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

Plan Heavy ion collisions Quakonium suppressions Insights and predictions from string theory  Propagation of heavy quakonia in a hot medium  potentials of infinitely heavy quarks  breakup of heavy quakonia in a hot medium

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

QCD Phase diagram Smooth crossover

Relativistic Heavy ion collisions

Relativistic heavy ion collisions Deconfinement crossover in QCD: T C ~ 170 MeV Deconfinement crossover in QCD: T C ~ 170 MeV LHC: Pb + Pb (2009) 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

QCD Phase diagram RHIC

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

String theory to the rescue!

AdS/CFT techniques have potential to make important impacts ! 2.Use strongly coupled N =4 SYM plasma as a benchmark for understanding the QCD QGP. Can N =4 SYM plasma serve as an ``Ising model’’ for QCD QGP? finite temperature helps! 1. Find gravity duals for gauge theories close to QCD

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: Shear viscosity Jet quenching Quarkonium suppression Things work better than expected !? heavy quark diffusion Thermodynamic properties …………… Many mysteries remain!

Quarkonium suppression: some predictions for LHC or RHIC

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.

Heavy quarkonia are good probes of QGP 1. The potential between the quark and anti-quark in the bound state is weakened by the color screening of the plasma. Due to their small sizes, heavy quakonia like J/ψ could survive the deconfinement transition. A quarkonium in QGP: 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

Dissociation temperature : T diss ~ 2 T C : T diss ~ 3 T C Asakawa, Hatsuda; Datta, Karsch, Petreczky, Wetzorke Dissociation temperature T d d: size of a meson Lattice estimate : L S (T): screening length (decreases with T) Their excited states already dissociate ~ 1.1 T C Color screening in a medium can be characterized by :

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

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

Insights and predictions from string theory Speed limit for heavy quakonia in a hot medium from potentials of infinitely heavy quarks break-up of heavy quakonia in a hot medium from string worldsheet instantons A qualitative predicition

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

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

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

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

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

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

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

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

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

Adding flavors in AdS/CFT Karch,Katz N =4 SYM theory does not contain dynamical quarks. Add N F hypermultiplets in fundamental representation to N =4 SYM  N =2 theory with flavors On gravity side, this can be achieved by adding N F D7-branes to the AdS 5 x S 5 geometry. mqmq Mesons: open string excitations on D7-branes. small T/m q Aharony, Fayyazuddin, Maldacena,

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

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

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

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

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

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

Worldsheet instantons

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

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

Meson widths Faulkner, HL

Do these features exist in QCD? Velocity scaling of screening length Speed limit for heavy quark mesons Velocity scaling of dissociation temperature Dramatic slowdown near T d 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 ! Dramatic increase of meson widths at large momenta

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