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23-Oct-08 W.A. Zajc Exploring the Lower Limits of Perfection W. A Zajc Columbia University DNP08 Workshop: Quantifying the Character of the sQGP.

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Presentation on theme: "23-Oct-08 W.A. Zajc Exploring the Lower Limits of Perfection W. A Zajc Columbia University DNP08 Workshop: Quantifying the Character of the sQGP."— Presentation transcript:

1 23-Oct-08 W.A. Zajc Exploring the Lower Limits of Perfection W. A Zajc Columbia University DNP08 Workshop: Quantifying the Character of the sQGP

2 23-Oct-08 W.A. Zajc Perfection  (No) Viscosity l Isotropic in rest frame  No shear stress  no viscosity,  = 0 l Primer: q Remove your organic prejudices q Viscosity ~ mean free path q Small viscosity  Small mfp q Zero viscosity  mfp = 0 (!) X

3 23-Oct-08 W.A. Zajc Pre-History l Landau (1955) significant extension of Fermi’s statistical model l Considers fundamental roles of q hydrodynamic evolution q entropy u “The defects of Fermi’s theory arise mainly because the expansion of the compound system is not correctly taken into account… (The) expansion of the system can be considered on the basis of relativistic hydrodynamics.”

4 23-Oct-08 W.A. Zajc Landau on Viscosity 1)Use of hydro relies on R/ >> 1 2)Negligible viscosity  equivalent to large Reynolds number Re   VR/  >>1  VR/  ~ V R / v th so for relativistic system V ~ v th and Re >>1  R / >> 1 ; see #1

5 23-Oct-08 W.A. Zajc RHIC Success

6 23-Oct-08 W.A. Zajc What Is The Viscosity at RHIC? l “Perfect fluid” (and/or “ideal hydrodynamics”) defined as “zero viscosity”. ?

7 23-Oct-08 W.A. Zajc Why  /s Matters l Any engineer will tell you q Kinematic viscosity  /  ~ [Velocity] x [Length] is what matters (see Landau’s remark on Reynolds number) l Any relativist will tell you q    + p l Any thermodynamicist will tell you q  + p = T s ( at  B =0 ) l So q  /   /  + p  (  /sT) = (  /s) (1/T) ~ (damping coefficient x thermal time)

8 23-Oct-08 W.A. Zajc Numerical Value of RHIC Viscosity l Input : l Estimating s QGP (per degree of freedom): q Method 1: q Method 2 (based on handy rule of thumb): l Number of (assumed massless) degrees of freedom:

9 23-Oct-08 W.A. Zajc A Long Time Ago (1985) l Miklos Gyulassy and Pawel Danielewicz: q Dissipative Phenomena in Quark-Gluon Plasmas P. Danielewicz, M. Gyulassy Phys.Rev. D31, 53,1985.Phys.Rev. D31, 53,1985. noted several restrictions on smallest allowed  : l Most restrictive: l > h/   > ~ n / 3 l But recall s = 3.6 n for the quanta they were considering l   /s > 1 / (3.6 x 3) ~ 1 / (4  ) !!

10 23-Oct-08 W.A. Zajc KSS Bound F This bound is (now) very well-known in the nuclear physics community: l “A Viscosity Bound Conjecture”, P. Kovtun, D.T. Son, A.O. Starinets, hep-th/0405231 P. KovtunD.T. SonA.O. Starinetshep-th/0405231 q Where do “ordinary” fluids sit wrt this limit? q RHIC “fluid” might be at ~2-3 on this scale (!) T=10 12 K (4 

11 AdS / CFT in Pictures l Google Image search on “AdS/CFT hologram boundary” Google Image AdS/CFT hologram boundary 23-Oct-08 W.A. Zajc

12 AdS / CFT for Dummies 23-Oct-08 W.A. Zajc Graviton with 5-momentum k in bulk satisfies k  k = 0  described by 4 numbers Those 4 numbers describe virtual gauge quanta on 4-d boundary ( Adopted from S. Brodsky figure )S. Brodsky figure

13 23-Oct-08 W.A. Zajc The (Assumed) Connection l Exploit Maldacena’s “D-dimensional strongly coupled gauge theory  (D+1)-dimensional stringy gravity” l Thermalize with massive black brane l Calculate viscosity  = “Area”/16  G l Normalize by entropy (density) s = “Area” / 4G l Dividing out the infinite “areas” : l Conjectured to be a lower bound “for all relativistic quantum field theories at finite temperature and zero chemical potential”. l See “Viscosity in strongly interacting quantum field theories from black hole physics”, P. Kovtun, D.T. Son, A.O. Starinets, Phys.Rev.Lett.94:111601, 2005, hep-th/0405231hep-th/0405231 Infinite “Area” ! hh AA A

14 23-Oct-08 W.A. Zajc Estimating  /s l Damping (flow, fluctuations, heavy quark motion) ~  /s q FLOW: Has the QCD Critical Point Been Signaled by Observations at RHIC?, R. Lacey et al., Phys.Rev.Lett.98:092301,2007 (nucl-ex/0609025)nucl-ex/0609025 q The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553)arXiv:0704.3553 q FLUCTUATIONS: Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061)nucl-th/0606061 q DRAG, FLOW: Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √s NN = 200 GeV (PHENIX Collaboration), A. Adare et al., to appear in Phys. Rev. Lett. (nucl-ex/0611018)nucl-ex/0611018 CHARM!CHARM!

15 23-Oct-08 W.A. Zajc Has the QCD Critical Point Been Signaled by Observations at RHIC?, R. Lacey et al., Phys.Rev.Lett.98:092301,2007 (nucl-ex/0609025)nucl-ex/0609025 l Signature: FLOW l Calculation: l Payoff Plot: Fit v 2 ~I 1 (w)/I 0 (w); w = m T /2T On-shell transport model for gluons, Z. Xu and C. Greiner, hep-ph/0406278. PHENIX v 2 /  data (nucl-ex/0608033) compared to R.S. Bhalerao et al. (nucl-th/0508009)

16 23-Oct-08 W.A. Zajc Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061)nucl-th/0606061 l Signature: FLUCTUATIONS l Calculation: l Payoff Plot: Diffusion eq. for fluctuations g Compare to STAR data on centrality dependence of rapidity width  of p T fluctuations Difference in correlation widths for central and peripheral collisions

17 23-Oct-08 W.A. Zajc The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553)arXiv:0704.3553 l Signature: FLOW l Calculation: l Payoff Plot: Knudsen number K Fits to PHOBOS v2 data to determine  for Glauber and CGC initial conditions Decrease in flow due to finite size

18 Closely Related Recent Development l Application of Drescher et al. methodology to STAR flow dataDrescher et al. q Yuting Bai, SQM08 q First extraction of  /s versus centrality 23-Oct-08 W.A. Zajc 10-Oct-08 STAR Preliminary

19 23-Oct-08 W.A. Zajc Moore and Teaney Phys.Rev.C71:064 904,2005 (perturbative, argue ~valid non-perturbatively) Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √s NN = 200 GeV (PHENIX Collaboration), A. Adare et al., Phys. Rev. Lett. 98:172301,2007 (nucl-ex/0611018)nucl-ex/0611018 l Signature: FLOW, ENERGY LOSS l Calculation: l Payoff Plot: Rapp and van Hees Phys.Rev.C71:034 907,2005, to fit both PHENIX v 2 (e) and R AA (e)

20 23-Oct-08 W.A. Zajc S. Gavin and M. Abdel-Aziz: PRL 97:162302, 2006 p T fluctuations STAR Comparison of estimates R. Lacey et al.: PRL 98:092301, 2007 v 2 PHENIX & STAR H.-J. Drescher et al.: arXiv:0704.3553 v 2 PHOBOS conjectured quantum limit l Estimates of  /s based on flow and fluctuation data q Indicate small value as well q Close to conjectured limit q Significantly below  /s of helium (  s ~ 9)

21 23-Oct-08 W.A. Zajc Compare to the Competition l Damping of breathing mode in cold Fermi gas l (All figures courtesy of John Thomas, Duke University) Strongly- Interacting Gas Duke, Science (2002) O’Hara et al. String-theory 1/4  Schafer, cond-mat 2006 3 He, 4 He near  point QGP simulations

22 23-Oct-08 W.A. Zajc Our Problem Is Much Harder l Non-relativistic: Damping given by l Relativistic: Causal, second-order expansion: q Relativistic Fluid Dynamics: Physics for Many Different Scales Relativistic Fluid Dynamics: Physics for Many Different Scales l Neglect various terms at your own risk: q Baier et al., Relativistic viscous hydrodynamics, conformal invariance, and holographyRelativistic viscous hydrodynamics, conformal invariance, and holography q Natsuume and Okamura, Comment on “Viscous hydrodynamics relaxation time from AdS/CFT correspondence” Comment on “Viscous hydrodynamics relaxation time from AdS/CFT correspondence”

23 22-Apr-08 W.A. Zajc x y Viscosity  Dissipation l Non-relativistic: Damping given by l Where does this come from? q Recall we’re interested in velocity gradients: q Remove uniform rotation: q Remove uniform (Hubble) expansion: x y

24 23-Oct-08 W.A. Zajc For Further Details l See “Virtual Journal on QCD Matter” q Steffen A. Bass, Berndt Mueller, William A. Zajc q qgp.phy.duke.edu qgp.phy.duke.edu l On the topic of 2 nd order hydro: q What a Difference a Term Makes What a Difference a Term Makes

25 23-Oct-08 W.A. Zajc Quantifying  /s Q: How? A: By performing detailed and systematic hydrodynamic simulations to understand sensitivity to  /s (and “everything” else) q Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99:172301, 2007 Phys. Rev. Lett. 99:172301, 2007 q Multiplicity Scaling in Ideal and Viscous Hydrodynamics, H. Song and U. Heinz, Phys. Rev. C78, 024902, 2008 Phys. Rev. C78, 024902, 2008 q Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at  s NN = 200 GeV, M. Luzum and P. Romatschke, Phys.Rev.C78:034915,2008. Phys.Rev.C78:034915,2008

26 23-Oct-08 W.A. Zajc Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99:172301, 2007Phys. Rev. Lett. 99:172301, 2007 l Signature: dN/dy, v 2, l Calculation: 2 nd order causal viscous hydro: (Glauber IC’s) l Payoff Plots:

27 23-Oct-08 W.A. Zajc Multiplicity Scaling in Ideal and Viscous Hydrodynamics, H. Song and U. Heinz, Phys. Rev. C78, 024902, 2008Phys. Rev. C78, 024902, 2008 l Signature: Famous “hydro limits” plot of v2/  vs (1/S)dN ch /dy l Calculation: Full Israel-Stuart equations (Glauber IC’s) l Payoff Plots:

28 23-Oct-08 W.A. Zajc Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99:172301, 2007Phys. Rev. Lett. 99:172301, 2007 l Signature: dN/dy, v 2, l Calculation: 2 nd order causal viscous conformal hydro: (Glauber and CGC IC’s) l Payoff Plots:

29 23-Oct-08 W.A. Zajc S. Gavin and M. Abdel-Aziz: PRL 97:162302, 2006 p T fluctuations STAR Comparison with other estimates R. Lacey et al.: PRL 98:092301, 2007 v 2 PHENIX & STAR H.-J. Drescher et al.: arXiv:0704.3553 v 2 PHOBOS conjectured quantum limit l Estimates of  /s based on flow and fluctuation data q Indicate small value as well q Close to conjectured limit q Significantly below  /s of helium (  s ~ 9) Various 2 nd order hydro calculations

30 23-Oct-08 W.A. Zajc Beyond ‘t Hooft Limit(?) l Just for fun: q Take “central value” of these estimates q Apply it in the most naïve mapping  s = g YM 2 /4  in u “Coupling constant dependence of the shear viscosity in N=4 supersymmetric Yang-Mills theory”, Buchel, Liu, Starinets, hep-th/0406264 hep-th/0406264   S = 0.28 (!!) q Amazingly consistent with estimates from AMY formalism of high p T energy loss (J. Nagle) l Just for perspective: q Allowed range 4   /s “s”“s”

31 23-Oct-08 W.A. Zajc The “Flow” Knows Quarks l The “fine structure” v 2 (p T ) for different mass particles shows good agreement with ideal (“perfect fluid”) hydrodynamics l Scaling flow parameters by quark content n q resolves meson-baryon separation of final state hadrons baryons mesons

32 23-Oct-08 W.A. Zajc Quasi-particles and Minimal Viscosity l If you’re doing Boltzmann transport: q  = energy density q  = lifetime of quasiparticle l Entropy density s ~ k B n  l where last step q follows from requirement that lifetime of quasiparticle must exceed ~ h / Energy q establishes that the bound is from below l But values not compatible with quasiparticles with lifetimes > h / mass q D. T. Son q Levy et al. Quasi-Particle Degrees of Freedom versus the Perfect Fluid as Descriptors of the Quark-Gluon Plasma.. Quasi-Particle Degrees of Freedom versus the Perfect Fluid as Descriptors of the Quark-Gluon Plasma. l How to reconcile with quark scaling of flow ?

33 23-Oct-08 W.A. Zajc Water  RHIC  Water  RHIC l The search for QCD phase transition of course was informed by analogy to ordinary matter l Results from RHIC are now “flowing” back to ordinary matter “On the Strongly-Interacting Low-Viscosity Matter Created in Relativistic Nuclear Collisions”, L.P. Csernai, J.I. Kapusta and L.D. McLerran, Phys.Rev.Lett.97:152303,2006, nucl-th/0604032nucl-th/0604032  / s

34 23-Oct-08 W.A. Zajc Is There a QCD Critical Point? l Here the analogy with phase transitions in ordinary matter breaks down: q Recall “ Properties of the medium are (at zero baryon number) uniquely determined by T ” ð Pressure = P(T) can’t vary independently (unlike water) q But if baryon number is non-zero  (intensive order parameter) baryon chemical potential  B : l To increase  B : q Lower collision energy q Raise atomic mass q Both part of RHIC II and GSI-FAIR

35 Conclusions l Can we say with confidence “the quark-gluon plasma displays less friction than any other known laboratory fluid” ? q Not yet: Cold atom competition l Can we say with confidence “  /s for sQGP saturates the quantum bound” ? q Not yet: q Still must quantify contributions from u Bulk viscosity u Anomalous viscosity u Eddy viscosity u Hadronic viscosity u Not to mention eccentricity fluctuations, EOS’s, freezeout schemes, … l What we can state with confidence: q Tremendous progress has been made in understanding the fundamental role of  /s and quantifying its value in the sQGP q This, more so than any other “observable”, has had the greatest impact on other fields in the history of relativistic heavy ion physics 23-Oct-08 W.A. Zajc

36 23-Oct-08 W.A. Zajc Summary l The near-simultaneous development of q RHIC Discoveries q Theoretical Synthesis q Overthrow of “classical” QGP q Emergence of AdS/CFT calculations represents a true paradigm shift l This workshop provides wonderful possibility to continue these compelling investigations

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