Steffen A. BassBulk QCD Matter: from RHIC to LHC #1 Steffen A. Bass Duke University RHIC: the emerging picture Modeling of Relativistic Heavy-Ion Collisions

Steffen A. Bass Bulk QCD Matter: from RHIC to LHC #1

Steffen A. BassDuke University

• RHIC: the emerging picture • Modeling of Relativistic Heavy-Ion Collisions

• Relativistic Fluid Dynamics• Hybrid Macro+Micro Transport• Model Validation: RHIC

• Predictions for LHC• Spectra & Yields• Collective Flow• Transport Coefficients: Low Viscosity Matter at LHC?

Dynamics of hot & dense QCD matter:

from RHIC to LHC

Dynamics of hot & dense QCD matter:

from RHIC to LHC

collaborators:• J. Ruppert• T. Renk• C. Nonaka• B. Mueller• A. Majumder• M. Asakawa


RHIC: the emerging picture


Exploring QCD Matter at RHIC and LHC

Exploring QCD Matter at RHIC and LHC

initial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronization

hadronic phaseand freeze-out

Lattice-Gauge Theory:

• rigorous calculation of QCD quantities• works in the infinite size / equilibrium limit

Experiments: • observe the final state + penetrating probes• rely on QGP signatures predicted by Theory

Phenomenology & Transport Theory:

• connect QGP state to observables• provide link between LGT and data


Current Picture of QGP Structure:

- Lessons from RHIC -

Current Picture of QGP Structure:

- Lessons from RHIC - Jet-Qenching & Elliptic Flow:• QGP produced at RHIC has very large opacity• behaves like an ideal fluid (vanishing viscosity)

Lattice Gauge Theory & Parton Recombination:• at TC, QGP degrees of freedom carry the quantum

numbers of quarks and recombine to form hadrons

Applicability of Ideal Fluid Dynamics and Statistical Model:

• matter produced is thermalized• thermalization (isotropization) occurs very early, ~0.6

fm/c


Modeling ofRelativistic Heavy-Ion Collisions


Survey of Transport Approaches

Survey of Transport Approaches


Relativistic Fluid Dynamics




• transport of macroscopic degrees of freedom• based on conservation laws: μTμν=0 μjμ=0

• for ideal fluid: Tμν= (ε+p) uμ uν - p gμν and jiμ = ρi uμ

• Equation of State needed to close system of PDE’s: p=p(T,ρi)

connection to Lattice QCD calculation of EoS

• initial conditions (i.e. thermalized QGP) required for calculation

• assumes local thermal equilibrium, vanishing mean free path

applicability of hydro is a strong signature for a thermalized system


3D-Hydro: Validation at RHIC

3D-Hydro: Validation at RHIC

separate chemical f.o.simulated by rescaling p,K

• 1st attempt to address all data w/ 1 calculation

b=6.3 fm

Nonaka & Bass: PRC75, 014902 (2007)See also Hirano; Kodama et al.


Ideal RFD: ChallengesIdeal RFD: Challenges

• centrality systematics of v2 less than perfect

• no flavor dependence of cross-sections• separation chemical and kinetic freeze-

out:• normalize spectra by hand

• PCE: proper normalization, wrong v2

Nu Xu

Viscosity:• success of ideal RFD argues for a

low viscosity in QGP phase compatible with AdS/CFT bound of

1/4π• viscosity will stongly change as

function of temperature during collision

need to account for viscous corrections in hadronic phase

Csernai

HG: Prakash et al.

QGP: Arnold, Moore & Yaffe


Hybrid Hydro+Micro Approaches


Full 3-d Hydrodynamics

QGP evolution Cooper-Fryeformula

UrQMD

t fm/c

hadronic rescattering

Monte Carlo

Hadronization

TC TSW

Bass & Dumitru, PRC61,064909(2000)Teaney et al, nucl-th/0110037Nonaka & Bass, PRC75, 014902 (2007)Hirano et al. nucl-th/0511046

3D-Hydro + UrQMD Model

3D-Hydro + UrQMD Model

• ideally suited for dense systems– model early QGP reaction stage

• well defined Equation of State• parameters:

– initial conditions– Equation of State

Hydrodynamics + micro. transport (UrQMD)• no equilibrium assumptions

model break-up stage calculate freeze-out includes viscosity in hadronic phase

• parameters:– (total/partial) cross sections

matching condition: • use same set of hadronic states for EoS as in UrQMD• generate hadrons in each cell using local T and μB


3D-Hydro+UrQMD: Validation

3D-Hydro+UrQMD: Validation

good description of cross section dependent features & non-equilibrium features of hadronic phase

hydrodynamic evolution used for calculation of hard probes


Predictions for LHC


Initial Conditions @ LHCInitial Conditions @ LHCrequired for all hydro-based calculations•can be obtained from:

ab-inito calculations of initial state analysis of LHC data phenomenological extrapolation of RHIC data

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

PHOBOS extrapolation:• extend longitudinal scaling• self-similar trapezoidal shape

Saturation model scaling:

• ASW: dNch/d=1650

• KLN: dNch/d=1800-2100

• EHNRR: dNch/d=2570

U. WiedemannQM06


3D-Hydro+UrQMD: Initial Conditions

3D-Hydro+UrQMD: Initial Conditions

• Initial Conditions:– energy density

– baryon number density

– parameters:

– flow profile:

• Equation of State

– 1st order phase transition

– Tc=160 MeV

• switching temperature– TSW=150 MeV

ε(x, y,η ) = ε maxW (x, y;b)H (η )

nB (x, y,) =nBmaxW(x,y;b)H()

vT=0vL=Bjorken’s solution);

0, εmax , nBmax, 0,

RHIC LHC-Bj

LHC-1

LHC-2

0(fm) 0.6 0.3 0.2 0.2

ε0

(GeV/fm3)55 230 1000 500

0 0.5 N/A 1.0 1.0

1.4 N/A 6.0 6.0

transverse planetransverse plane

•note that LHC-Bj initial conditions were not meant to provide a reasonable guess for LHC but rather elucidate a scenario more extreme than RHIC

longitudinal profilelongitudinal profile


Spectra & Yields

Disclaimer:•do not take the following “predictions” too seriously•they only represent placeholders to demonstrate the capabilities of this particular transport approach•once data are available, the parameters of the initial condition will be adjusted in order to establish whether 3D-Hydro+UrQMD can provide a viable description of QGP dynamics at LHC


Blast from the Past: Bj-Hydro+UrQMD

Blast from the Past: Bj-Hydro+UrQMD

SAB & A. Dumitru: Phys. Rev. C61 064909 (2000):• boost-invariant 1+1D RFD with UrQMD as hadronic afterburner• RFD validated with SPS data [Dumitru & Rischke: PRC59 354 (1999)]

dynamic transition from QGP & mixed phase to hadronic phase

• increase in <pt> as function of hadron mass less than linear due to flavor-dependence of hadronic rescattering


From SPS to LHCFrom SPS to LHC

• from RHIC to LHC: lifetime of QGP phase nearly doubles• only 33% increase in collision numbers of hadronic phase


3D-Hydro+UrQMD: Multiplicities

3D-Hydro+UrQMD: Multiplicities

dN/dy at yCM

LHC-1

LHC-2

+ 1715 904

K+ 228 123

p 57 34

0+0 33 19

+ 4.3 2.5

- 0.85 0.52


3D-Hydro+UrQMD: Spectra

3D-Hydro+UrQMD: Spectra


3D-Hydro+UrQMD: dissipative effects

3D-Hydro+UrQMD: dissipative effects

• significant dissipative effects early chemical freeze-out manifest in proton distribution (pure Hydro would need PCE)

• hadronic phase “cools” pion spectrum• built-up of radial flow for heavier particles pion wind


Hybrid RFD+Boltzmann Summary

Hybrid RFD+Boltzmann Summary

• validated at RHIC for soft sector and jet energy-loss• treatment of viscosity in hadronic phase• separation of thermal & chemical freeze-out allows for consistent treatment of bulk matter dynamics and hard probes


Collective Flow


Collision Geometry: Elliptic Flow

Collision Geometry: Elliptic Flow

elliptic flow (v2):

• gradients of almond-shape surface will lead to preferential emission in the reaction plane• asymmetry out- vs. in-plane emission is quantified by 2nd Fourier coefficient of angular distribution: v2

calculable with fluid-dynamics

Reaction plane

x

z

y

The applicability of fluid-dynamics suggests that the medium is in local thermal equilibrium!

Note that fluid-dynamics cannot make any statements how the medium reached the equilibrium stage…


spatial eccentricity

momentumanisotropy

initial energy density distribution:

Elliptic flow: early creation

Elliptic flow: early creation

time evolution of the energy density:

P. Kolb, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909

Most hydro calculations suggest that flow anisotropies are generated at the earliest stages of the expansion, on a timescale of ~ 5 fm/c if a QGP EoS is assumed.


3D-Hydro (+UrQMD): Elliptic Flow

3D-Hydro (+UrQMD): Elliptic Flow

• dissipative effects in hadronic phase do not affect built-up of elliptic flow robust early time signal

• no significant sensitivity to the two initial conditions( note Kolb, Sollfrank & Heinz: PLB459 (1999) 667: only small rise)


Transport Coefficients:Low Viscosity Matter

M. Asakawa, S.A. Bass & B. Mueller: Phys. Rev. Lett. 96 (2006) 252301Prog. Theo. Phys. 116 (2006) 725


initial state

pre-equilibrium


hadronization


Viscosity: from RHIC to LHC

Viscosity: from RHIC to LHC

expanding hadron gasw/ significant & increasing

mean free path:large viscosity

large elliptic flow& success of ideal RFD:zero/small viscosity

• viscosity of matter changes strongly with time & phase• Hydro+UrQMD: viscous corrections for hadron gas phase • how to understand low viscosity in QGP phase?• will low viscosity features persist at LHC?


The sQGP DilemmaThe sQGP Dilemma

• microscopic transport theory shows that assuming quasi-particle q & g degrees of freedom would require unphysically large parton cross sections to match elliptic flow data

• even for λ0.1 fm (close to uncertainty bound) dissipative effects are large

does a small viscosity have to imply that matter is strongly interacting? consider effects of (turbulent) color fields

the success of ideal hydrodynamics has led the community to equate low viscosity with a vanishing mean free path and thus large parton cross sections: strongly interacting QGP (sQGP)

D. Molnar


Anomalous ViscosityAnomalous Viscosity

• Plasma physics: – A.V. = large viscosity induced in nearly collisionless plasmas by long-range fields

generated by plasma instabilities.

• Astrophysics - dynamics of accretion disks: – A.V. = large viscosity induced in weakly magnetized, ionized stellar accretion

disks by orbital instabilities.

• Biophysics:– A.V. = The viscous behavior of nonhomogenous fluids, e.g., blood, in which the

apparent viscosity increases as flow or shear rate decreases toward zero.

• Can the QGP viscosity be anomalous?– Expanding plasmas (e.g. QGP @ RHIC) have anisotropic momentum distributions

– plasma turbulence arises naturally in plasmas with an anisotropic momentum distribution (Weibel-type instabilities).

soft color fields generate anomalous transport coefficients, which may give the medium the character of a nearly perfect fluid even at moderately weak coupling.

Anomalous Viscosity: any contribution to the shear viscosity not explicitly

resulting from momentum transport via a transport cross section


Weibel (two-stream) instability

Weibel (two-stream) instability

Ultra-Relativistic Heavy-Ion Collision: two streams of colliding color charges• consider the effect of a seed magnetic field with 0, 0B p k p⋅ = ⋅ =

rr r r

• induced current creates B, adds to seed B • opposing currents repel each other: filamentation exponential Weibel instability

Guy Moore, McGill Univ.

• pos. charges deflect as shown: alternately focus and defocus

• neg. charges defocus where pos. focus and vice versa

net-current induced, grows with time


Hard Thermal Loops: Instabilities

Hard Thermal Loops: Instabilities

( )2 2eq( ) 1 ( )f p f p p nξ ξ= + + ⋅

r r r rfind HTL modes for anisotropic

distribution:

for any ξ0 there exist unstable modes

energy-density and growth rate of unstable modes can be calculated:

Romatschke & Strickland, PRD 68: 036004 (2003)Arnold, Lenaghan & Moore, JHEP 0308, 002 (2003)Mrowczynski, PLB 314, 118 (1993)

aa c

aba

cbdp dQ

gQ u gfF u Qd d

Aμ

ν νμν ν

= =

Nonabelian Vlasov equations describe interaction of “hard” (i.e. particle) and “soft” color field modes and generate the “hard-thermal loop” effective theory:

2HTL

221

4 ( )( )2

ab

a a a bg C p pdpf p

pL F F F F

p Dνμ λμ

μν μν

νλ−

⋅= ∫

rEffective HTL theory permits systematic study of instabilities of “soft” color fields:

( ) ( ) ( ) ( ( ))i i ii

J x d Q u x x

gD F Jν ν

μμ

νν

δ = −

=

∑∫


Anomalous Viscosity Derivation: Sketch

Anomalous Viscosity Derivation: Sketch

• linear Response: connect η with momentum anisotropy Δ:

• use color Vlasov-Boltzmann Eqn. to solve for f and Δ:

• Turbulent color field assumption:• ensemble average over fields: diffusive Vlasov-Boltzmann Eqn:

• example: anomalous viscosity in case of transverse magnetic fields

• complete calculation of η via variational principle:

( )( )

3 40

3 2

1

15 2 p p

fd p

T E Eη

π

∂= − Δ

∂∫p

p

( ) ( ) [ ], 0, , ,ap

af t fv g Ct fx

μμ

∂+ ⋅∇ + =

∂r p r pF

( ) ( ) ( ) ( ) ( )(mag) (mag),a b a ai j i jabUx xx x t tτ σ′ ′ ′= Φ − Φ −′ x x%B B B B

( ) ( ) [ ], , 0, ,p pv f t CD f fx

tμμ

−∇ ⋅∂

+⋅∇ =∂

pp rr

( )( )(gluo6

a

n)

2

2 m g

16 6 1c

c m

A

N T

N gπη

ς

τ

−=

2B( ) 2

(quark)6

2 2 mag

62 6 f

m

AcN N T

gη

ς

π τ=

2B

1 1 1A C − − −= +


collisional viscosity:• derived in HTL weak coupling limit

anomalous viscosity:• induced by turbulent color fields, due to momentum-space anisotropy

• with ansatz for fields:

for reasonable values of g: A < C

Collisional vs. Anomalous Viscosity

Collisional vs. Anomalous Viscosity

4 1

5

lnC

s g g

−≈

A

s=O 1( )

Nc2 −1( )Nc

T 6

g2 B2 m

⇒A

s:

1

B2

3/5

0 2A T

cs g u

⎛ ⎞= ⎜ ⎟⎜ ⎟∇⎝ ⎠ M. Asakawa, S.A. Bass & B. Mueller:

Phys. Rev. Lett. 96 (2006) 252301Prog. Theo. Phys. 116 (2006) 725


Time-Evolution of ViscosityTime-Evolution of Viscosity

initial state

pre-equilibrium


hadronization


A C < A C < A C > HG

1 11

A C = +

A : C : HG :viscosity: ? ?

• relaxation rates are additive sumrule for viscosities:

smaller viscosity dominates in system w/ 2 viscosities!

temperature evolution:


Viscosity at LHC: Two Scenarios

Viscosity at LHC: Two Scenarios

field picture: • (turbulent) color fields induce an anomalous viscosity, which

keeps the total shear-viscosity small during the QGP evolution

perfect liquidity in the weak coupling limit

collisional picture: • weaker coupling at LHC vs. RHIC will lead to a larger viscosity increase in dissipative effects, deviations from ideal fluid

elliptic flow at LHC compared to RHIC can act as a decisive measurement for the dominance of anomalous viscosity


Summary and OutlookSummary and Outlook• Heavy-Ion collisions at RHIC have produced a state of matter

which behaves similar to an ideal fluid Hydro+Micro transport approaches are the best tool to

describe the soft, non-perturbative physics at RHIC after QGP formation

at LHC, such hybrid models should perform well if QGP matter is found to have a low viscosity

• a small viscosity does not necessarily imply strongly interacting matter!

(turbulent) color fields induce an anomalous viscosity, which keeps the total sheer-viscosity small during the QGP evolution

elliptic flow at LHC as decisive measurement on impact of anomalous viscosityNote:

• due to it’s slow & nearly isotropic expansion, the early Universe most likely did not have an anomalous contribution to its viscosity


The End


Elliptic Flow: ultra-cold Fermi-Gas

Elliptic Flow: ultra-cold Fermi-Gas

• Li-atoms released from an optical trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions

Elliptic flow is a general feature of strongly interacting systems!

Documents

Steffen A. BassBulk QCD Matter: from RHIC to LHC #1 Steffen A. Bass Duke University RHIC: the emerging picture Modeling of Relativistic Heavy-Ion Collisions