the strongly coupled quark-gluon plasma edward shuryak department of physics and astronomy state...
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The The strongly coupled strongly coupled Quark-Gluon PlasmaQuark-Gluon Plasma
Edward ShuryakEdward ShuryakDepartment of Physics and AstronomyDepartment of Physics and Astronomy
State University of New YorkState University of New York
Stony Brook NY 11794 USAStony Brook NY 11794 USA
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Outline: Outline: The Little Bang, not a firework of minijetsThe Little Bang, not a firework of minijets Collective flows: radial and elliptic, Collective flows: radial and elliptic,
systematics: => systematics: => viscosityviscosity Where the energy of jets go? A ``sonic Where the energy of jets go? A ``sonic
boom” boom” What does the ``strong coupling” mean?What does the ``strong coupling” mean? Quasiparticles and Potentials at T>TcQuasiparticles and Potentials at T>Tc The phase diagram and few puzzlesThe phase diagram and few puzzles Hadronic bound states at T>TcHadronic bound states at T>Tc ColoredColored bound state and EoS bound state and EoS Strongly coupled atomsStrongly coupled atoms Strongly coupled N=4 SUSY YM and Strongly coupled N=4 SUSY YM and
AdS/CFT correspondenceAdS/CFT correspondence
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The Big vs the Little The Big vs the Little BangBang Big Bang is an Big Bang is an
explosion which explosion which created our Universe. created our Universe.
Entropy is conserved.Entropy is conserved. Hubble law v=Hr forHubble law v=Hr for distant galaxies. H is distant galaxies. H is
isotropic. isotropic. ““Dark energy”Dark energy”
(cosmological (cosmological constant) seems to constant) seems to lead to accelerated lead to accelerated expansionexpansion
Little Bang is an Little Bang is an explosionexplosion
of a small fireball of a small fireball created in created in high energy high energy collisioncollision of two nuclei. of two nuclei.
Also entropy is well Also entropy is well conservedconserved
Hubble law, but Hubble law, but anisotropic (see below)anisotropic (see below)
The ``The ``vacuum vacuum pressurepressure” works against ” works against expansionexpansion
(And that is why it was (And that is why it was soso
difficult to produce it)difficult to produce it)
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The vacuum vs the The vacuum vs the QGPQGP The vacuum is very The vacuum is very
complicated, dominated complicated, dominated by ``topological by ``topological objects”objects”
Vortices, monopolesVortices, monopoles and and instantonsinstantons
Among other changes it Among other changes it shifts its energy shifts its energy downdown compared to ancompared to an
““empty” vacuum, known empty” vacuum, known asas
The Bag terms, The Bag terms, p=#T^4-Bp=#T^4-BEpsilon=#T^4+BEpsilon=#T^4+B
The QGP, as any The QGP, as any plasma, screens them, plasma, screens them, and is nearly free from and is nearly free from themthem
So, when QGP is So, when QGP is produced, produced, the vacuum the vacuum tries to expel ittries to expel it
(recall here pumped out (recall here pumped out Magdeburg Magdeburg hemisphereshemispheres
By von Guericke in 1656 By von Guericke in 1656 we learned at school)we learned at school)
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Magdeburg hemispheres 1656
We cannot pump the QCD vacuum out, but we can pump in something else, namely the Quark-Gluon Plasma
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The map: the QCD Phase The map: the QCD Phase DiagramDiagram
T
The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland)
Chemical potential mu
Theory prediction (numerical calculation, lattice QCD, Karsch et al) the pressure as a function of T (normalized to that for free quarks and gluons)
p= #T^4 – B, the vacuum pressure
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Collective flows: bits Collective flows: bits of historyof history
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Early days
• L.D.Landau, 1953 => first use of hydrodynamics• L.D.Landau, S.Z.Belenky 1954 Uspechi => compression shocks => resonance gas (Delta just discovered)• G.A.Milekhin 1958 => first numerical solution for the
transverse flow
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My hydro
• Hydro for e+e- as a spherical explosion PLB 34 (1971) 509
=> killed by 1976 discovery of jets in e+e-• Looking for transverse flow at ISR,
ES+Zhirov, PLB (1979) 253 =>Killed by apparent absence of flow in pp ES+Hung, prc57 (1998) 1891, radial flow
at SPS with correct freezeout surface, Tf vs centrality dependence predicted
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QM99 predictions for v2(with D.Teaney)
RQMD
HIJING
Our hydro/cascade
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Main findings at RHICMain findings at RHIC
Partciles are produced from matter which Partciles are produced from matter which seems to be seems to be well equilibratedwell equilibrated (by the time it is (by the time it is back in hadronic phase), N1/N2 =exp(-(M_1-back in hadronic phase), N1/N2 =exp(-(M_1-M_2)/T)M_2)/T)
Very robust Very robust collective flowscollective flows were found, were found,
indicating very strongly coupled Quark-Gluon indicating very strongly coupled Quark-Gluon Plasma Plasma (sQGP)(sQGP)
Strong quenching of large pt jetsStrong quenching of large pt jets: they do : they do not fly away freely but are mostly (up to 90%) not fly away freely but are mostly (up to 90%)
absorbed by the matter. The deposited energy absorbed by the matter. The deposited energy seemseem
To go into To go into hydrodynamical motion (conical flow) hydrodynamical motion (conical flow)
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TμTμ
Tμ/2
/)(
/)(
ee
e
p
pE
E
ReminderReminderStatistical Model Statistical Model
Works well with just two parametersWorks well with just two parameters
ReminderReminderStatistical Model Statistical Model
Works well with just two parametersWorks well with just two parameters
Hadro-chemistry seems to be all done at the critical lineHadro-chemistry seems to be all done at the critical line
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Hydrodynamics is simple Hydrodynamics is simple and very predictive, but and very predictive, but one has to understand few one has to understand few things,things,and so not all hydros are and so not all hydros are the samethe same EoS from Lattice QCD
Dynamic Phenomena •Expansion, Flow•Space-time evolution of thermodynamic variables
Caveat: Why and when the equilibration takes place is a tough question to answer
Local Energy-momentum
conservation:Conserved number:
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Thinking About EoSThe Latent Heat and the ``softest point”
(Hung, ES 1995)
4T
T
T
4T
P
partonichadronic
LH T
P
0.2
0.33
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Understanding of the freezeouts(which some hydro groups forgot)
• Chemical freezeout at Tch means that atT<Tch hadronic matter is indeed chemically
frozen => different EoS with nonzero mu’s• Kinetic freezout at fixed Tf is wrong: the
larger systems cool to LOWER Tf, one has to calculate the freezeout surface (Hung,ES) or use afterburner (RQMD) (Teaney, ES)
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hydro describes both radial and elliptic hydro describes both radial and elliptic
flowsflows (from Phenix) v_2=<cos(2 phi)>(from Phenix) v_2=<cos(2 phi)>proton pion
Hydro models:Teaney(w/ & w/oRQMD)
Hirano(3d)
Kolb
Huovinen(w/& w/oQGP)
nucl-ex/0410003
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V2 systematics:V2 systematics:it depends on many variablesit depends on many variables
• Particle type => y_t^2 m scalingParticle type => y_t^2 m scaling
• Collision energy s –dependenceCollision energy s –dependence
• (pseudo) rapidity (eta) y-dependence(pseudo) rapidity (eta) y-dependence
• Pt: rapid growth with saturationPt: rapid growth with saturation
• Centrality => v2/s2 scalingCentrality => v2/s2 scaling
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A Hydrodynamic A Hydrodynamic Description of Heavy Ion Description of Heavy Ion Collisions at the SPS and Collisions at the SPS and RHICRHICD. Teaney,D. Teaney, J. Lauret,J. Lauret, and and E.V. ShuryakE.V. Shuryaknucl-th/0110037 v2 6 Dec nucl-th/0110037 v2 6 Dec 20012001
The dependence on The dependence on dN/dydN/dyhas a growing trend, with has a growing trend, with a saturationa saturation
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More on Elliptic FlowMore on Elliptic Flow
See recent reviews, P.Huovinen (QM2002) , nucl-th/0305064; P.Kolb and U.Heinz, nucl-th/0305084; E.Shuryak, hep-ph/0312227
Hydro: P.Kolb et al.(’99)(Note: Hydro+RQMD
gives a better description.D.Teaney et al.(’01))
STAR, PRC66(’02)034904
Hydro: P.Huovinen et al.(’01)
PHENIX, PRL91(’03)182301.
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The (pseudo)rapidity distribution of v2 (from PHOBOS) is not the same as that
of the particles
v2 vs eta PHOBOS
0
0.01
0.02
0.03
0.04
0.05
0.06
-6 -4 -2 0 2 4 6
eta
v2
19.6 GeV
62.4 GeV
130 GeV
200 GeV
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Particle distribution over Particle distribution over (pseudo) rapidity(pseudo) rapidity
• Number of charged particles Number of charged particles per unit of pseudorapidityper unit of pseudorapidity
200 GeV Au-Au PHOBOS
0
100
200
300
400
500
600
700
-6 -4 -2 0 2 4 6
eta
dN
/d_
eta
: 0 to 6 %
: 6 to 15 %
: 15 to 25
: 25 to 35
: 35 to 45
130 GeV AU-AU PHOBOS
0
100
200
300
400
500
600
700
-6 -4 -2 0 2 4 6
eta
dN
/d_
eta
0 - 6 %
6 - 15 %
15 - 25 %
25 - 35 %
35 - 45 %
45 - 55 %
19.6 Gev Au-Au PHOBOS
0
100
200
300
400
500
600
700
-6 -4 -2 0 2 4 6
eta
dN
/d_e
ta
: 0 - 6 %
: 6 - 15
: 15 - 25
: 25 - 35
: 35 - 45
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But the trend roughly follows the But the trend roughly follows the (BJ-like) hydro predictions, (BJ-like) hydro predictions, which which is is also about s-independentis is also about s-independent
v2 vs. dn_deta
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0 100 200 300 400 500 600 700 800
dN/d_eta
v2
200 GeV central
130 GeV central
19.6 GeV central
TLS LH8 EOS
TLS LH8 Hydro Only
LH16 EOS
LH_inf
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Are Are the fine structure the fine structure of vof v22 hydrodynamical hydrodynamical for all secondaries? for all secondaries? (PHENIX, R.Lacey)(PHENIX, R.Lacey) Scaling from (nucl-th/0402036)Scaling from (nucl-th/0402036)
12
0
( )
( )
I wv
I w
22 0 3 01 2
20 1 1
~ 1 ..T
T k Tk kv y m
T k m k m
22 0 3 01 2
20 1 1
~ 1 ..T
T k Tk kv y m
T k m k m
2fsT m Ty k y m 2fsT m Ty k y m
we then define a “fine
structure” variable
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The data scale as hydro:The data scale as hydro:2fs
T m Ty k y m 2fsT m Ty k y m
pT (GeV/c)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
v 2
0.00
0.05
0.10
0.15
0.20
0.25
pK
s 200 GeVNNAu Au
0 1 2 3
v 2
0.00
0.05
0.10
0.15
0.20
s 200 GeVNNAu Au
p
fsTy
5 < Centrality < 30 %
K
(PHENIX)
(PHENIX)
(PHENIX)
0.0 0.5 1.0 1.5 2.0 2.5
v 2
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
fsTy
Kp
Hydro
Au Au data look like hydro!
Kolb, et al
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Sonic boom from Sonic boom from quenched jets quenched jets Casalderrey,ES,Teaney, hep-ph/0410067; Casalderrey,ES,Teaney, hep-ph/0410067; H.Stocker…H.Stocker… the energy deposited the energy deposited
by jets into liquid-like by jets into liquid-like strongly coupled QGP strongly coupled QGP must go into must go into conical conical shock wavesshock waves, similar , similar to the well known to the well known sonic boom from sonic boom from supersonic planes.supersonic planes.
We solved relativistic We solved relativistic hydrodynamics and hydrodynamics and got the flow picture got the flow picture
If there are start and If there are start and end points, there are end points, there are two spheres and a two spheres and a cone tangent to bothcone tangent to both
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Distribution of radial Distribution of radial velocity v_r (left) and velocity v_r (left) and modulus v (right).modulus v (right).(note tsunami-like features, a (note tsunami-like features, a positive and negative parts of the positive and negative parts of the wave)wave)
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Is such a sonic boom already Is such a sonic boom already observed?observed?Mean Cs=.33 time average over 3 stages=>Mean Cs=.33 time average over 3 stages=>
M.Miller, QM04
flow of matter normal to the Mach cone seems to be observed! See data from STAR,
+/-1.23=1.91,4.37
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PHENIX jet pair distribution 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
<p_t(\phi)> at
180 degr., with
a value
Consistent with background
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Away <pAway <pTT> vs > vs centralitycentrality
Away core <pT> drops with centrality faster than corona <pT>.Core hadrons almost identical to medium in central collisions.A punch-though at the highest trigger?
STAR,Preliminary
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away <pT> dependence on away <pT> dependence on angle angle (STAR,preliminary)(STAR,preliminary)
Preliminary
<pT> (phi) has a dip structure in central AA.
Mach shock wave?
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Collective flows Collective flows =>collisional regime =>collisional regime
=> hydrodynamics=> hydrodynamicsThe main assumption:The main assumption:
l << Ll << L(the micro scale) << (the macro scale)(the micro scale) << (the macro scale)
(the mean free path) << (system size)(the mean free path) << (system size)
(relaxation time) << (evolution (relaxation time) << (evolution duration) duration)
II
In the zeroth order in l/L it is ideal hydro with a local stress tensor. Viscosity appears as a first order correction l/L, it has velocity gradients. Note that it is inversely proportional to the cross section and thus is (the oldest) strong coupling expansion
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Viscosity of QGPViscosity of QGPQGP at RHIC seem to be the most idealfluid known, viscosity/entropy =.1 or so water would not flow if only a drop with 1000 molecules be made
• viscous corrections1st order correction to dist. fn.:
:Sound attenuation length
Velocity gradients
Nearly ideal hydro !? D.Teaney(’03)
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Theory and Theory and phenomenology of phenomenology of sQGPsQGP
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How to get 20 times How to get 20 times pQCD pQCD ??
(Zahed and ES,2003)(Zahed and ES,2003)
Quark-antiquark bound states don’t all Quark-antiquark bound states don’t all melt at Tc (charmonium from lattice melt at Tc (charmonium from lattice known prior to that…) known prior to that…)
Many more colored channelsMany more colored channels all q,g have strong rescattering qqbar all q,g have strong rescattering qqbar
mesonmesonResonance enhancementsResonance enhancements Huge cross section due to resonance Huge cross section due to resonance
enhancement causes enhancement causes elliptic flow of elliptic flow of trapped trapped Li atomsLi atoms
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Scattering amplitudesScattering amplitudesfor quasiparticlesfor quasiparticlesM. Mannarelli. and R. Rapp hep-ph/05050080
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Elliptic flow with ultracold trapped Li6 atoms, a=> 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”
The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a
Micro-Bang ! (O’Hara et al, Duke )
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Hydro works for up to Hydro works for up to 1000 oscillations1000 oscillations! ! The z mode frequency agrees with hydro The z mode frequency agrees with hydro (red star) at resonance, with universal (red star) at resonance, with universal EoS EoS Viscosity has a strong minimum thereViscosity has a strong minimum there
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``Quantum viscosity”``Quantum viscosity” <= universality <= universality
• There is no need There is no need to specify to specify constituents or a constituents or a mean free path:mean free path:
• Hydro: Hydro: damping damping of sound wavesof sound waves can provide a can provide a definitiondefinition
•For cold T=0 atoms ``quantum viscosity”
• =hbar n
Should be the universal dimensionless constant•Scattering rate must be -1= const hbar/F
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So what is the viscosity?
• B.Gelman, ES,I.Zahed
nucl-th/0410067
• At the minimum alpha_eta is about .5+- .3 or so =>
• This liquid is about as perfect as sQGP at RHIC!
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Bound states in sQGPBound states in sQGP
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The map: the QCD Phase Diagram
T
The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland)
Chemical potential mu
Theory prediction (numerical calculation, lattice QCD, Karsch et al) the pressure as a function of T (normalized to that for free quarks and gluons)
p/psb=0.8 weak or strong coupling?
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How strong is strong?For a screened Coulomb potential, Schr.eqn.=>a simple
condition for a bound state
• (4/3)s (M/MDebye) > 1.68
• M(charm) is large, MDebye is about 2T
• If (Md) indeed runs and is about ½-1, it is large enough to bind charmonium till about T=3Tc (above the highest T at RHIC)
• Since q and g quasiparticles are heavy,
M about 3T, they all got bound as well !
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Fitting F to screened Coulomb
• Fit from Bielefld group hep-lat/0406036
•Note that the Debye radius corresponds to
``normal” (enhanced by factor 2) coupling, while the overall strength of the potential is much larger •It becomes still larger if V is usedinstead of F, see later
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Here is the binding and |psi(0)|^2
E/2MVs T/Tc
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Solving for binary bound statesES+I.Zahed, hep-ph/0403127
• In QGP there is no confinement =>
• Hundreds of colored channels should have bound states as well!
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The pressure puzzle is resolved!Masses, potentials and EoS from lattice are
mutually consistentM/Tc vc T/Tc and p/pSB vs T/Tc
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Can we verify existence of Can we verify existence of bound states at T>Tc bound states at T>Tc experimentally?experimentally?Dileptons from sQGP:Dileptons from sQGP:
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Jet quenching by Jet quenching by ``ionization”``ionization”of new bound states in QGP?of new bound states in QGP?
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Calculation of the ionization Calculation of the ionization raterateES+Zahed, hep-ph/0406100ES+Zahed, hep-ph/0406100• Smaller than Smaller than radiative radiative
lossloss if if L>.5-1 fmL>.5-1 fm• Is there mostly near Is there mostly near
the zero binding lines,the zero binding lines,• Thus it is different from Thus it is different from
both both radiative radiative and and elasticelastic looses, which looses, which are simply proportional are simply proportional to densityto density
• Relates Relates to non-trivial to non-trivial energy dependence of energy dependence of jet quenchingjet quenching (smaller (smaller at 62 and near absent at 62 and near absent at SPS)at SPS)
dE/dx in GeV/fm vs T/Tc for a gluon 15,10,5 GeV. Red-elastic, black -ionization
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Theoretical sQGP in Theoretical sQGP in N=4 SUSY YM and N=4 SUSY YM and AdS/CFTAdS/CFT
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A gift by the A gift by the stringstring theorists: AdS/CFT theorists: AdS/CFT correspondencecorrespondence
The viscosity/entropy => 1/4Pi is very small and about as observed at RHIC (D.Son et al 2003)
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QCD vs CFT: let us start with EoS
(The famous .8 explained!)
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Bound states in AdS/CFT(ES and Zahed, PRD 2004)
• The quasiparticles are heavy
M_q =O(sqrt(lambda) T) >> T
• But there are light binary bound states with the mass = O(M_q/sqrt(lambda))=O(T)
Out of which the matter is made of!
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A complete ``gravity dual” for RHIC from 10-d GR? (ES,Sin,Zahed, in progress)
• Black Holes + Howking rad. Is used to mimic the finite T
• How black hole is produced can be calculated from GR (tHooft … Nastase)
• Entropy production => black hole formation, falling into it is viscosity
• Moving brane => hydro expansion
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ConclusionsConclusions
QGP as a “matter” in QGP as a “matter” in the usual sense, not the usual sense, not a bunch of particles, a bunch of particles, has been produced has been produced at SPS/RHICat SPS/RHIC
It shows very robust It shows very robust collective flows. The collective flows. The EoS is as expected: EoS is as expected: the vacuum pressure the vacuum pressure of about .5 GeV/fm3 of about .5 GeV/fm3 observed.observed.
QGP seems to be the QGP seems to be the most ideal fluid most ideal fluid known known
eta/hbar s=.1-.2 <<1eta/hbar s=.1-.2 <<1
All of this hints that All of this hints that QGP is a liquidQGP is a liquid, in a , in a strong coupling strong coupling regimeregime
Interesting Interesting analogies with other analogies with other strongly coupled strongly coupled systems systems
``quantum gases”``quantum gases” AdS/CFTAdS/CFT Strongly coupled Strongly coupled
e/m plasmas e/m plasmas