Understanding the Quark-Gluon Plasma via String Theory

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Understanding the Quark-Gluon Plasmavia String
Theory

• Hong Liu

Massachusetts Institute of Technology
HL, Krishna Rajagopal, Urs A. Wiedemann
hep-ph/0605178, hep-ph/0607062, hep-ph/0612168
Qudsia Ejaz, Thomas Faulkner, HL, Krishna
Rajagopal, Urs Wiedemann
to appear
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Plan

• Heavy ion collisions

• Shear viscosity (a quick overview)

• Jet quenching

• J/? suppression a prediction

• N4 SYM v.s. QCD

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Quark-Gluon Plasma
At room temperature, quarks and gluons are
always confined inside colorless objects
(hadrons)
protons, neutrons, pions, ..
Very high temperature (asymptotic freedom)
? Interactions become weak
? quarks and gluons deconfined
? Quark-gluon plasma (QGP)
Infinitely high temperature QGP
behaves like an ideal gas.
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Is there a deconfinement phase transition
separating the hadronic and QGP phases?
Can one create quark-gluon plasma in the lab?
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QCD Phase diagram (2006)
Smooth crossover at
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Relativistic Heavy ion collisions
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Relativistic Heavy Ion Collider (RHIC)

• RHIC AuAu

center of mass energy per pair of nucleons
Au 197 nucleons Total 39.4 TeV

• Energy density (peak)
• gt 5 GeV/fm3

• Temperature (peak)
• 300 MeV

LHC Pb Pb (2009)
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Creating a little Big Bang
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Experimental probes of the QGP ?
Some basic questions
Has the created hot matter reached thermal
equilibrium? If yes, when?
Has the QGP been formed?
What are its signatures?
Properties weakly or strongly coupled?
equation of state? Viscosity? opacity?
QGP at RHIC exists for about 10-23 sec (5 fm),
making it impossible to study it using any
external probes.
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Quark-gluon fluid of RHIC

• Collective behavior of the observed
  final-state hadrons
• (elliptic
  flow)

• Interaction of produced hard probes with the
  medium
• (jet quenching, J/?
  suppression)

Nearly ideal, strongly coupled fluid (sQGP)
Main theoretical tool for strong coupling
Lattice calculation
But information on dynamical quantities scarce
and indirect
New theoretical tools are needed!
But information on dynamical quantities scarce
and indirect
New theoretical tools are needed.
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String theory to the rescue!
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Collective motion and shear viscosity of sQGP
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Collective motion
If lots of pp collisions plus free streaming
final state momenta uniformly distributed in
azimuth angle .
If interaction ? equilibration ? pressure ?
pressure gradients ?collective motion

• anisotropy of momenta distribution in .

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Near-perfect fluid discovered

• Elliptic flow

Strong signal !
Created hot matter equilibrates very early
before 1fm.
likely strongly interacting !
Shear viscosity should be small!
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Universality of Shear viscosity

• RHIC

Teaney (2003)

• Water

• N4 SYM

Policastro, Son, and Starinets (2001)

• The value turned out to be
  universal for all
• strongly coupled QGPs with a gravity description.

Kovton, Son and Starinets (2003) Buchel, J. Liu

• Lattice

Meyer (2007)
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AdS/CFT and Jet quenching
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Hard probes
Hard scatterings in pp collisions produce
back-to-back high energy quarks ("jets).
The presence of hot matter modifies the
properties of jets.
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Jet Quenching

• The number of high energy
• particles observed should be
• much smaller than expected
• from pp collisions

Only 20 !
2. monojets sometimes they never make
out.
QGP
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Parton energy loss in QGP
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Toward understanding Opacity
Experimental estimate
Hadronic gas
Perturbation theory
Strongly coupled QGP?
Theoretical challenge non-perturbative
calculation of for QCD QGP slightly above
TC .
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Strategy

• Need a non-perturbative definition of
• Compute in SYM theory using AdS/CFT

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a non-perturbative formulation
Hard weakly coupled
Soft likely strongly coupled
Assume E gtgt ? gtgt k- gtgtT
multiple rescatterings of hard particles with
the medium
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Soft scatterings
Zakharov (1997) Wiedemann (2000)

• Amplitude for a particle propagating in the
  medium

Soft scatterings are captured by Light like
Wilson lines.
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A non-perturbative definition of
Wiedemann HL, Rajagopal, Wiedemann
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Wilson loop from AdS/CFT
Maldacena (1998) Rey and Yee (1998)
Recipe
area of string worldsheet with boundary C
horizon

• Black hole in AdS spacetime
• radial coordinate r,
• horizon rr0
• constant r surface (31)-dim Minkowski spacetime

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Extremal configuration
rr0
rr0
extremal string configuration string
touches the horizon.
two disjoint strings
Interactions between the quark and the medium
Interaction of the string with the horizon of a
black hole.
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Wilson loop
With
The corresponding BDMPS transport coefficient
reads
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of N4 SYM theory
BDMPS transport coefficient reads

• It is not proportional to number of scattering
  centers

• Experimental estimates 5-15 GeV2/fm

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and number of degrees of freedom

• General conformal field theories (CFT) with a
  gravity dual (large N and strong coupling)

HL,Rajagopal Wiedemann,
sCFT entropy density
For non-conformal theories, it may decrease with
RG flow.
an estimate for QCD
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Summary

• In QGP of QCD, the energy loss of a high energy
  parton can be described perturbatively up to a
  non-perturbative jet-quenching parameter.
• We calculate the parameter in N4 SYM (not
  necessarily full energy loss of SYM)
• It appears to be close to the experimental value.

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Quarkonium suppression a prediction for
LHC or RHIC II
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Heavy quarkonium in a QGP
Above TC, light-quark mesons no longer exist due
to deconfinement.
Heavy quarkonia are bound by short-distance
Coulomb interaction may still exist above TC .
In a QGP, interactions between a quark and an
anti-quark are screened by the plasma. A heavy
quark meson will dissociate when the screening
length becomes of order the bound state size.
Tdiss 2.1 TC
Tdiss 3.6 TC
while their excited states already dissociate
above 1.2 TC.
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Quarkonium suppression
J/?
Quarkonium suppression is a sensitive probe of
QGP.
Matsui and Satz (1987)
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Connecting lattice QCD directly to heavy ion
phenomenology is difficult
Heavy quark mesons produced in heavy ion
collisions could move very fast relative to the
hot medium
How does the screening effect depend on the
velocity?
Velocity dependence of the Tdiss ?
(not known in QCD)
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Static quark potential in N4 SYM
Maldacena Rey, Yee Rey, Theisen
Yee Brandhuber, Itzhaki, Sonnenschein
Yankielowicz ..
probe brane
Ls
Finding string shape of minimal energy
event horizon
quarks are screened
In the large NC and large
limit
quark potential energy of open string
connecting the pair
,
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Quark potential at finite velocity
HL, Rajagopal Wiedemann
Moving at a finite velocity v
Finding string shape of minimal energy
Event horizon
In a rest frame of quark pair, the medium is
boosted
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Velocity dependence of dissociation temperature
Dissociation temperature Td
d size of a meson
Given
this suggests
What would happen if QCD also has similar
velocity scaling?
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Has RHIC reached Td for J/? ?
Lattice J/? may survive up to 2TC
Similarity of the magnitude of J/?
suppression at RHIC and SPS
Karsch, Kharzeev, Satz,
RHIC has not reached Tdiss for J/?.
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Quarkonium suppressiona prediction via string
theory
HL,Rajagopal,Wiedemann
Heavy quark mesons with larger velocity
dissociate at a lower temperature.
Expect significant suppression at large PT.
J/psi
This effect may be significant and tested at
RHIC II or LHC
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Data to come
RHIC low statistics on J/? with 2 lt PT lt 5 GeV,
no data for PTgt 5GeV
Reach in PT will extend to 10 GeV in coming
years at RHIC.
LHC will reach even wider range.
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N4 SYM versus QCD
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N4 SYM versus QCD
N4 SYM theory

• Conformal
• no asymptotic freedom,
• no confinement
• supersymmetric
• no chiral condensate
• no dynamical quarks, 6 scalar and 4 Weyl
  fermionic fields in the adjoint representation.

Physics near vacuum and at very high energy is
very different from that of QCD
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N4 SYM versus QCD (continued)
N4 SYM at finite T
QCD at T TC -3 TC

• conformal
• no asymptotic freedom,
• no confinement
• supersymmetric (badly broken )
• no chiral condensate
• no dynamical quarks, 6 scalars and 4 fermions in
  the adjoint representation.

• near conformal (lattice)
• not intrinsic properties of sQGP
• not present
• not present
• may be taken care of by proper normalization

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N4 SYM versus QCD
Ideal gas (T infinity QCD)
Strongly coupled N4 SYM at finite T
T0 QCD confinement
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N4 SYM versus QCD

• It is likely that QCD has a string dual in the
  large N limit.
• Finite-T QCD in a strongly coupled regime could
  be described
• by a black hole in this string theory.

• Universality of black hole (horizon physics)

Universality between QCD and N4 SYM for
observables probing intrinsic properties of the
medium.
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Summary

• String theory techniques provide qualitative,
  and
• semi-quantitative insights and predictions
  regarding
• properties of strongly interacting quark-gluon
  plasma

• Shear viscosity

• Jet quenching parameter

(a prediction)

• Quarkonium suppression

• Expect many more chapters to be written for
  the marriage
• between string theory and physics of QCD in
  extreme
• conditions.

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Energy and entropy density
Karschhep-lat/0106019
QCD
Gubser, Klebanov,Peet (1998)
N4 SYM
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Speed of sound
Karsch, hep-ph/0610024
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Jet quenching monojet phenomenon
STAR collaboration nucl-ex/0501009
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Jet quenching data (II)
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