1. APCTP FRP@KNU of Transportation Siyoung Nam (CQUeST) Dissociation of Quarkonia in Quark Medium Based on hep-th/1512.XXXXX W/ Bum-Hoon Lee, Chanyong Park

2. Contents 1.Basics of Wilson Loop in Gauge/Gravity Duality 2.Known Results about Quarkonia in Hot medium 3.Dissociation of Quarkonia in Quark Matter

3. 1-1 Open String as a Color Flux tube Hadronic Resonances of high spins observed in 1960’s experiments are distributed along so-called Regge trajectories : As a qualitative explanation, the rotational d.o.f.’s of a relativistic rigid string give rise to Regge behaviors. Suppose that the open string w/ length L and tension T be rotating around its center of mass. Mass M ~ T L Angular momentum J ~ P L Since P ~ M in the relativistic theory, then or

4. In modern language, Meson open string The energy grows linearly w/ length as a model of confinement.

5. 1-2 : Wilson Loop in gauge/Gravity Duality Path-ordered integral of the holonomy of a gauge field transforming a representation R along a closed curve C Wilson Loop in gauge/gravity duality = Study a catenary curve for a hanging string in classical AdS (super)gravity

6. 1-2 : Wilson Loop in gauge/Gravity Duality The expectation value of the Wilson loop contains information about the non- perturbative physics of non-Abelian gauge theories and have applications to many physical phenomena such as confinement, quark screening, etc. For these applications it is useful to think of the path C as that traversed by the quark-antiquark pair. = Amplitudes for a creation of the quark-antiquark pair which propagates and is annihilated afterwards Introduce a quark-antiquark pair associated to the symmetry breaking which we perform by separating a D3. After ‘t Hooft limit, the Nc D3 are replaced by the background.

7. 1-2 : Wilson Loop in gauge/Gravity Duality The endpoints of the open string on the D3 are dual to the quarks, so the boundary of the string worldsheet must coincide with the path C traversed by the quark pair. This suggests that we must identify Maldacena TH/9803002 S.Rey,J.Yee TH/9803001

8. 1-2 : Wilson Loop in gauge/Gravity Duality To have infinitely heavy (non-dynamical) quarks, push the D3 to the AdS boundary, which means that lies within the AdS boundary. Large Nc & limits greatly simplify the string partition function, The classical action S(C) can be obtained by extremizing the NG action for the string worldsheet with the boundary condition.

9. 1-3 : Some Examples Ex 1 : Rectangular Loop : Vacuum Bulk geometry = 5-dimensional AdS In this case, the expectation value of the Wilson loop with suitable holographic renormalization gives the potential energy between the quark-antiquark pair. Heavy quark potential

10. 1-3 : Some Examples Ex 2 : Rectangular Loop at Finite Temperature S.Rey,J.Yee TH/9803135 Brandhuber, Itzhaki,Sonnenschein,Yankielowicz TH/9803137 Bulk Geometry = Black Brane Some maximum value Ls, beyond which no nontrivial solutions exist.

11. 1-3 : Some Examples The Precise value of Ls is defined as the quark-antiquark separation at which the free energy of the disconnected configuration becomes smaller than that of the connected configuration. Once L > Ls, the quark-pair separation can then be increased further at no additional energy cost, so the quark and antiquark are perfectly screened from each other by the hot plasma between them.

12. 1-3 : Some Examples

13. 2 : Known Results about Quarkonia in Hot Matter Matsui & Satz (’86) Quarkonia = Heavy quark-antiquark pair charmonium bottomonium The dissociation of quarkonia bound states has been proposed as a signal for the foration of a hot and deconfined QGP in heavy ion collisions. Due to their smaller size than typical hadrons in QCD, they survive as bound states even at temperature above the crossover Tc from a hadron gas to QGP. suppression @ CERN SPS, RHIC, LHC

14. The screening of the force between color charges due to the presence of the medium manifests itself in the flattening of the heavy quark potential for L greater than some characteristic length scale, called the screening length Ls. In heavy ion collisions, quarkonium mesons are produced with velocity v with respect to the medium. (in a sense, some kind of blue-shifted heat bath) To describe the interaction between into a frame in which the quark dipole is at rest, but feels a hot wind of QGP blowing past them. Liu, Rajagopal, Wiedemann PH/0607062,0612168 Chernicoff, Garcia, Guijosa TH/0607084 2 : Known Results about Quarkonia in Hot Matter

15. decreases with increasing velocity, indicating that quarkonia dissociate at a lower temperature when they move. The dependence of the screening length and the heavy quark potential on the angle between the quark dipole and the wind are very weak. (roughly ~12% of eta- dependence effect) Debye screening mass Calculations about the free energy of quark-antiquark pair were the earlier lattice results that substantiated an idea that a quarkonium bound state, placed in hot QCD matter, dissociates(“melts”) above a critical dissociation temperature Td. At zero temperature, these are well approximated by the ansatz like Cornell- potential, 2 : Known Results about Quarkonia in Hot Matter

16. Karsch-Merh-Satz Model is a Coulomb coupling constant and is a constant that appears due to regularization procedure. An mechanism underlying the dissociation is the weakening attraction between the heavy quark and antiquark in the bound state because the force between their color charges is screened by the medium such as temperature, flow moving, alignment. 2 : Known Results about Quarkonia in Hot Matter

17. 3 : Dissociation of Quarkonia in Quark Matter

27. 4 : Conclusion