Transcript Toward the theory of strongly coupled Quark

Transport properties of
strongly coupled Quark-Gluon
Plasma (sQGP)
Edward Shuryak
Department of Physics and Astronomy
State University of New York
Stony Brook NY 11794 USA

Two types of transport
particles <=> momentum
(diffusion <=> viscosity)
 x^2  (1/6)D
In gases both are proportional to the same collision cross section, but
as coupling strength goes up
 U  /T in MD,   g^2Nc
Diffusion constant indefinitely
decreases <=
Particles ``get stuck”

and cannot move
Related to drag force
By Einstein relation
Dp/dx \sim 1/D
inAdS/CFT
Viscosity only decreases for a while,
And then other means of momentum
Trasfer -- via collective modes -- appears
viscosity is again large
And
in glasses and solids at very strong coupling
Viscosity-diffusion summary plot
^
Better
liquid
AdS/CFT
eta/s: Kovtun,Son,
Starinets,hep-th/0405231
Dc:Casalderrey, Teaney,
PRD 74,085012 (06)
Colored lines:
Classical MD for a strongly
Coupled plasma with
Monopoles:
Liao,ES hep-ph/0611131,v2
(and this fig, is from its)
wCFT:
eta:Huot et al hep-ph/0608062
Dc:Chesler and Vuirinen hepph/0607148
==> particle gets less mobile
Plasma coupled stronger
Why do we think that QGP is strongly
coupled at RHIC?
I-RHIC phenomenology
• 1a: hydro works => viscosity is very low:
eta/s=.1-.2 << 1 (Teaney,ES)
• 1b: Because parton cascade requires huge cross
sections >> (pQCD predictions) (Molnar-Gyulassy)
(a comment: they are not the same => a cascade makes no sense in a strongly
coupled regime, while hydro only works better)
• 1c: charm diffusion: Dc << pQCD predicts
(from R_AA and v2 of electrons at RHIC <= Moore+Teaney)
• 1d: very strong jet quenching, including charm, again
well beyond pQCD predictions
• 1e: conical flow from quenched jets in Mach direction
(Casalderrey-Teaney –ES) seem to be observed
Sonic boom from quenched jets
Casalderrey,ES,Teaney, hep-ph/0410067; H.Stocker…
• the energy deposited by
jets into liquid-like
strongly coupled QGP
must go into conical
shock waves
• We solved relativistic
hydrodynamics and got
the flow picture
• If there are start and
end points, there are
two spheres and a cone
tangent to both
Wake effect or “sonic boom”
PHENIX jet pair distribution
Note: it is only
projection of a
cone to asymuth
Note 2: more
recent data on 3body
correlators,
from both
STAR/PHENIX
are consistent
with conical
flow , not a
deflected jet
Why do we think that QGP is strongly
coupled at RHIC?
II-lattice+QM
• 2a: ``New spectroscopy”: Interaction is strong enough
to make multiple bound states (ES+Zahed, 03), s-wave
n=1mesons, colored pairs like qg or non-singlet gg
• 2b: Marginal states with small binding may lead to small
m.f.p. <= (ES+Zahed, 03) a la Feshbach resonances
for ultracold trapped atoms –charmed (Rapp, van Hees)
• 2c: Baryons seem to survive till about 1.6Tc (Liao,ES)
• 2d: large energy (up to 4 GeV) and entropy (up to 20)
of a heavy dipole around Tc (Karsch et al,04) remains a
mystery: huge number of states, many quasiparticles?
Protostrings =>Polymeric “electric” chains of gluons
barQ - g - g … Q (Liao,ES)
Why do we think that QGP is strongly coupled at RHIC?
III: AdS/CFT
N=4 SUSY YM theory at strong coupling at finite T  sQGP at RHIC
• 3a: p,e=O( N^2 T^4)
even the famous
coefficient .8 is better reproduced by the large-g (Klebanov…96) series (3/4+…)
• 3b: viscosity is small: eta/s=1/4pi (Son et al,04)
• 3c:Heavy quark drag and diffusion constant are OK
(Yaffe et al, Casalderrey-Teaney) and conical flow is seen
(Gubser et al)
a complete gravity dual to RHIC
collisions => departing black hole/
horizon=>ES,Sin+Zahed, Janik-Peschanski, Gubser…
• 3e: quasiparticles are heavy M*=sqrt(lambda)T>>T and have
• 3d:
huge number of bound states
Why do we think that QGP is strongly coupled at RHIC?
IV-Electric/Magnetic duality
• N=2 SUSY YM (``Seiberg-Witten theory”) is a working
example of confinement due to condenced monopoles
• It teached us that monopoles must be very light and
weakly interacting (in IR) near the critical point
• This + Dirac condition => [(e g)/hbar c=1/2] =>
electric coupling must be large there
• e/m equilibrium at (1.2-1.5)Tc: gluons and monopoles
have comparable masses and couplings =>
• New picture: sQGP is a plasma of fighting
electric and magnetic quasiparticles
New (compactified) phase diagram
describing an electric-vs-magnetic fight
Dirac condition
Thus at the e=g line
Near deconfinement line g->0 in IR
(Landau’s U(1) asymptotic freedom)
=>
e-strong-coupling
Why this diagram is better? => in all blue region
There are e-flux tubes, not only in the confined phase!
In fact, they are maximally enhanced at Tc, not below it.
Entropy (and energy) associated with
a static dipole gets huge at Tc
(shown at large r only vs T/Tc )
•#(states) =exp(S)=e^16
What those states may be?
• string picture provides
the answer
(Polyakov 78 =>
Klebanov,Maldacena,Thorn et al
hep-
th/0602255)
• EQP language: electric
polymers (Liao,ES hep-ph/0508035 Ads/CFT
Minahan 98)
Kaczmarec et al hep-lat/0510094
are there e-flux tubes in QGP?
• Dual superconductivity as a confinement
mechanism (‘tHooft, Mandelstam 1980’s) =>
monopole condensation at T<Tc explains it =>
Meissner effect confines electric fluxes (dual to
Abrikosov vortices)
• But at T>Tc (uncondenced) MQPs do the
same! Due to Lorentz force they are reflected
from a region with E field => compressing
into flux tubes, even in classical
plasma!
E
magnetic flux tubes at the Sun,
(work without any superconductor!)
where classical electrons rotate
around it
• B: about 1 kG,
• Lifetime: few months
Electric and magnetic screening masses
E/M equilibrium
Dual Superconductor model
works well
• vacuum with monopole condensate
• flux tube as Abrikosov vortex
• Seiberg-Witten, a working example
E dominated
Mdomi
nated
A. Nakamura, et al, PRD69(2004)014506
G. S. Bali, hep-ph/9809351
Approaching Tc from above:
• E-screening mass decrease
 less E-charge
 E-charge getting heavier
• M-screening mass increase
 more M-charge
 M-charge getting lighter
Classical strongly coupled plasmas
As Gamma= <|Epot|>/<Ekin> grows
gas => liquid => solid
Gelman,ES,Z
ahed,nuclth/0601029
With a non-Abelian color
=> Wong eqn
Gas,
liquid
solid
MD simulation for plasma with monopoles
(Liao,ES hep-ph/0611131)
monopole admixture matters: 50-50 mixture makes the best liquid
diffusion decreases indefinitely, viscosity does not
(1000 particles in a stable spherical drop)
D 1/^( 0.6  0.8)

Diffusion can be stopped
A flurry of recent papers on heavy
quark dynamics in N=4 plasma
• HKKKY hep-th/0605158
• J.Casalderrey and
D.Teaney hep-ph/0605199
diffusion constant for heavy
quark
• Agree nicely via
Einstein relation (very
nontrivial in string
setting)
• Qualitatively agree
with classical MD
results!
dp / dt  (T ^2  / 2)v / 1  v^2
D  2 / T   Dp  1/ 4
Now we compare Dc to weak
and strong coupling predictions
1/DT  
==>
Range from MD
With different
EQPs/MQPs ratio

==>
Strong:
not very
Diferent from MD
D 1/^( 0.6  0.8)
The cross is
phenomenological
range
added by me, following
Moore-Teaney R_AA,
v2
Weak coupling

Chester and Vuorinen,
Hep-ph/0607148
Floating matter destribution
Friess et al, 0607022
Subsonic emission => no cone
(as in b-tagged jets – Antinori,ES, nucl-th/0507046)
subsonic
Supersonic
Note how
angle
moves as
v->cs
Short history of developing
``gravity dual” for RHIC
from basically 5dim GR
• AdS+Black Hole: Hawking radiation from the
horizon is used to mimic non-zero T (Witten,98)
• receeding BH/horizon from collapsing matter
=>cooling+expansion (ES,Sin,Zahed,05)
• Stretching black hole => Large-time solution
(Janik-Peschanski,05) reproduces Bjorken hydro, even with viscosity
(Nakamura+Sin,06,Janik 06)
• Falling objects produced in a collision form a
membrane falling under its own weight =>
(Shu Lin and ES,hep-ph/0610168) <= Israel’s junction cond.1966
•
nov.06 Gubser et al Departing point black hole solution
=> spherically expoding fireballl
  t^2  x^2
AdS5 center
(Shu Lin and ES,hep-ph/0610168)

departing 2 heavy ultrarelativistic quarks
stretch a longitudinal string
5-dim Pythia model in which strings don’t break
But fall instead into the 5th dimension
y  (1/2)log[( t  x) /(t  x)]

z( , y)  g(y)
Scaling solution
(used in
Euclidean appl. By Gross et al,

AdS5 center
is only stable if
Y<.27 and exist if Y<.5
Makeenko)
The non-scaling solution
approach rectangular shape,
small fragmentation region
and rapidity-independent bulk
All objects – massless, massive close strings, open strings =>
fall
in AdS and form a massive membrane because they tend to
the same trajectory at large time
=> Observer at z=0 (r=infty) sees induced Tmn with hydro flow
Strething black hole has approximately
conserved horizon area => entropy
Old AdS metric
New metric, JP
at late time
(I disagree with
Janik on singularity issue)

z(horison )   ^(1/ 3)

Conclusions
Strongly
coupled QGP
has been
produced at
RHIC
 robust
collective
flows, even
for charm
 Strong jet
quenching
leading to robust
conical flow,

now supported by 3body correlators
at (1-1.4)Tc
dominated by
magnetic QPs

postconfinement
with e-flux tubes 
•Classical MD
is being done,
smaller
viscosity due
to monopoles
AdS/CFT =>
strongly coupled
conformal regime
not too close to Tc
Heavy quark
diffusion and
quenching in the
right ballpark
conical flow seen
hydro explosion can
be derived from GR
=>
Collapsing membrane,
bh formation
