Understanding strongly coupled quark-gluon plasma (sQGP)

1
Understanding strongly coupled quark-gluon
plasma (sQGP)

• (SIS program,
• Cambridge, Aug.2007)
• Edward Shuryak
• Stony Brook

2
The emerging theory of sQGP
Quantum mechanics
Stronly coupled cold trapped atoms
Manybody theory
Lattice simulations
Quasiparticles Potentials correlators
Bound states of EQP and MQP J/psi,mesons,baryons,
calorons
Bose-Einstein Condensation -gt confinement
EoS
Flux tubes-gt

• sQGP

RHIC data
Hydrodynamics
Molecular dynamics
Monopoles
Transport properties
Plasma physics
E/M duality
Energy loss, Collective modes Mach cones
AdS/CFT
Gauge theories, SUSY models
String theory
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Outline

• Qs Why do we have strongly coupled quark-gluon
  plasma (sQGP) at RHIC? Is it related to
  deconfinement (T(1-1.5)Tc) or quasi-conformal
  behaviour at Tgt1.5Tc? What is the role of
  magnetic objects? Can one explain RHIC results
  using AdS/CFT? A picture is emerging
• RHIC findings collective flows and jet quenching
• Viscosity and diffusion constant from AdS/CFT,
  complete gravity dual?
• Phase diagram and lattice. Electric and magnetic
  quasiparticles (EQPs and MQPs) are fighting for
  dominance (J.F.Liao,ES, hep-ph/0611131,PRC 07)
  Flux tube existence/dissolution (J.F.Liao,ES,
  0706.4465hep-ph) the magnetic bottle effect
• molecular dynamics (MD) of Non-Abelian plasma
  with monopoles(B.Gelman, I.Zahed,ES,
  PRC74,044908,044909 (2006), J.F.Liao,ES,
  hep-ph/0611131,PRC 07)
• transport summary From RHIC to LHC
• Summary are two explanations related???

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RHIC findings

• Strong radial and elliptic flows are very well
  described by ideal hydro gt perfect liquid
• Strong jet quenching, well beyond pQCD gluon
  radiation rate, same for heavy charm quarks (b
  coming)
• Jets destroyed and their energy goes into
  hydrodynamical conical flow

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From Magdeburg hemispheres (1656) to dreams of
1970s
QCD vacuum is so compicated

• We cannot pump out complicated objects
  populating the QCD vacuum, but we can pump in
  something else, namely the Quark-Gluon Plasma,
  and measure explosion
• (QGP in 1970s was expected to be just a simple
  near-ideal quark-gluon gas, to fill the bag)

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One may have an absolutely correct theory and
stillmake accidental discoveries
Columbus believed if he goes west he should
eventually come to India
But something else was on the way
We believed if we increase the energy density, we
should eventually get weakly interacting QGP.
But something else was found on the way, sQGP
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How Hydrodynamics Works at RHIC
Elliptic flow
How does the system respond to initial spatial
anisotropy?
Dense or dilute? If dense, thermalization? If
thermalized, EoS?
)
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The coolest thing on Earth, T10 nK or 10(-12)
eV can actually produce a Micro-Bang ! (OHara et
al, Duke )
Elliptic flow with ultracold trapped Li6 atoms,
agt infinity regime The system is extremely
dilute, but can be put into a hydro regime, with
an elliptic flow, if it is specially tuned into
a strong coupling regime via the so called
Feshbach resonance Similar mechanism was proposed
(Zahed and myself) for QGP, in which a pair of
quasiparticles is in resonance with their bound
state at the zero binding lines
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2001-2005 hydro describes radial and elliptic
flows for all secondaries , ptlt2GeV,
centralities, rapidities, A (Cu,Au)
Experimentalists were very sceptical but
wereconvinced and near-perfect liquid is now
official, gtAIP declared this to be discovery 1
of 2005 in physics v_2ltcos(2 phi)gt
PHENIX, Nucl-ex/0410003 red lines are for
ESLauretTeaney done before RHIC data, never
changed or fitted, describes SPS data as well! It
does so because of the correct hadronic matter
/freezout via (RQMD)
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One more surprise from RHIC strong jet quenching
and flow of heavy quarks
nucl-ex/0611018
Heavy quark quenching as strong as for light
gluon-q jets! Radiative energy loss only fails
to reproduce v2HF. Heavy quark elliptic flow
v2HF(ptlt2GeV) is about the same as for all
hadrons! gt Small relaxation time t or diffusion
coefficient DHQ inferred for charm.
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Sonic boom from quenched jets Casalderrey,ES,Teane
y, 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

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Two hydro modes can be excited(from our
linearized hydro solution)
a diffuson a sound
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2 Mach cones in strongly coupled plasmas(thanks
to B.Jacak)
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PHENIX jet pair distribution
Note it is only projection of a cone on
phi Note 2 more recent data from STAR find also
a minimum in ltp_t(\phi)gt at 180 degr., with a
value Consistent with background
The most peripheral bin, here no matter
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AdS/CFTfrom gravity in AdS5 to strongly coupled
CFT (N4 SYM) plasma

• what people dream about for LHC
• experments -- a black hole formation --
• does happen, in each and every RHIC AuAu event
  gt
• thermalization, All info is lost except the
  overall entropyarea of newly formed b.h.horizon

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viscosity from AdS/CFT (Polykastro,Son,
Starinets 03)Kubo formula ltTij(x)Tij(y)gtgt

• Left vertical line is our 4d Universe, (x,y are
  on it)
• Temperature is given by position of a horizon
  (vertical line, separationg
• From interier ofblack brane TT(Howking
  radiation) (Witten 98)
• Correlator needed is just a graviton propagator
  G(x,y)
• Blue graviton path does not contribute to Im G,
  but
• the red graviton path (on which it is absorbed)
  does
• Both viscosity and entropy are proportional to
  b.h. horizon, thus such a simple asnwer

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Heavy quark diffusion J.Casalderrey
D.Teaney,hep-ph/0605199,hep-th/0701123
W O R L D
One quark (fisherman) is In our world, The other
(fish) in Antiworld (conj.amplitude) String
connects them and conduct waves in one direction
through the black hole
A N T I W O R L D
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subsonic
supersonic
Left P.Chesler,L.Yaffe Up- from Gubser et
al Both groups made Amasingly
detailed Description of the conical flow from
AdS/CFTgt not much is diffused
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Gravity dual to the whole collision Lund
model in AdS/CFT

• Expanding/cooling fireball departing Black Hole
• (Nastase 03, Sin,ES and Zahed 04,Janik-Peschanski
  05)
• If colliding objects made of heavy quarks
• Stretching strings -- unlike Lund model those are
  falling under the AdS gravity and dont break
  (Lin,ES hep-ph/0610168)
• The falling membrane is created which separate
  two regions of two different metrics it is
  becoming a b.h. horizon
• Now linearized version in progress
• (field from a static Maldacena string recently
  done Lin,ES arXiv0707.3135, T00 -gt1/r7 )

AdS5 Center Extremal b.h.
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AdS/CFT suggests completely new pictures of gauge
theory topology

• Instantons D-1 branepoint in the bulk, at
  large Nc coalesce together (Mattis,Khose,Dorey
  90s)
• Monopoles endpoints of D1 (string-like) branes
• Electric-magnetic duality includes duality
  between baryons and calorons (finite T
  instantons) as Nc monopoles (known before ads lt
  Kraan,van Baal .)

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Explaining transport in sQGPelectric/magnetic
fightClassical QGP and its Molecular Dynamics
Electrons have the same charge -e all the
time, but our quasiparticles (quarks, gluons,)
have colors which is changing in time Fraction
of quasiparticles are magnetically Charged
(monopoles and dyons) which fight each other At
TltTc they somehow (?) make a dual
superconductor gtconfinement.
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An example of dyonic baryonfinite T
instantontop.charge Q1 config.,dyons
identified via fermionic zero modes
Berlin group - Ilgenfritz et al Red, blue and
green U(1) fields 3 dyons with corresp. Field
strengths, SU(3), Each (1,-1,0) charges
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Electric and magnetic scrreningMasses, Nakamura
et al, 2004My arrow shows the self-dual EM
point
MeltMm Magnetic Dominated At T0
magnetic Screening mass Is about 2 GeV (de
Forcrand et al) (a glueball mass) Other data
(Karsch et al) better show how Me Vanishes at Tc
MegtMm Electrric dominated
ME/TO(g) ES 78 MM/TO(g2) Polyakov 79
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New (compactified) phase diagramdescribing an
electric-vs-magnetic competition
Dirac condition (old QED-type units e2alpha,
deliberately no Nc yet)
lt- n2 adjoint
Thus at the eg line
Near deconfinement line g-gt0 in IR (Landaus
U(1) asymptotic freedom) gt e-strong-coupling
because g in weak!
Why is this diagram better? gt There are e-flux
tubes in all blue region, not only in the
confined phase! In fact, they are maximally
enhanced at Tc
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Energy and entropy associated with 2 static
quarksis very large near Tc from lattice
potntials Bielefeld-BNL
pQCD predicts a negative U

• R-gtinfinity means there are 2 separate objects
• Entropy20 implies exp(20) states
• At R(.3-1.2)fm both are about linear in R lt
• What object is that?

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Energy and entropy associated with 2 static
quarksis very large near Tc from lattice
potntials Bielefeld-BNL
pQCD predicts a negative U

• R-gtinfinity means there are 2 separate objects
• Entropy20 implies exp(20) states
• At R(.3-1.2)fm both are about linear in R lt
• What object is that?

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e-flux tubes above Tc?(with J.F.Liao, archive
0706.4465 hep-ph)

• Dual superconductivity at TltTc as a confinement
  mechanism (tHooft, Mandelstam 1980s) gt
  monopole Bose condensation gt
  electric flux tubes (dual to
  Abrikosov-Nielsson-Olesen vortices)
• Can uncondenced MQPs do the same at TgtTc ? MQPs
  are reflected from a region with E field gt
  pressure gt flux tubes compression in plasma
• We solve quantum mechanics of motion in each
  partial wave

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magnetic flux tubes at the Sun,(work without any
superconductor!) so we need to work out the
exact conditions

• where classical electrons rotate around it
• B about 1 kG,
• Lifetime few months

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Classical and quantum mechanics of the flux tube
Red trajectory A gt nu0 (velocity at large r
directed to the center) Black one B gt m0 (which
goes through the center because no m2/r2
barrier)
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Self-consistent solution gt stability condition
of the flux tube
Zexp(-mu/T)
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dissolution of the tube roughly at
Tgt1.4Tc(lattice Bielefeld-BNL)

• Assuming this is the case and using our criterion
  we get density of magnetic QPsgt
• n(magnetic,T1.3Tc)(4-6)fm-3
• Twice less than about 10 fm-3 at T0 (Bali et
  al, from vacuum confining strings)

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Is sQGP full of flux tubes? evolution with
T

• T0, dual Meissner gtANO
• At TltTc complicated shape can produce
  entropyo(L) but it is Nc independent gt no
  electric objects, no color changed
• At TgtTc heavy gluon (and quark) quasiparticles
  first appear as beads S(L/a)log7(L/b)lo
  g(Nc)
• As T grows further gt less monopoles of higher
  energy gt no electric field flux suppression
  gtelectric polymers
• Very high T gt wQGP, electric plasma, no bound
  states

(Presumably gluons-in-the-tube correspond to
AdS/CFT Minahan string solutions and are also
dual to monopoles-in-the-tube solutions
recently Worked out by Tong et al,Shifman et al)
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Bose-Einstein condensation of interacting
particles (monopoles) (with M.Cristoforetti,Tren
to)

• Feynman theory (for liquid He4) polygon jumps
  BEC if exp(-?S(jump))gt.16 or so (1/Nnaighbours)

• We calculated instantons for particles jumping
  paths in a liquid and
• solid He4 incuding realistic atomic potentials
  and understood 2 known effects
• Why Tc grows with repulsive interactionlt because
  a jump proceeds faster under the barrier
• (ii) no supersolid He gt density too large and
  action above critical
• Marco is doing Path Integral simulations with
  permutations numerically, to refine conditions
  when BEC transitions take place

Jumping paths Feynman, interacting
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BEC (confinement) condition for monopoles

• For charged Bose gas (monopoles) the action for
  the jump can be calculated similarly, but
  relativistically jumps in space d and in time
• Comparable)
• ?SM sqrt(d2(1/Tc)2) ?S(interaction) Sc
  1.65-1.89
• (first value from Einstein ideal gas, second from
  liquid He)
• provides the monopole mass M at Tc
• M Tc approx 1.5 gt
• M as low as 300 MeV

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Strong coupling in plasma physics Gamma
ltEpotgt/ltEkingt gtgt1gas gt liquid gt solid

• This is of course for /- Abelian charges,
• But green and anti-green quarks do the
  same!

• local order would be preserved in a liquid also,
• as it is in molten solts (strongly coupled TCP
  with
• ltpotgt/ltkingtO(60), about 3-10 in sQGP)

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Wong eqn can be rewritten as x-p canonical
pairs, 1 pair for SU(2), 3 for SU(3), etc.
known as Darboux variables. We did SU(2) color
gt Q is a unit vector on O(3)
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Gelman,ES,Zahed,nucl-th/0601029
With a non-Abelian color gt Wong eqn
Gas, liquid
solid
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So why is such plasma a good liquid? Because of
magnetic-bottle trapping static eDipoleMPS
Note that Lorentz force is O(v)!

E
M
V
E-
-
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We found that two charges play ping-pong by a
monopole without even moving!
Chaotic, regular and escape trajectories for a
monopole, all different in initial condition by
1/1000 only!

• Dual to Budkers
• magnetic bottle

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MD simulation for plasma with monopoles (Liao,ES
hep-ph/0611131) monopole admixture M5050
etcagain diffusion decreases indefinitely,
viscosity does not
It matters 50-50 mixture makes the best liquid,
as it creates maximal confusion
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short transport summary log(inverse viscosity
s/eta)- vs. log(inverse heavy q diffusion const
D2piT) (avoids messy discussion of couplings)
-gtStronger coupled -gt
Most perfect liquid

• RHIC data very small viscosity and D
• vs theory - AdS/CFT and MD(soon to be explained)

4pi
MD results, with specified monopole fraction
Weak coupling end gt (Perturbative results shown
here) Both related to mean free path
50-50 E/M is the most ideal liquid
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From RHIC to LHC(no answers, only 1bn
questions)

• Will perfect liquid be still there?
• Is jet quenching as strong, especially for c,b
  quark jets and much larger pt?
• Is matter response (conical flow at Mach angle)
  similar? (This is most sensitive to viscosity)

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From SPS to LHC

• lifetime of QGP phase nearly doubles, but v2
  grows only a little, to a universal value
  corresponding to EoS p(1/3)epsilon
• radial flow grows by about 20 gt less mixed /
  hadronic phase (only 33 increase in collision
  numbers of hadronic phase in spite of larger
  multiplicity)

(hydro above from S.Bass)
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Conclusions

• RHIC data on transport (eta,D), ADS/CFT and
  classical MD all qualitatively agree !
• Are these two pictures related?

• Good liquid because of magnetic-bottle trapping
• Classical MD is being done, lowest viscosity for
  50-50 electric/magnetic plasma
• AdS/CFT gt natural applications of string theory
• N4 SYM is nonconfining and
• Strongly coupled!

• Strongly coupled QGP is produced at RHIC
  T(1-2)Tc
• This is the region where transition from
  magnetic to electric dominance happen
• at Tlt1.4 Tc still Lots of magnetic objects gt
• E-flux tubes

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reserve
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Effective coupling is large! alphasO(1/2-1) (not
lt0.3 as in pQCD applications)tHooft
lambdag2Nc4piNcO(20)gtgt1-1
Bielefeld-BNL lattice group Karsch et al
48

• At em line both effective gluons and monopoles
  have masses M about 3T exp(-3)ltlt1 is our
  classical parameter
• (Boltzmann statistics is good enough)
• At TTc monopoles presumably go into
  Bose-Einsetein condensation gt new semiclassical
  theory of it for strongly interacting Bose gases,
  tested on He4
• (M.Cristoforetti, ES, in progress)