Understanding the Quark-Gluon Plasma via String Theory

1. Understanding the Quark-Gluon Plasmavia String Theory Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs A. Wiedemann hep-ph/0605178, hep-ph/0607062, hep-ph/0612168 Qudsia Ejaz, Thomas Faulkner, HL, Krishna Rajagopal, Urs Wiedemann to appear

2. Plan • Heavy ion collisions • Shear viscosity (a quick overview) • Jet quenching • J/ψsuppression: a prediction • N=4 SYM v.s. QCD

3. Quark-Gluon Plasma At room temperature, quarks and gluons are always confined inside colorless objects(hadrons): protons, neutrons, pions, ….. Very high temperature (asymptotic freedom):  Interactions become weak  quarks and gluons deconfined  Quark-gluon plasma (QGP) Infinitely high temperature: QGP behaves like an ideal gas.

4. Is there a deconfinementphase transition separating the hadronic and QGP phases? Can one create quark-gluon plasma in the lab?

5. QCD Phase diagram(2006) Smooth crossover at

6. Relativistic Heavy ion collisions

7. Relativistic Heavy Ion Collider (RHIC) RHIC: Au+Au : center of mass energy per pair of nucleons Au: 197 nucleons; Total: 39.4 TeV • Energy density (peak) • > 5 GeV/fm3 • Temperature (peak) • ~ 300 MeV LHC: Pb + Pb (2009)

8. Creating a little Big Bang

9. Experimental probes of the QGP ? Some basic questions: Has the created hot matter reached thermal equilibrium? If yes, when? Has the QGP been formed? What are its signatures? Properties: weakly or strongly coupled? equation of state? Viscosity? opacity? QGP at RHIC exists for about 10-23 sec (5 fm), making it impossible to study it using any external probes.

10. Quark-gluon fluid of RHIC • Collective behavior of the observed final-state hadrons • (elliptic flow) • Interaction of produced hard probes with the medium • (jet quenching, J/Ψ suppression) Nearly ideal, strongly coupled fluid (sQGP) Main theoretical tool for strong coupling: Lattice calculation But information on dynamical quantities: scarce and indirect New theoretical tools are needed! But information on dynamical quantities: scarce and indirect New theoretical tools are needed.

11. String theory to the rescue!

12. Collective motion and shear viscosity of sQGP

13. y x Collective motion If lots of p+p collisions plus free streaming: final state momenta uniformly distributed in azimuth angle . If interaction  equilibration  pressure  pressure gradients collective motion • anisotropy of momenta distribution in .

14. Rough agreement with hydrodynamic models based on perfect liquid. Near-perfect fluid discovered • Elliptic flow Strong signal ! Created hot matter equilibrates very early: before 1fm. likely strongly interacting ! Shear viscosity should be small!

15. Universality of Shear viscosity • RHIC: Teaney (2003) • Water • N=4 SYM: Policastro, Son, and Starinets (2001) • The value turned out to be universal for all • strongly coupled QGPs with a gravity description. Kovton, Son and Starinets (2003) Buchel, J. Liu • Lattice: Meyer (2007)

16. AdS/CFT and Jet quenching

17. Hard probes Hard scatterings in p+p collisions produce: back-to-back high energy quarks ("jets“). The presence of hot matter modifies the properties of jets.

18. They lose energy! QGP Jet Quenching • The number of high energy • particles observed should be • much smaller than expected • from p+p collisions: Only 20% ! 2. monojets: sometimes they never make out. QGP

19. The dominant effect of the medium on a high energy parton is medium-induced Bremsstrahlung. Baier, Dokshitzer, Mueller, Peigne, Schiff (1996): : reflects the ability of the medium to “quench” jets. Parton energy loss in QGP

20. : 5-15 GeV2/fm : < 1 GeV2/fm : < 0.1 GeV2/fm Toward understanding Opacity Experimental estimate: Hadronic gas: Perturbation theory: Strongly coupled QGP? Theoretical challenge: non-perturbative calculation of for QCD QGP slightly above TC .

21. Need a non-perturbative definition of • Compute in SYM theory using AdS/CFT Strategy:

22. : a non-perturbative formulation Hard: weakly coupled Soft: likely strongly coupled Assume: E >> ω >> k┴ >>T : multiple rescatterings of hard particles with the medium

23. High energy limit (eikonal approximation): Soft scatterings Zakharov (1997); Wiedemann (2000) • Amplitude for a particle propagating in the medium Soft scatterings are capturedby Light like Wilson lines.

24. Light-like Wilson loop: L: conjugate to the pT : length of the medium Assuming: Thermal average (Hard to calculate using lattice) Nonperturbative definition of A non-perturbative definition of Wiedemann HL, Rajagopal, Wiedemann

25. Wilson loop C in our world Our (3+1)-dim world, Wilson loop from AdS/CFT Maldacena (1998); Rey and Yee (1998) Recipe: : area of string worldsheet with boundary C horizon • Black hole in AdS spacetime: • radial coordinate r, • horizon: r=r0 • constant r surface: (3+1)-dim Minkowski spacetime

26. Extremal configuration r=r0 r=r0 extremal string configuration: string touches the horizon. two disjoint strings Interactions between the quark and the medium Interaction of the string with the horizon of a black hole.

27. Wilson loop With The corresponding BDMPS transport coefficient reads

28. Take: of N=4 SYM theory BDMPS transport coefficient reads: • It is not proportional to number of scattering centers • Experimental estimates: 5-15 GeV2/fm

29. and number of degrees of freedom General conformal field theories (CFT) with a gravity dual: (large N and strong coupling) HL,Rajagopal Wiedemann, sCFT : entropy density For non-conformal theories, it may decrease with RG flow. an estimate for QCD:

30. Summary • In QGP of QCD, the energy loss of a high energy parton can be described perturbatively up to a non-perturbative jet-quenching parameter. • We calculate the parameter in N=4 SYM (notnecessarily full energy loss of SYM) • It appears to be close to the experimental value.

31. Quarkonium suppression: a prediction for LHC or RHIC II

32. Heavy quarkonium in a QGP Above TC, light-quark mesons no longer exist due to deconfinement. Heavy quarkonia are bound by short-distance Coulomb interaction: may still exist above TC . In a QGP, interactions between a quark and an anti-quark are screened by the plasma. A heavy quark meson will dissociate when the screening length becomes of order the bound state size. : Tdiss = 2.1 TC : Tdiss = 3.6 TC while their excited states already dissociate above 1.2 TC.

33. Quarkonium suppression J/ψ Quarkonium suppression is a sensitive probe of QGP. Matsui and Satz (1987)

34. Connecting lattice QCD directly to heavy ion phenomenology is difficult: Heavy quark mesons produced in heavy ion collisions could move very fast relative to the hot medium: How does the screening effect depend on the velocity? Velocity dependence of the Tdiss ? (not known in QCD)

35. Static quark potential in N=4 SYM Maldacena; Rey, Yee; Rey, Theisen Yee; Brandhuber, Itzhaki, Sonnenschein Yankielowicz …….. probe brane Ls Finding string shape of minimal energy event horizon quarks are screened In the large NC and large limit: quark potential = energy of open string connecting the pair ,

36. Quark potential at finite velocity HL, Rajagopal Wiedemann Moving at a finite velocity v Finding string shape of minimal energy Event horizon In a rest frame of quark pair, the medium is boosted:

37. Velocity dependence of dissociation temperature Dissociation temperature Td : d: size of a meson Given: this suggests: What would happen if QCD also has similar velocity scaling?

38. Has RHIC reached Td forJ/ψ ? Lattice: J/ψ may survive up to 2TC Similarity of the magnitude of J/ψsuppression at RHIC and SPS Karsch, Kharzeev, Satz, RHIC has not reached Tdiss for J/ψ.

39. Quarkonium suppression:a prediction via string theory HL,Rajagopal,Wiedemann Heavy quark mesons with larger velocity dissociate at a lower temperature. Expect significant suppression at large PT. J/psi This effect may be significant and tested at RHIC II or LHC

40. Data to come RHIC: low statistics on J/ψ with 2 < PT < 5 GeV, no data for PT> 5GeV Reach in PT will extend to 10 GeV in coming years at RHIC. LHC will reach even wider range.

41. N=4 SYM versus QCD

42. N=4 SYM versus QCD N=4 SYM theory • Conformal • no asymptotic freedom, no confinement • supersymmetric • no chiral condensate • no dynamical quarks, 6 scalar and 4 Weyl fermionic fields in the adjoint representation. Physics near vacuum and at very high energyis very different from that of QCD

43. N=4 SYM versus QCD (continued) N=4 SYM at finite T QCD at T ~TC-3 TC • conformal • no asymptotic freedom, no confinement • supersymmetric (badly broken ) • no chiral condensate • no dynamical quarks, 6 scalars and 4 fermions in the adjoint representation. • near conformal (lattice) • not intrinsic properties of sQGP • not present • not present • may be taken care of by proper normalization

44. N=4 SYM versus QCD Ideal gas (T= infinity QCD) Strongly coupled N=4 SYM at finite T T=0 QCD confinement

45. N=4 SYM versus QCD • It is likely that QCD has a string dual in the large N limit. • Finite-T QCD in a strongly coupled regime could be described • by a black hole in this string theory. • Universality of black hole (horizon physics) Universality between QCD and N=4 SYM for observables probing intrinsic properties of the medium.

46. Summary • String theory techniques provide qualitative, and • semi-quantitative insights and predictions regarding • properties of strongly interacting quark-gluon plasma: • Shear viscosity • Jet quenching parameter (a prediction) • Quarkonium suppression • Expect many more chapters to be written for the marriage • between string theory and physics of QCD in extreme • conditions.

48. Energy and entropy density Karsch:hep-lat/0106019 QCD: Gubser, Klebanov,Peet (1998) N=4 SYM:

49. Speed of sound Karsch, hep-ph/0610024

50. Jet quenching:monojetphenomenon STAR collaboration: nucl-ex/0501009