1 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Primary focus: Scaling properties of flow & Jet quenching

Flow & Jet quenching are important probes of the QGP!  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 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University pT < GeV/c Flow pT > GeV/c Jet suppression 2 Eccentricity driven & acoustic 3-4 < pT < 8-10 GeV/c Path length (L & ∆L) driven More suppression Less suppression Transition Region Flow and Jet suppression are linked to Geometry & the interactions in the QGP

3 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 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

The Flow Probe 4 Initial Geometry characterized by many shape harmonics (ε n )  drive v n Acoustic viscous modulation of v n Staig & Shuryak arXiv: RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Scaling expectations Note that v n is related to v 2 Particle Distribution

5 High precision double differential Measurements for Pb+Pb are pervasive  Do they scale? RIKEN Workshop, April , Roy A. Lacey, Stony Brook University v n (ψ n ) Measurements - ATLAS Note v n increase from central to peripheral collisions ATLAS data - Phys. Rev. C86, (2012 ) & ATLAS-CONF

6 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University v n (ψ n ) Measurements - LHC Double differential Measurements for p+Pb are pervasive  Do they scale? Recent p+Pb measurements ATLAS Data - arXiv: ALICE Data - arXiv: Note increase of v 2 (or s 2 ) from peripheral to central collisions

7 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling – n 2 Characteristic n 2 viscous damping validated Characteristic 1/(p T ) α dependence of extracted β values validated Constraint for η/s and δf ATLAS data - Phys. Rev. C86, (2012 ) arXiv:

8 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Characteristic (n 2 – 4) viscous damping validated Characteristic 1/(p T ) α dependence of β validated Constraint for η/s Acoustic Scaling - Ratios arXiv:

9 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Fits performed for each centrality Acoustic Scaling - Ratios arXiv:

10 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling - Ratios The expected relation between v n and v 2 is validated arXiv:

11 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University For partonic flow, quark number scaling expected  single curve for identified particle species v n Flow is partonic & Acoustic? Note species dependence for all v n arXiv:

KE T & scaling validated for v n  Partonic flow 12 v n PID scaling Flow is partonic & acoustic RIKEN Workshop, April , Roy A. Lacey, Stony Brook University arXiv: J.Phys. G38 (2011)

13 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling – 1/R Specific dependence dictated by sound attenuation Centrality 5-70% ATLAS data - Phys. Rev. C86, (2012 )

14 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling – 1/R CMS Data - JHEP 1108,141 (2011)

15 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling – 1/R slope  β constraint STAR Data - PhysRevC

16 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling – 1/R ATLAS data - Phys. Rev. C86, (2012 ) Note slope difference

17 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Increase of s 2 (v 2 ) with centrality for p+Pb collisions is to be expected If the mechanism is similar!  Effects of system size (R) dominates Acoustic Scaling – 1/R v 2 increases with centrality ATLAS Data - arXiv: e 2 decreases with centrality

18 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling – 1/R Slope difference encodes viscous coefficient difference Compare system RHIC Viscous coefficient larger for more dilute system

19 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling – 1/R

20 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Jet suppression Probe Suppression (∆L) – pp yield unnecessary Jet suppression drives R AA & azimuthal anisotropy with specific scaling properties Suppression (L), Phys.Lett.B519: ,2001 For Radiative Energy loss: Modified jet More suppression Less suppression Fixed Geometry Path length (related to collision centrality)

R AA Measurements - CMS Specific p T and centrality dependencies – Do they scale? 21 Eur. Phys. J. C (2012) 72:1945 arXiv: Centrality dependence p T dependence RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

L scaling of Jet Quenching - LHC R AA scales with L, slopes (S L ) encodes info on α s and q Compatible with the dominance of radiative energy loss 22 arXiv: ˆ, Phys.Lett.B519: ,2001 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

23 Phys.Rev.C80:051901,2009 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University L scaling of Jet Quenching - RHIC R AA scales with L, slopes (S L ) encodes info on α s and q Compatible with the dominance of radiative energy loss ˆ

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 24 arXiv: p T scaling of Jet Quenching ˆ, Phys.Lett.B519: ,2001 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

Consistent obtained 25 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University q LHC ˆ Heavy quark suppression

Specific p T and centrality dependencies – Do they scale? 26 RIKEN Workshop, April , 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? 27 arXiv: p T dependence Centrality dependence RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

28 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: RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

29 ∆L Scaling of high-pT v 2 – LHC & RHIC Combined ∆L and 1/√p T scaling  single universal curve for v 2 arXiv: RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

30 RIKEN Workshop, April , 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

31 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 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University (z ~.62) ATLAS

32 Jet suppression from high-pT v 2 Jet suppression obtained directly from pT dependence of v 2 arXiv: R v2 scales as 1/√p T, slopes encodes info on α s and q ˆ RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

33 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! arXiv: arXiv: Conclusion similar to those of Liao, Betz, Horowitz,  Stronger coupling near T c ? q RHIC > q LHC ˆ q LHC ˆ RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

Robust scaling 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! 34  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 – Note density increase from RHIC to LHC RHIC to LHC  Flow is acoustic Flow is pressure driven Obeys the dispersion relation for sound propagation clear system size dependence  Flow is partonic exhibits scaling  Constraints for: ε, β, and δf RHIC (~ 1/4π) LHC a bit larger than at RHIC What do we learn? Summary RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

End 35 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University

36 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Centrality – 5-70% Acoustic Scaling – 1/R ATLAS data - Phys. Rev. C86, (2012 )

37 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Acoustic Scaling – 1/R  Eccentricity change alone is not sufficient To account for N part dependence of v 2 In light & heavy systems STAR Data - PhysRevC ATLAS data - Phys. Rev. C86, (2012 )

38 RIKEN Workshop, April , Roy A. Lacey, Stony Brook University Larger Slope for LHC  Viscosity LHC RHIC Acoustic Scaling – 1/R p T dependence of slope  δf constraint Compare RHIC & LHC