# Presentation: 657663

## The  strongly coupled Quark-Gluon Plasma

**Edward Shuryak**
**Department of Physics and Astronomy**
**State University of New York**
**Stony Brook NY 11794 USA**

**Notes:**
Talk in Sydney March 2004

## Outline: 

- The Little Bang, not a firework of minijets
- Collective flows: radial and elliptic, systematics: => viscosity
- Where the energy of jets go? A ``sonic boom”
- What does the  ``strong coupling” mean?
- Quasiparticles and Potentials at T>Tc
- The phase diagram and few puzzles
- Hadronic bound states at T>Tc
- Colored bound state and EoS
- Strongly coupled atoms
- Strongly coupled N=4 SUSY YM and AdS/CFT correspondence

## The Big vs the Little Bang

- Big Bang is an explosion which created our Universe.
- Entropy is conserved.
-  Hubble law v=Hr for
-    distant galaxies. H is isotropic.
- “Dark energy” (cosmological constant) seems to lead to accelerated expansion

- Little Bang is an explosion
-     of a small fireball created in high energy collision of two nuclei.
- Also entropy is well conserved
- Hubble law, but anisotropic (see below)
-  The ``vacuum pressure” works against expansion
-    (And that is why it was so
-     difficult to produce it)

## The vacuum vs the QGP

- The vacuum is very complicated, dominated by ``topological objects”
- Vortices, monopoles and instantons
- Among other changes it shifts its energy down compared to an
- “empty” vacuum, known as
- The Bag terms,
- p=#T^4-B
- Epsilon=#T^4+B

- The QGP, as any plasma, screens them, and is nearly free from them
- So, when QGP is produced, the vacuum tries to expel it
- (recall here pumped out Magdeburg hemispheres
- By von Guericke in 1656 we learned at school)

## Magdeburg hemispheres 1656

**We cannot pump the QCD vacuum out, but we can pump in something else, namely the Quark-Gluon Plasma**

## The map: the QCD Phase Diagram

- <date/time>

- 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

## Collective flows: bits of history

## 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

## 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

## QM99 predictions for v2(with D.Teaney)

**RQMD**
**HIJING**

**Our hydro/**
**cascade**

## Main findings at RHIC

**Partciles are produced from matter which seems to be ****well equilibrated**** (by the time it is back in hadronic phase), N1/N2 =exp(-(M_1-M_2)/T)**
**    **
**Very robust ****collective flows**** were found, indicating very strongly coupled Quark-Gluon Plasma ****(sQGP)**** **
**Strong quenching of large pt  jets****: they  do not fly away freely but are mostly (up to 90%) **
**  ****absorbed by the matter. The deposited energy seem**
**To go into ****hydrodynamical motion  (conical flow) **

## Reminder

_***Reminder***_
***Statistical Model  ***
***Works well with just two parameters***

***Hadro-chemistry  seems to be all done at the critical line***

## Hydrodynamics is simple and very predictive, but one has to understand few things,and so not all hydros are the 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:**

## Thinking About EoSThe Latent Heat and the ``softest point” (Hung, ES 1995)

## Understanding of the freezeouts(which some hydro groups forgot)

- Chemical freezeout at Tch means that at
- T<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)

##   hydro describes both radial and elliptic flows (from Phenix)  v_2=<cos(2 phi)>

**Hydro models:**
**Teaney**
***(w/ & w/o***
***RQMD)***
**Hirano**
***(3d)***
**Kolb**
**Huovinen**
***(w/& w/o***
***QGP)***

**nucl-ex/0410003**

## V2 systematics:it depends on many variables

- Particle type => y_t^2 m scaling
- Collision energy s –dependence
- (pseudo) rapidity (eta) y-dependence
- Pt: rapid growth with saturation
- Centrality => v2/s2 scaling

## A Hydrodynamic Description of Heavy Ion Collisions at the SPS and RHICD. Teaney, J. Lauret, and E.V. Shuryaknucl-th/0110037 v2 6 Dec 2001The  dependence on dN/dyhas a growing trend, with a saturation

## More 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.

## The (pseudo)rapidity distribution of v2 (from PHOBOS) is not the same as that of the particles

## Particle distribution over (pseudo) rapidity

- Number of charged particles per unit of pseudorapidity

## But the trend roughly follows the (BJ-like) hydro predictions,  which  is is also about s-independent

## Are the fine structure of v2 hydrodynamical for all secondaries? (PHENIX, R.Lacey)

- Scaling from (nucl-th/0402036)

**we then define a “fine **
**structure” variable**

## The data scale as hydro:

## 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****, similar to the well known sonic boom from supersonic planes.**
**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**
** **

## Distribution of radial velocity v_r (left) and modulus v (right).(note tsunami-like features, a positive and negative parts of the wave)

## Is such a sonic boom  already observed?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**

## 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  **

## Away <pT> vs centrality

- 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

##  away <pT> dependence on angle (STAR,preliminary)

- <pT> (phi) has a dip structure in central AA.
-  Mach shock wave?

## Collective flows =>collisional regime   => hydrodynamics

- The main assumption:
- l << L
- (the micro scale) << (the macro scale)
- (the mean free path) << (system size)
- (relaxation time) << (evolution duration)
- I

- 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

##  Viscosity of QGP

** ****Viscosity of QGP**

**QGP at RHIC seem to be the most ideal**
**fluid known, viscosity/entropy =.1 or so**
**  ****water would not flow if only a drop with 1000 molecules be made                            **

**  ****viscous corrections**

**1****st**** order correction to dist. fn.:**

**:Sound attenuation length**

**Velocity gradients**

- Nearly ideal hydro !?

**D.Teaney(’03)**

## Theory and phenomenology of sQGP

## How to get 20 times pQCD ?

**(Zahed and ES,2003)**
**Quark-antiquark bound states  don’t all melt at Tc (charmonium from lattice known prior to that...) **
**Many more colored channels**
**all q,g have strong rescattering qqbar ******** meson**
**Resonance enhancements**** **
**Huge cross section due to resonance enhancement causes  ****elliptic flow of **** trapped Li atoms**

## Scattering amplitudesfor quasiparticlesM. Mannarelli. and R. Rapp hep-ph/05050080

## The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a Micro-Bang ! (O’Hara et al, Duke )

**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 )

##  Hydro works for up to 1000 oscillations! The z mode frequency agrees with hydro (red star) at resonance, with universal EoS  Viscosity has a strong minimum there

## ``Quantum viscosity” <= universality

**There is no need to specify constituents or  a mean free path:**
**Hydro: **** ****damping of sound waves**** can provide a definition**

**For cold T=0 atoms ``****quantum viscosity”**
** ********=hbar n **********
**Should be the universal **
**dimensionless constant**
**Scattering rate must be   ********-1****= const**** ****hbar****/********F****  **

## 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!**

## Bound states in sQGP

## 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**?

## 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 1⁄2-1, 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 !

## 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 used**
**instead of F, see later**

## Here is the binding and |psi(0)|^2

**E/2M**
**Vs ****T/Tc**

## Solving for binary bound statesES+I.Zahed, hep-ph/0403127

**In QGP there is no confinement**** => **
**Hundreds of colored channels ****should have bound states as well!**

## The pressure puzzle is resolved!Masses, potentials and EoS from lattice are mutually consistent

**M/Tc vc T/Tc  and p/p****SB**** vs T/Tc**

## Can we verify existence of bound states at T>Tc experimentally?Dileptons from sQGP: 

## Jet quenching by ``ionization”of new bound states in QGP?

## Calculation of the ionization rateES+Zahed, hep-ph/0406100

- Smaller than radiative loss if L>.5-1 fm
- Is there mostly near the zero binding lines,
- Thus it is different from both radiative and elastic looses, which are simply proportional to density
- Relates to non-trivial energy dependence of jet quenching (smaller at 62 and near absent at SPS)

**dE/dx in GeV/fm vs T/T****c**** for a gluon 15,10,5 GeV.                ****Red-elastic****, black -ionization**

## Theoretical sQGP in N=4 SUSY YM and AdS/CFT

## A gift by the string theorists: AdS/CFT correspondence

- The viscosity/entropy => 1/4Pi is very small and about as observed at RHIC (D.Son et al 2003)

## QCD vs CFT: let us start with EoS(The famous .8 explained!)

## 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!

## 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

## Conclusions

**QGP as a “matter” in the usual sense, not a bunch of particles, has been produced at SPS/RHIC**
**It shows very robust collective flows. The EoS is as expected: the vacuum pressure of about .5 GeV/fm3 observed.**
**QGP seems to be the most ideal fluid known **
**   ****eta/hbar s=.1-.2 <<1**

-  **All of this hints that ****QGP is a liquid****, in a strong coupling regime**
**Interesting analogies with other strongly coupled systems **
** ****``quantum gases”**
**   ****AdS/CFT**
**Strongly coupled e/m plasmas **