Martin Way Retail Pad a Se Lacey, Washington Lacey ashington
v n in relation to initial-state geometry and medium properties Roy A. Lacey Chemistry Dept.,
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Transcript of 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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
4 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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)
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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?
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 8
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 9
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 10
arXiv:1202.5537
ˆ and qs
Scaling of Jet QuenchingScaling of Jet Quenching
High-pT vHigh-pT v22 measurements measurements
Specific pT and centrality dependencies – Do they scale?
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 11
arXiv:1204.1850
pT dependence
Centralitydependence
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 12
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 13
Scaling of high-pT vScaling of high-pT v22
Combined ∆L and 1/√pT scaling single universal curve for v2
arXiv:1203.3605
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 14
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 15
Scaling of Jet QuenchingScaling of Jet Quenching
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012 16
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
17 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
18 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
19 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
20 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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?
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
ATLAS-CONF-2011-074
22
High precision double differential Measurements are pervasiveDo they scale?
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
23 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
22, exp 0
3
tT t k k T
s T
2 gR n LHCRHIC
2expn
n
vn
24 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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 (%)
25 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
Decoupling the Interplay between Decoupling the Interplay between εεnn and and ηη/s/s
http://arxiv.org/abs/1105.3928
28 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
29 Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
SummarySummary
End
31Roy A. Lacey, Stony Brook University; Ridge
Workshop, INT, Seattle, May 7-11, 2012