Quarkonium suppression in Heavy Ion Collisions and AdS /CFT

1. Quarkonium suppression in Heavy Ion Collisions and AdS/CFT Hong Liu Massachusetts Institute of Technology HL, K. Rajagopal, U. A. Wiedemannhep-ph/0607062, hep-ph/0612168 Q. Ejaz, T. Faulkner, HL, K. Rajagopal, U. A. WiedemannarXiv:0712.0590 T. Faulkner, HL, arXiv:0807.0063

2. Plan • Heavy ion collisions • Quakoniumsuppressions • Insights and predictions from string theory • potentials of infinitely heavy quarks • Propagation of heavy quakonia in a hot medium • breakup of heavy quakonia in a hot medium

3. QCD QCD has presented us many fascinating dynamical phenomena: Confinement, chiral symmetry breaking, asymptotic freedom, internal structure of nucleons …… largely guided by experiments, great challenges for theorists. Recently, heavy ion collision experiments opened new windows into probing dynamical phenomena in QCD: Many body physics, collective phenomena, ……. thermalization, finite temperature, ……

4. QCD Phase diagram Smooth crossover

5. Relativistic Heavy ion collisions

6. Relativistic heavy ion collisions RHIC (2000): Au+Au : center of mass energy per pair of nucleons Au: 197 nucleons; Total: 39.4 TeV Temperature (1 fm after collision) ~ 250 MeV Baryon chemical potential ~ 27 MeV Deconfinement crossover in QCD: TC ~ 170 MeV LHC: Pb + Pb (2009)

7. QCD Phase diagram RHIC

8. Quark-gluon fluid of RHIC QGP has been formed RHIC Experiments : many dynamical phenomena: thermalization, collective flow, jet quenching, J/ψ suppression, ……… RHIC QGP: behaves very differently from a weakly coupled QGP gas (Perturbation theory: inadequate ) strongly coupled, liquid-like (nearly ideal ) exciting opportunities, but difficult challenges But information on dynamical quantities: scarce and indirect But information on dynamical quantities: scarce and indirect New theoretical tools are needed.

9. String theory to the rescue!

10. AdS/CFT techniques have potential to make important impacts ! Find gravity duals for gauge theories close to QCD Use strongly coupled N=4 SYM plasma as a benchmark for understanding the QCD QGP. CanN=4 SYM plasma serve as an ``Ising model’’ for QCD QGP? finite temperature helps!

11. Heavy ion collisions and AdS/CFT String theory techniques provide qualitative, and semi-quantitative insights and predictions regarding properties of strongly interacting quark-gluon plasma: • Thermodynamic properties • Shear viscosity • Jet quenching • heavy quark diffusion • Quarkonium suppression …………… Things work better than expected !? Many mysteries remain!

12. Quarkonium suppression: some predictionsfor LHC or RHIC

13. Heavy Quarkonia Charm: The radii of charmonium (J/ψ, ψ′, ...) and bottomonium (ϒ, ϒ’, ...) families provide a unique set of decreasing length scales in QCD.

14. Heavy quarkonia are good probes of QGP Due to their small sizes, heavy quakonia like J/ψ could survive thedeconfinement transition. A quarkonium in QGP: 1. The potential between the quark and anti-quark in the bound state is weakened by the color screening of the plasma. shallower bound state or no bound state et al 2. The bound state can be broken apart by collisions with gluons and quarks in the plasma. medium-induced width

15. Dissociation temperature • Color screening in a medium can be characterized by : LS (T): screening length (decreases with T) • Dissociation temperature Td d: size of a meson • Lattice estimate: : Tdiss~ 2 TC Asakawa, Hatsuda; Datta, Karsch, Petreczky, Wetzorke : Tdiss~ 3 TC Their excited states already dissociate ~ 1.1 TC

16. Quarkonium suppression J/ψ Heavy ion collisions: color screening in the produced medium Matsui and Satz (1987) J/ψ suppression One of the most important probes of the QGP.

17. Basic theoretical questions To understand the pT dependence: How does the screening effect depend on the velocity ? Velocity dependence of the dissociation temperature Td ? How does QGP affects the propagation of J/ψ? momentum-dependence of the width ? Not known in QCD Lattice: Hard Strategy: see what happens in our ``Ising model’’

18. Insights and predictions from string theory • frompotentials of infinitely heavy quarks A qualitative predicition • Speed limit for heavy quakonia in a hot medium • break-up of heavy quakonia in a hot medium from • string worldsheetinstantons

19. Our (3+1)-dim world, Static quark potential Gauge theory description: gluon flux lines String theory description: Maldacena; Rey, Yee String lives in one extra dimension Gravity approximation: finding minimal energy string shape

20. (3+1)-dim world at temperature T, Screening of quarks in a QGP Rey, Theisen Yee; Brandhuber, Itzhaki, Sonnenschein Yankielowicz …….. Ls event horizon Quarks are screened N=4 : , QCD (2 flavor): (lattice)

21. Finite velocity scaling Moving at a finite velocity v Finding string shape of minimal energy Event horizon HL,Rajagopal,Wiedemann Chernicoff, Garcia, Guijosa; Peeters, Sonnenschein, Zamaklar

22. Dissociation temperature Td : d: size of a meson this suggests: Does the scaling apply to QCD?

23. A simple argument In a rest frame of quark pair, the medium is boosted:

24. If similar kind of scaling does apply to QCD, any implication? Should be used as a basic theoretical input in any phenomenological modeling of J/ψ suppression

25. A prediction from string theory HL,Rajagopal,Wiedemann zero velocity : (lattice) : Tdiss~ 2.1 TC : Tdiss~ 3.6 TC RHIC ~1.5 Tc LHC? Could lead to significant suppression at large PT. J/ψ RHIC This effect may be tested at RHIC II or LHC

27. Data to come RHIC: low statistics on J/psi with 2 < PT < 5 GeV, very low statistics for PT> 5GeV Reach in PT will extend to 10 GeV in coming years at RHIC. LHC will reach even wider range.

28. Beyond quark potential So far: crude extrapolation from infinitely heavy quark potential Next step: genuine heavy-quark mesons Want to understand:

29. Adding flavors in AdS/CFT Aharony, Fayyazuddin, Maldacena, Karch,Katz N=4 SYM theory does not contain dynamical quarks. Add NFhypermultiplets in fundamental representation to N=4 SYM N=2 theory with flavors On gravity side, this can be achieved by adding NF D7-branes to the AdS5 x S5 geometry. Mesons: open string excitations on D7-branes. small T/mq mq

30. Meson Spectrum Meson spectrum can be found by solving linearized Laplace equations for small fluctuations on the D7-brane. mq One finds a discrete spectrum of mesons: , Bare quark mass: Meson masses: Babington, Erdmenger, Evans, Guralnik, Kirsch; Kruczenski, Mateos, Myers, Winters; λ: ‘t Hooft coupling Very tightly bound:

31. Meson “Dissociation” Babington, Erdmenger, Evans, Guralnik, Kirsch Mateos, Myers and Thomson, Hoyos, Landsteiner, Montero Meson dissociation: Gravity approximation: Mesons are stable at T < Td. completely disappear for T > Td

32. Propagation of mesons in QGP Does the screening affect the propagation of mesons in a QGP? Mateos, Myers and Thomson Speed limit: Ejaz, Faulkner, HL, Rajagopal, Wiedemann vC: speed of Light at the tip As , As v > vC(T), quark and anti-quark get completely screened.

33. Speed limit at a generic temperature vC(T) Stable Mesons “Td(v)’’ Inference from infinitely heavy quark potential remarkably accurate. Large k behavior of the dispersions relation of mesons are controlled by the screening behavior.

34. Width of mesons? Gravity approximation: Mesons are stable for T < Td, no width mq completely disappear for T > Td Open strings on D7-brane sees a geometry which is smoothly capped off. In fact mesons are stable to all orders in perturbativeα’ expansion. However, bound states should always have a nonzero width in a finite temperature medium.

35. Field theory considerations On the field theory side, meson widths receive contributions from: • Mesons -> glue balls , lighter mesons, or other gauge singlets (1/Nc suppressed, present at zero temperature) • Breakup by high energy gluons: • Breakup by collisions with thermal medium quarks Non-perturbative in α’, worldsheetinstantons

36. Worldsheetinstantons

37. Gauge theory interpretation Medium modified quark mass: Instanton action: μ: chemical potential for quark number D: worldsheet determinant A Boltzmann gas of thermal quarks instantons

38. Meson widths Open strings can tunnel into the black hole through the disk instantons Mesons become unstable and obtain a nonzero width. Gauge theory:

39. Meson widths Faulkner, HL

40. Do these features exist in QCD? • Velocity scaling of screening length • Velocity scaling of dissociation temperature • Speed limit for heavy quark mesons Dramatic slowdownnear Td • Dramatic increase of meson widths at large momenta All of them are rather qualitative features, which may not depend on the precise details of the underlying theory. Far from being obvious in perturbation theory !

41. Conclusion String theory has immediate testable predictions for experiments after all …….