Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Take home message  The scaling (p T, ε, R, ∆L, etc) properties of azimuthal anisotropy measurements at RHIC & the LHC, inform crucial mechanistic insights and constraints for characterization of the QGP?

2 RHIC (0.2 TeV)  LHC (2.76 TeV) Power law dependence (n ~ 0.2)  increase ~ 3.3  Multiplicity density increase ~ 2.3  increase ~ 30% Lacey et. al, Phys.Rev.Lett.98:092301,2007 Relevant questions:  How do the transport coefficients evolve with T?  Any indication for a change in coupling close to T o ? Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Energy scan Why RHIC and LHC Measurements? The energy density lever arm

Why Azimuthal Anisotropy Measurements?  This implies very specific scaling properties for flow and jet suppression (respectively), which can be tested experimentally  Scaling validation provide important insights, as well as straightforward probes of transport coefficients Scaling validation provide important insights, as well as straightforward probes of transport coefficients Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University pT < GeV/c Flow pT > GeV/c Jet suppression 3 Eccentricity driven & acoustic 3-4 < pT < 8-10 GeV/c Path length (∆L) driven More suppression Less suppression Transition Region Flow and Jet suppression are linked to Geometry & the interactions in the QGP

4 Geometric Quantities for scaling A B  Geometric fluctuations included  Geometric quantities constrained by multiplicity density. Phys. Rev. C 81, (R) (2010) arXiv: σ x & σ y  RMS widths of density distribution Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

Scaling properties of high-p T anisotropy Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University5

6 Jet suppression Probe Suppression (∆L) – pp yield unnecessary Suppression (L), Phys.Lett.B519: ,2001 For Radiative Energy loss: Modified jet More suppression Less suppression Fixed Geometry Path length (related to collision centrality)

Specific p T and centrality dependencies – Do they scale? 7 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University High-pT v 2 measurements - PHENIX p T dependence Centrality dependence

High-pT v 2 measurements - CMS Specific p T and centrality dependencies – Do they scale? 8 arXiv: p T dependence Centrality dependence Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

9 High-pT v 2 scaling - LHC v 2 follows the p T dependence observed for jet quenching Note the expected inversion of the 1/√p T dependence arXiv: Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

10 ∆L Scaling of high-pT v 2 – LHC & RHIC Combined ∆L and 1/√p T scaling  single universal curve for v 2  Constraint for ε n arXiv: Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

11 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University ∆L Scaling of high-pT v 2 - RHIC Combined ∆L and 1/√p T scaling  single universal curve for v 2  Constraint for ε n

12 Jet v 2 scaling - LHC v 2 for reconstructed Jets follows the p T dependence for jet quenching Similar magnitude and trend for Jet and hadron v 2 after scaling Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University (z ~.62) ATLAS 10-20%

13 Jet suppression from high-pT v 2 Jet suppression obtained directly from pT dependence of v 2 Compatible with the dominance of radiative energy loss arXiv: R v2 scales as 1/√p T, slopes encodes info on α s and q ˆ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

R AA scales as 1/√p T ; slopes (S pT ) encode info on α s and q L and 1/√p T scaling  single universal curve Compatible with the dominance of radiative energy loss 14 arXiv: p T scaling of Jet Quenching ˆ, Phys.Lett.B519: ,2001 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

15 Extracted stopping power Phys.Rev.C80:051901,2009  obtained from high-pT v 2 and R AA [same α s ]  similar  - medium produced in LHC collisions less opaque! (note density increase from RHIC to LHC) arXiv: arXiv: Conclusion similar to those of Liao, Betz, Horowitz,  Stronger coupling near T c ? q RHIC > q LHC ˆ q LHC ˆ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

Consistent obtained 16 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University q LHC ˆ Heavy quark suppression

Scaling properties of low pT anisotropy Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University17

The Flow Probe 18 Idealized Geometry Crucial parameters Actual collision profiles are not smooth, due to fluctuations! Initial Geometry characterized by many shape harmonics (ε n )  drive v n Initial eccentricity (and its attendant fluctuations) ε n drive momentum anisotropy v n with specific scaling properties Acoustic viscous modulation of v n Staig & Shuryak arXiv: Isotropic p Anisotropic p Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Yield(  ) =2 v 2 cos[2(   ]

Characteristic n 2 viscous damping for harmonics  Crucial constraint for η/s Associate k with harmonic n 19 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University ε n drive momentum anisotropy v n with modulation Scaling expectation Acoustic Modulation Characteristic centrality (1/R) viscous damping for a given harmonic  Crucial constraint for η/s Particle Distribution Note that v n is related to v 2

Characteristic n 2 viscous damping and 1/(p T ) α dependence  Crucial constraint for η/s and δf 20 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Is viscous hydrodynamic flow acoustic? Note: the hydrodynamic response to the initial geometry [alone] is included

ATLAS-CONF High precision double differential Measurements are pervasive Do they scale? Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University v n (ψ n ) Measurements - ATLAS

22 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Acoustic Scaling Characteristic n 2 viscous damping validated Characteristic 1/(p T ) α dependence of β validated Constraint for η/s

23 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Acoustic Scaling Characteristic n 2 viscous damping validated Characteristic 1/(p T ) α dependence of β validated Constraint for η/s

24 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Acoustic Scaling Straightforward constraint for eccentricity models

25 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Acoustic Scaling Characteristic 1/R viscous damping validated A further constraint for η/s Centrality – 5-50%

26 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Acoustic Scaling Characteristic 1/R viscous damping validated A further constraint for η/s

27 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University  Flow increases from RHIC to LHC Sensitivity to EOS increase in  Proton flow blueshifted [hydro prediction] Role of radial flow Role of hadronic re- scattering? Flow increases from RHIC to LHC

28 β  Important constraint for η/s and δf Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Constraint for η/s & δf ~ 1/4π at RHIC; 25-30% increase for LHC arXiv: Phys.Rev. C80 (2009)

Remarkable scaling have been observed for both Flow and Jet Quenching They lend profound mechanistic insights, as well as New constraints for estimates of the transport and thermodynamic coefficients! 29  R AA and high-pT azimuthal anisotropy stem from the same energy loss mechanism  Energy loss is dominantly radiative  R AA and anisotropy measurements give consistent estimates for  R AA and anisotropy measurements give consistent estimates for  R AA for D’s give consistent estimates for  R AA for D’s give consistent estimates for  The QGP created in LHC collisions is less opaque than that produced at RHIC  Flow is acoustic Flow is pressure driven Obeys the dispersion relation for sound propagation  Flow is partonic exhibits scaling  Constraints for: initial geometry small increase in η/s from RHIC ( ~ 1/4π) to LHC What we learn? Summary Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

End 30 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

31 Flow Saturates for GeV Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University  No sizeable beam energy dependence observed for v 2 and v 3 for each particle species  flow saturates for GeV  Soft EOS

32 Flow is the LHC Scaling for partonic flow validated after accounting for proton blueshift Larger partonic flow at the LHC Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

33 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University For partonic flow, quark number scaling expected  single curve for identified particle species v n Is flow partonic? Note species dependence for all v n

34 Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University Acoustic Scaling Increase of s 2 for most central collisions is to be expected

35 RHIC and the LHC Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University  Multiplicity-weighted PIDed flow results reproduce inclusive charged hadron flow results at RHIC and LHC respectively  Charge hadron flow RHIC & LHC