v n in relation to initial-state geometry and medium properties Roy A. Lacey Chemistry Dept.,

1 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012

A central IssueA central Issue

How to fully characterize of the QGP produced How to fully characterize of the QGP produced in RHIC & LHC collisions?in RHIC & LHC collisions?

Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 20122

T, cs, ˆ, , , etc ?qs s

Characterization requires

Development of experimental constraints for thermodynamic and transport coefficients

Development of quantitative model descriptions of these properties

Essential question: Do azimuthal anisotropy (vn) measurements provide constraints

to nail down initial-state geometry & the transport properties of the QGP?

Focus The role of scaling in answering this question!

A scenario for Azimuthal AnisotropyA scenario for Azimuthal Anisotropy

This scenario implies very specific scaling properties which must be validated experimentally

Scaling validation Scaling validation Flow and Jet Quenching provide Flow and Jet Quenching provide straightforward probes of the QGPstraightforward probes of the QGP


pT <

4 G

eV/c

Flow

pT > 10 GeV/c

Jet quenching

3

Pressure driven(acoustic )

1234< pT <10 GeV/c

TransitionRegion

Both are linked by Geometry & interactions in the sQGP

Path length (∆L)driven

The Flow ProbeThe Flow Probe

s/

P ² Bj

, , , , Tsc s s

, , , , Tsc s s

20

3

1 1

~ 5 15

TBj

dE

R dy

GeV

fm


2 2

2

cos sinn npart part

nn

r n r n

r

Idealized Geometry

2 2

2 2

y x

y x

Control parametersControl parameters

Actual collision profiles are not smooth, due to fluctuations!

Initial Geometry characterized by many harmonics

Initial eccentricity (and its attendant fluctuations) εn drive momentum anisotropy vn with specific scaling properties

22, exp 0

3

tT t k k T

s T

Acoustic viscous damping

Jet quenching Jet quenching Probe Probe

Color charge Color charge scattering centersscattering centers

22

ˆ ~ ~Tkq

22

ˆ ~ ~Tkq

Range of Color Range of Color ForceForce

Scattering PowerScattering PowerOf MediumOf Medium Density of Density of

Scattering centersScattering centers

ObtainObtain

via Rvia RAAAA

measurements measurements

ˆ and q

2~ T

dEL k

dx

Radiative:Radiative:

Jet quenching drives RAA & azimuthal anisotropy with specific scaling properties

AAAA

binary AA pp

YieldR

N Yield

5

Gyulassy, Wang, Müller, …

2( , ) [1 2 ( )cos(2 )]T TN p v p

2

AA 20

AA 2

(90 , ) 1 2 ( )( , )

(0 , ) 1 2 ( )

oT T

v TT T

R p v pR p L

R p v p

Tˆ, p , L, qs Tˆ, p , L, qsControl parametersControl parameters


Suppression for ∆L

6

Geometric Quantities for scaling

A B

Geometric fluctuations included Geometric quantities constrained by multiplicity density.

~

L R

L R

*cosn nn

Phys. Rev. C 81, 061901(R) (2010)


arXiv:1203.3605

σx & σy RMS widths of density distribution

Scaling properties of Jet QuenchingScaling properties of Jet Quenching

Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 7

RRAAAA Measurements - LHC Measurements - LHC

Specific pT and centrality dependencies – Do they scale?


Eur. Phys. J. C (2012) 72:1945 arXiv:1202.2554

Centralitydependence

pT dependence

Scaling of Jet QuenchingScaling of Jet Quenching

RAA scales with L, slopes (SL) encodes info onCompatible with the dominance of radiative energy loss


arXiv:1202.5537

ˆ and qs

RAA scales as 1/√pT , slopes (SpT) encodes info on L and 1/√pT scaling single universal curveCompatible with the dominance of radiative energy loss


arXiv:1202.5537

ˆ and qs


High-pT vHigh-pT v22 measurements measurements

Specific pT and centrality dependencies – Do they scale?


arXiv:1204.1850

pT dependence

Centralitydependence


Scaling of high-pT vScaling of high-pT v22

v2 follows the pT dependence observed for jet quenchingNote the expected inversion of the 1/√pT dependence

arXiv:1203.3605


Scaling of high-pT vScaling of high-pT v22

Combined ∆L and 1/√pT scaling single universal curve for v2

arXiv:1203.3605


Jet suppression from high-pT vJet suppression from high-pT v22

Jet suppression obtained directly from v2

arXiv:1203.3605

2( , ) [1 2 ( )cos(2 )]T TN p v p

2

AA 20

AA 2

(90 , ) 1 2 ( )( , )

(0 , ) 1 2 ( )

oT T

v TT T

R p v pR p L

R p v p

Rv2 scales as 1/√pT , slopes encodes info on ˆ and qs



2

ˆ ~ 0.75 RHIC

GeVq

fm

Phys.Rev.C80:051901,2009

2

ˆ ~ 0.56 LHC

GeVq

fm

obtained from high-pT v2 and RAA [same αs] similar - medium produced in LHC collisions less opaque!

arXiv:1202.5537 arXiv:1203.3605

ˆ ˆq qRHIC LHC

q̂LHC

Conclusion similar to those of Liao, Betz, Horowitz,

Scaling patterns of low-pScaling patterns of low-pTT azimuthal anisotropy azimuthal anisotropy


Essential argument:

Flow is dominantly partonicFlow is pressure driven (acoustic)

viscous damping follows dispersion relation for sound propagation These lead to characteristic scaling patterns which must be experimentally validated

Is hydrodynamic flow acoustic?Is hydrodynamic flow acoustic?

Characteristic n2 viscous damping for harmonics Crucial constraint for η/s

Deformation n

kR


2 gR n

Note: the hydrodynamic response to the initial geometry [alone] is included

εn drive momentum anisotropy vn with modulation

22, exp 0

3

tT t k k T

s T

2expn

n

vn

Modulation Acoustic

Not analogousCBM

2expn

n

vn

Constraint forConstraint for ηη/s & /s & δδf f

Deformation n

kR


2

0

2

, exp 0

Particle Dist. ( )

( ) ~

T

TT

f

T t k n T

f f f p

pf p

T

Characteristic pT dependence of β expected, reflects the influence of δf

pT (GeV/c)0 1 2 3

(p T

)0.00

0.05

0.10

0.15

0.20

0.25

0.30

4s = 1.25

(pT)-1/2

4s = 0.04s = 1.25 f~pT

1.5

20-30%

Hydro - Schenke et al.

Deformation n

kR


Is flow partonic?Is flow partonic?

/2 n, 2, /2

vv ( ) ~ v or

( )n

n q T q nq

pn

AMPT – Simulations with fluctuating initial conditions

Characteristic scaling patterns are to be expected for the ratios of vn

Deformation n

kR


Is flow partonic?Is flow partonic?

/2 n, 2, /2

vv ( ) ~ v or

( )n

n q T q nq

pn

AMPT – Simulations with (w) and without (wo) fluctuating initial conditions

Characteristic scaling patterns are to be expected for identified particle species vn

v4(ψ4) ~ 2v4(ψ2)

21

Phys.Rev.Lett. 107 (2011) 252301 (arXiv:1105.3928)

vvnn(ψn) Measurements Measurements

High precision double differential Measurements are pervasiveDo they scale?


ATLAS-CONF-2011-074

22

High precision double differential Measurements are pervasiveDo they scale?


vvnn(ψn) Measurements Measurements

Flow is acousticFlow is acoustic

Characteristic viscous dampingCharacteristic viscous dampingof the harmonics validatedof the harmonics validated Crucial constraint for Crucial constraint for ηη/s/s

Deformation n

kR


22, exp 0

3

tT t k k T

s T

2 gR n LHCRHIC

2expn

n

vn


2 4 6

v n/ n

0.01

0.1

1 10-20%

n2 4 6

20-30%

2 4 6

30-40%

2 4 6

v n/ n

0.01

0.1

140-50%

Pb+Pb - 2.76 TeV

pT = 1.1 GeV/c

Acoustic ScalingAcoustic Scaling 2expn

n

vn

β is essentially independent of centrality for a broad centrality range

15 30 45

0.00

0.05

0.10

0.15

0.20

0.25

pT = 1.1 GeV/c

Pb+Pb - 2.76 TeV

Centrality (%)


2 4 6

v n/ n

0.01

0.1

1

0.7 GeV/c

n2 4 6

1.3 GeV/c

2 4 6

1.9 GeV/c

2 4 6

v n/ n

0.01

0.1

1

2.3 GeV/c

Pb+Pb - 2.76 TeV

20-30%

2expn

n

vn

Acoustic ScalingAcoustic Scaling

β scales as 1/√pT

pT (GeV/c)1 2

0.00

0.05

0.10

0.15

0.20

0.25

20-30%

Pb+Pb - 2.76 TeV

2expn

n T

vn

p

Similar scaling observed at the LHC

26Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012

Scaling for partonic flow validated for vn

Constraints for εn

Flow is partonicFlow is partonic

KET/nq (Gev)

0.0 0.5 1.0 1.5 2.0 2.5

v n/(n

q)n/

2

0.00

0.01

0.02

0.03

0.04Kp

n=30-60%

(KET/nq) (GeV)0 1 2

v 3/(n

q)3/

2

0.00

0.01

0.02

0.03

0.04

0.05

Kp

Au+Au 200 GeVNNs

20-50%Flow is partonic

Flow is partonic

Flow is partonicFlow is partonic

KET & scaling validated for v3

Partonic flow

/2n

qn

Scaling for partonic flow validated for vn

27

PHENIX

vv33 PID scaling PID scaling

STAR


Decoupling the Interplay between Decoupling the Interplay between εεnn and and ηη/s/s

http://arxiv.org/abs/1105.3928


v3 breaks the ambiguity between MC-KLN vs. MC-Glauber initial conditions and η/s, because of the n2 dependence of viscous

corrections

ηη/s estimates – QM2009/s estimates – QM2009

Good Convergence

4πη/s ~ 1

Temperature dependenceNot fully mapped yet

Conjectured Lower bound


Much work remains to be done

Remarkable scaling have been observed for both Flow and Remarkable scaling have been observed for both Flow and Jet QuenchingJet Quenching

They lend profound mechanistic insights, as well as New constraints forThey lend profound mechanistic insights, as well as New constraints forestimatesestimates of transport and thermodynamic coefficients! of transport and thermodynamic coefficients!

30

RRAAAA and high-pT azimuthal and high-pT azimuthal

anisotropy stem from the same anisotropy stem from the same energy loss mechanismenergy loss mechanism Energy loss is dominantly Energy loss is dominantly radiativeradiative RRAAAA and anisotropy and anisotropy

measurements give consistent measurements give consistent estimates for ˆq estimates for ˆq The QGP created in RHIC The QGP created in RHIC collisions is less opaque than collisions is less opaque than that produced at the LHCthat produced at the LHC

Flow is acousticFlow is pressure driven Obeys the dispersion relation for sound propagation

Flow is partonic exhibits scaling

Constraints for:initial geometry η/s

viscous horizon sound horizon

What do we learn?

/2 n, 2, /2

vv ( ) ~ v or

( )n

n q T q nq

pn


SummarySummary

End

31Roy A. Lacey, Stony Brook University; Ridge

Workshop, INT, Seattle, May 7-11, 2012

Documents

v n in relation to initial-state geometry and medium properties Roy A. Lacey Chemistry Dept.,