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Heavy Quarkonium melting with Holographic Potential
Defu Hou (CCNU,Wuhan)
SQM2008 , Beijing , Oct. 6-10, 2008
With Hai-cang Ren, JHEP 0801:029,2008.
• Motivations
• Potential from AdS/CFT
• Heavy quarkonium melting T
• Summary
OUTLINES
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, …
Motivation
QCD Diagramm
AdS/CFT now being applied to RHIC physics
• Viscosity, /s.• EOS
• Jet quenching
• “Sound” waves
• Photon production
• Friction …
• Heavy quarkonium
• Hardron spectrum (ADS/QCD)
Heavy meson melting
• 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
See the talk by H. Satz on Oct.7
Nonperturbative calculation of Td
• Potential model
Lattice F. Karsch , Brambilla…
AdS/CFT Maldacena, Rey, Liu , Avramis
• Spectral function
Lattice Karch
AdS/CFT Hoyos, Kim et al
Q Qr
1/Tt
Extracting V(r) from Wilson loop
• F(r,t) is the free energy excess of a static pair of qq
The internal energy reads
• F-ansatz
V(r) =F(r,T)
• U –ansatz
V(r)=U(r, T)=F+T S
Poential From Lattice • Quarkonium probes non-perturbative information about medium. How?
W (C) 1
NTr P exp i A
C
W (C)Texp iLtime E(L) E ren
• Wilson loop is static time-like and in fundamental representation:
• Wilson loop is calculable in lattice QCD
Bielefeld Group, hep-lat/0509001time
distance
L
Ltime
Matsui, Satz 1986
AdS/CFT at finite temperature
Classical Supergravity on AdS-BH×S5
4dim. Large-Nc strongly coupledSU(Nc) N=4 SYM at finite temperature(in the deconfinement phase).
conjecture
=
Witten ‘98
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.
WL at Zero T (Maldacena 98)
• Euler Lagrangian EQ Solution,
bounded by the loop C, when y goes to infinity, y->1 BH
Wilson-loop at finite temperature
Minimizing the world sheet area (the Nambu-Goto action)
qq r qq r
BH
+_
y
Free energy
Result of pentential
F(r,T)
r
r0
Bound state & Schrődinger equation
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
Dissociation Temperature
Hou, Ren JHEP01 (08)
Holographic potential model with an IR cutoff
Hard Wall : Erlich, Katz, Son, Stephanov
• In the hadronic phase
• In the plasma phase
• 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
• Free energy
Td with deformed metric
AdS/CFT and Lattice
Summary
We calculated dissociation temperatures Td of heavy quarkonium states from holographic potential
The computed Td have remarkable features compariable with that from Lattice
ButN=4 SYM is not real QCD with less stronger screening
q̂