Heavy Quarkonium melting with Holographic Potential

1. Heavy Quarkonium melting with Holographic Potential With Hai-cang Ren,JHEP 0801:029,2008.   Defu Hou (CCNU,Wuhan) SQM2008 , Beijing , Oct. 6-10, 2008

2. OUTLINES • Motivations • Potential from AdS/CFT • Heavy quarkonium melting T • Summary

3. Motivation Many interesting phenomena in QCD lie in the strongly-coupled region. Non-perturbative methods for analysis Lattice: problematic with finite chemical potentioal, time- dependent problems AdS/CFT: Notable success in RHIC physics Viscosity, Jet quenching, …

4. QCD Diagramm

5. AdS/CFT now being applied to RHIC physics • Viscosity, /s. • EOS • Jet quenching • “Sound” waves • Photon production • Friction … • Heavy quarkonium • Hardron spectrum (ADS/QCD)

6. Heavy meson melting See the talk by H. Satz on Oct.7 • At T<Tc, confined ,potenial linearing rises • At T>Tc, deconfined, short range attraction range: screening length Lsc As T↗, Lsc↘, there exists a Td : the potential no longer binding for T>Td ( Melting Temperature) Heavy quakonium melting is an important signal of QGP

7. Nonperturbative calculation of Td • Potential model Lattice F. Karsch , Brambilla… AdS/CFT Maldacena, Rey, Liu , Avramis • Spectral function Lattice Karch AdS/CFTHoyos, Kim et al

8. Extracting V(r) from Wilson loop t 1/T r Q Q

9. F(r,t) is the free energy excess of a static pair of qq The internal energy reads

10. F-ansatz V(r) =F(r,T) • U –ansatz V(r)=U(r, T)=F+T S

11. Poential From Lattice • Quarkonium probes non-perturbative information about medium. How? Matsui, Satz 1986 • Wilson loop is static time-like and in fundamental representation: • Wilson loop is calculable in lattice QCD time Bielefeld Group, hep-lat/0509001 Ltime L distance

12. = conjecture AdS/CFT at finite temperature Classical Supergravity on AdS-BH×S5 Witten ‘98 4dim. Large-Nc strongly coupled SU(Nc) N=4 SYM at finite temperature (in the deconfinement phase).

13. Potential from AdS/CFT • According to the holographic principle, the thermal average of a WL operator in 4D N=4 SYM at large N_c and large 't Hooft coupling corresponds to the minimum area of the string world sheet in the 5D AdS metric with a Euclidean signature.

15. WL at Zero T (Maldacena 98)

16. Euler Lagrangian EQ Solution,

19. Wilson-loop at finite temperature bounded by the loop C, when y goes to infinity, y->1 BH

20. Minimizing the world sheet area (the Nambu-Goto action)

21. q q q r r q y _ + BH

22. Free energy

23. Result of pentential

24. F(r,T) r r0

26. Bound state & Schrődinger equation

27. Numerical Results • Value of ‘t Hooft coupling. • Upper limit : QCD value of coupling at RHIC • Lower limit: heavy quark potential , (Gubser) • Mc=1.65Gev, Mb=4.85Gev, Tc=186MeV

28. Dissociation Temperature Hou, Ren JHEP01 (08)

29. Holographic potential model with an IR cutoff Hard Wall : Erlich, Katz, Son, Stephanov

30. In the hadronic phase • In the plasma phase

31. Soft-wall model 1 : Karch, Katz, Son, Stephanov A dilaton is introduced, Metrics are the same. • Soft-wall model 2 : Andreev,Zakharov;Kajantie modify string frame metric by a conformal factor

32. Free energy

34. Td with deformed metric

35. AdS/CFT and Lattice

36. Summary We calculated dissociation temperatures Td of heavy quarkonium states from holographic potential The computed Td have remarkable features compariable with that from Lattice But N=4 SYM is not real QCD with less stronger screening