Λ + P + 0 ◮ Characteristic evolution time for parton modes k − ∼ 2 k + = 2 P + ∆ x + ∼ 1 x k 2 k 2 ⊥ ⊥ ◮ Static modes (sources): x ∼ 1 ◮ Fluctuational modes (fields): x ≪ 1 QCD physics at high energies is that of fields with x ≪ 1 A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Nuclei before collision: fields The fields A a µ and the source J a µ are related by the equation [ D µ , F µν ] = J ν ⇔ J µ = δ µ + ρ 1 ( x ⊥ , x − ) Solution of classical equations: A − = 0 A + = 0 , i A i g U ( x ⊥ , x − ) ∂ i U † ( x ⊥ , x − ) = where � � � x − U ( x ⊥ , x − ) dy − α ( x ⊥ , x − ) = P exp ig −∞ α ( x ⊥ , x − ) − ρ ( x ⊥ , x − ) / ∇ 2 = ⊥ A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Nuclei before collision: observable quantities ◮ Charge density ρ ( x ⊥ , x − ) is random. Event-by-event averaging with respect to ρ ( x ⊥ , x − ) is described by some functional W Λ + [ ρ ] ◮ For the simplest Gaussian ensemble A δ ab δ 2 ( x ⊥ − y ⊥ ) δ ( x − − y − )) � ρ a ( x ⊥ , x − ) ρ b ( y ⊥ , y − ) � = g 2 µ 2 ◮ Structure function: 2 k + dN (2 π ) 3 � A i a ( k , x + )) A i a ( − k , x + )) � W Λ+ = d 3 k 1 � � �� � A i a (0)) A i − x 2 ⊥ Q 2 S ln( x 2 ⊥ µ 2 ) a ( x )) � ∼ 1 − exp x 2 ⊥ ◮ Q 2 S - saturation scale, 0 e λ s Y , Q 2 S ( Y ) ≃ Q 2 Q 2 0 ∼ A 1 / 3 A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Nuclei before collision: quantum evolution x = k + 1 δ S ⊥ ∼ P + Q 2 A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Nuclei before collision: quantum evolution fields sources k + Λ + Λ + P + 1 0 δ T NLO T LO ◮ Structure function, classical approximation � < AA > = [ d ρ ] W Λ + [ ρ ] A cl . ( ρ ) A cl . ( ρ ) ◮ Arbitrary observable, classical approximation � �O� Y = [ d α ] O [ α ] W Y [ α ] ◮ Quantum evolution: JIMWLK equation: � ∂ �O [ α ] � Y = � 1 δ δ Y ( x ⊥ ) χ ab x ⊥ , y ⊥ [ α ] Y ( y ⊥ ) O [ α ] � Y δα a ∂ Y 2 δα b x ⊥ , y ⊥ A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Nuclei before collision: quantum evolution ◮ The JIMWLK equation is Hamiltonian: ∂ �O [ α ] � Y = �H JIMWLK O [ α ] � Y ∂ Y ◮ Kernels of JIMWLK equation: � d 2 z ⊥ ( x ⊥ − z ⊥ )( y ⊥ − z ⊥ ) χ ab x ⊥ y ⊥ [ α ] = 4 π 3 ( x ⊥ − z ⊥ ) 2 ( y ⊥ − z ⊥ ) 2 �� � � �� 1 − U † 1 − U † x ⊥ U z ⊥ z ⊥ U y ⊥ ◮ Nonlinear dependence on sources � � � x − U † ( x ⊥ , x − ) = P exp dy − α a ( x ⊥ , x − ) T a ig −∞ ◮ In the limit of small α JIMWLK turns into BFKL A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Nuclear collision: classical solution [ D µ , F µν ] = J ν J µ = δ µ + ρ 1 ( x ⊥ , x − ) + δ µ + ρ 2 ( x ⊥ , x − ) Look for a solution in all orders in ρ 1 , 2 A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Boost-invariant classical solution ◮ Coordinates τ, η x 0 + x 3 = τ e η , x 0 − x 3 = τ e − η ◮ For a single source one uses gauges A ± = 0 ◮ For the two-source problem it is convenient to use the mixed gauge A τ = 0 A τ = A τ ≡ 1 τ ( x + A − + x − A + ) ◮ Boost-invariant solution does not depend on η A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Boost invariant classical solution t x + x − η = cst. τ = cst. (3) A µ = ? (1) (2) z A µ = pure gauge 1 A µ = pure gauge 2 (4) A µ = 0 ◮ Look for the η - independent solution of the form: θ ( − x + ) θ ( x − ) A i (1) + θ ( x + ) θ ( − x − ) A i (2) + θ ( x + ) θ ( x − ) A i A i = (3) θ ( x + ) θ ( x − ) A η A η = (3) ◮ Matching conditions at τ = 0 : A i A i (1) + A i (3) | τ =0 = (2) ig � � A η A i (1) , A i (3) | τ =0 = (2) 2 A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Immediately after collision there form longitudinal chromoelectric and chromomagnetic fields - glasma : . . . . . . . . . . . . . . . . . . . . . . . . . . � � E z A i (1) , A i = ig (2) ig ǫ ij � � (1) , A j B z A i = (2) A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Initial conditions: hydrodynamics? ◮ Equations of motion ∂ µ T µν = 0 ◮ Equation of state p = f ( ǫ ) ◮ Initial conditions set at some τ = τ 0 T µν ( τ = τ 0 , η, x ⊥ ) ◮ Generic structure of T µν :   ǫ ǫ T µν =   3   ǫ   3 ǫ 3 A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions

Initial conditions, Color Glass Condensate For a configuration E a µ = λ B a µ   ǫ ǫ   � T µν ( τ = 0 + , η, x ⊥ ) � =   ǫ   − ǫ Does not look as hydro at all but is very similar to QCD string models (negative p z !) Glasma flux tubes strings Negative p z string tension Glasma instabilities string breaking Isotropisation mechanism? A. Leonidov Turbulent nonabelian matter in high energy nuclear collisions