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A prediction from string theory, with strings attached. Hong Liu. Massachusetts Institute of Technology. HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062 , hep-ph/0612168. Qudsia Ejaz, Thomas Faulkner , HL, Krishna Rajagopal, Urs Wiedemann. arXiv:0712.0590 . Plan. - PowerPoint PPT Presentation
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A prediction from string theory,with strings attached
Hong Liu
Massachusetts Institute of Technology
HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062, hep-ph/0612168
Qudsia Ejaz, Thomas Faulkner, HL, Krishna Rajagopal, Urs Wiedemann
arXiv:0712.0590
Plan• Heavy ion collisions and AdS/CFT
• J/ψ suppression
• A prediction from string theory
• Propagation for heavy quark mesons in a hot medium
QCDQCD 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 diagramSmooth crossover
Relativistic Heavy ion collisions
Relativistic heavy ion collisions
Deconfinement crossover in QCD: TC ~ 170 MeV
LHC: Pb + Pb (2009) GeVsNN 500,5
GeVsNN 17SPS (CERN):
RHIC (2000): Au+Au GeVsNN 200
NNs : 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
RH
IC
Quark-gluon fluid of RHIC
RHIC QGP: strongly coupled, nearly ideal fluid (sQGP)
Main theoretical tool for strong coupling: Lattice calculation
But information on dynamical quantities: scarce and indirect
RHIC Experiments revealed many dynamical phenomena:
thermalization, collective flow, jet quenching, J/ψ suppression, ………
Perturbation theory: inadequate
Many new challenges
String theory to the rescue!
AdS/CFT techniques have potential to make important impact !
It is NOT yet known what is the precise string theory description of QCD.
• What are the commonalities and differences of quark-gluon plasmas in different gauge theories?
• Discovery machine: experiments
deeper understanding of both QCD and AdS/CFT
Perturbative Lattice Strongly coupledtheories from AdS/CFTexperiments
AdS/CFT
Heavy ion collisions and AdS/CFTString 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: a prediction for LHC or RHIC
Heavy Quarkonia
Charm:
J/ψ ( ) : BNL and SLAC (1974, November revolution)cc
11))((~ QCDSH dmd
1)( , S HQCDH mm
3.0)( GeV, 3.1 S cc mm
fm 5.0dHeavy quakonia like J/ψ could survive deconfinement transition.
Heavy quarkonia are good probes of QGP
The potential between the quark and anti-quark in a quarkonium bound state is sensitive to the screening of the plasma.
A hallmark of QGP is that it screens color objects.
more unstable
Quarkonium suppression
J/ψ
Heavy ion collisions: color screening in the produced medium
J/ψ suppression Matsui and Satz (1987)
)collisions p pin p of observed J/ of (#NcollisionsAu Au in p of observed J/ of #)(
Tcoll
TJ/
TAA pR
Screening of heavy quarks in the Quark gluon plasma
O.Kaczmarek, F. Karsch, P.Petreczky,F. Zantow, hep-lat/0309121
Heavy quark potential for T > TC
Screening length: TLS /5.0~
Quarkonia above TC
/ (c c)J
(b b)
: Tdiss ~ 2 TC
: Tdiss ~ 3 TC
Asakawa, Hatsuda;Datta, Karsch, Petreczky, Wetzorke
• Dissociation temperature Td
d: size of a meson
Charmonium spectra at different temperatures
Satz, hep-ph/0512217
• Lattice estimate:
)(~ dS TLd
Basic theoretical questions
How does the screening effect depend on the velocity ?
To understand the pT dependence:
Velocity dependence of the dissociation temperature Td ?
Lattice: Hard
Propagation of J/ψ in a QGP.
Not known in QCD
)collisions p pin p of observed J/ of (#NcollisionsAu Au in p of observed J/ of #)(
Tcoll
TJ/
TAA pR
Try to gain insight from string theory by studying relatives of QCD.
Static quark potentialGauge theory description:
gluon flux linesString theory description:
0z
Our (3+1)-dim world,
String lives in one extradimension Gravity approximation: finding
minimal energy string shape
Maldacena; Rey, Yee
Screening of quarks in a QGP
0.277 /SL T
(3+1)-dim world at temperature T,
event horizon
Quarks are screened
Ls
N=4 : , QCD (2 flavor): ~ 0.5 /SL T(lattice)
Rey, Theisen Yee;Brandhuber, Itzhaki, Sonnenschein Yankielowicz ……..
Finite velocity scaling
Finding string shapeof minimal energy
Event horizon
Moving at a finite velocity v
TLL SS
1)v1(~)v1)(0(~v)( 4/124/12
HL,Rajagopal,Wiedemann
Chernicoff, Garcia, Guijosa
Peeters, Sonnenschein, Zamaklar
Dissociation temperature Td :
d: size of a meson
this suggests:
TLL SS
1)v1(~)v1)(0(v)( 4/124/12
)(~ dS TLd
)0()v-(1~v)( 4/12dd TT
Does the scaling apply to QCD?
A simple argument
2 1/ 41
2 4
1 1(v) ~ (1 v ) ~(1 v )
SL TT
In a rest frame of quark pair, the medium is boosted:
44/124
2
2
2
2)v1(~
v11~)0(
v11~v)( TT
4~)0( T
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
Quarkonium suppression:a prediction via string theory
Heavy quark mesons with larger velocity dissociate at a lower temperature
HL,Rajagopal,Wiedemann
This effect may be significant and tested at RHIC II or LHC
Could lead to significant suppression at large PT.
J/psi
)0()v-(1~v)( 4/12dd TT
RHIC has not reached Td for J/ψ.
Quark Matter 2008, Jaipur, India, Feb. 4-10, 2008
28Zebo Tang, USTC/BNL
Nuclear modification factor RAA
• Double the pT range to 10GeV/c
• Consistent with no suppression at high pT: RAA(pT>5 GeV/c) = 0.89±0.20
• Indicates RAA increase from low pT to high pT
• Different from expectation of most models: AdS/CFT:
H. Liu, K. Rajagopal and U.A. Wiedemann, PRL 98, 182301(2007) and hep-ph/0607062 Two Component Approach: X. Zhao and R. Rapp, hep-ph/07122407
Charmonium Spectral functions
( ) ( )2ik k
( )k
Study of genuine quarkonia requires understanding behaviorof spectral functions.
J/ψ : poles in the complex plane.
Velocity effect:
Can AdS/CFT help?
Need genuine mesons.
So far: crude extrapolation from infinite heavy quark potential.
Satz
( )k,
Adding flavors in AdS/CFTKarch,Katz
N=4 SYM theory does contain dynamical quarks.
Add NF hypermultiplets 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.
mq
Mesons: excitations on D7-branes.
small T/mq
Aharony, Fayyazuddin, Maldacena,
Meson masses
Size of a meson:
Bare quark mass: qm
Meson masses: qmM ~
qmMd ~1~
Babington, Erdmenger, Evans, Guralnik, Kirsch; Kruczenski, Mateos, Myers, Winters;
Meson DissociationMateos, Myers and Thomson, Hoyos, Landsteiner, Montero
Gravity approximation: Mesons are stable at low temperature.
Meson dissociation:
We would like to understand how the screening effect is reflected in the meson spectrum.
q
d
mMT ~~
Babington, Erdmenger, Evans, Guralnik, Kirsch
Dispersion relation
, Cv k k
0.88 for 0.65 C dv T T
0.35 for 0.98 C dv T T
V0: speed of lightat the tip
Mateos, Myers and Thomson
In the hot medium, mesons travel at a velocity smaller than the vacuum speed of light !
General results
In the large k limit: (exact analytic result)
v0 is precisely given by the local speed of light at the tip.
Ejaz, Faulkner, HL, Rajagopal, Wiedemann
Embedding of the brane and fluctuations
Embedding of D7-brane:
Action for fluctuations: (scalar mesons)
(can only be solved numerically)
Solving the Laplace equations: discrete spectrum, dispersion relations
Large k limitIn the large k limit, the wave equations for mesons become that of a four-dimensional spherical harmonic oscillator localized near the tip of the brane and thus be solved exactly.
Wave function
Group Velocity
T2
T1
T3
T3 > T2 > T1
maximum
Speed limit at a generic temperature
Stable Mesons
v0(T)
“Td(v)’’
Near Td, v0 (T) 0, for arbitrary large k.
Inference from infinitely heavy quark potential remarkably accurate.
Size of a mesonSemi-classical analysis:
TLS
1)v1(~v)( 4/12
This gives maximal meson size at a given v and T
Td 1)v1(~ 4/12
max
D7-brane story: from IR/UV connection,
Trr
rR
rRd
tiptip
1)v1(~~~ 4/120
0
22
max
why the wave function of a large k meson is localized at tip?
Increasing k, the meson becomes more loosely bounded, and its size should increase, eventually to the maximally possible size allowed by the v0 (T).
From IR/UV connection, its wave function should more and more localized to the tip.
Summary
(Real part) of the dispersions relation and wave function of hologrpahic mesons match very well with (in some sense are controlled by) the screening behavior.
In order to understand the ``dissociation’’, one needs to understand the momentum dependence of the imaginary part of dispersion relation.
HL, Faulkner, in progress
Fast mesons: good probes of the geometry near the horizon
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 Td
All of them are rather qualitative features, which may not depend on the precise details of the underlying theory.
Local speed of light in the bulk
Far from being obvious in perturbation theory !
Is the modified dispersion relation observable?
v>v0
Will J/ψ break apart?
Or will it slow down and survive the medium
What happens when medium disappears?
Time delay?
J/ψ suppression
………………
Conclusion
String theorists have a lot to learn from experiments.
String theorists also have a lot to offer for experiments.
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