# Presentation: 614482

## Quark-Gluon Plasma From ConceptsTo “Precision” Science

- Berndt Mueller
***RHIC Users Meeting***
- BNL - March 28, 2008

## Part 1...

- The Quest for the
- Quark-Gluon Plasma

## QCD phase diagram

## QCD equation of state

## The QCD EoS (at =0)

- The precise value of Tc is still under debate:
- Tc = 170 ± 20 MeV with 20 - 30 MeV width.
- EoS near Tc is far from ideal ultrarelativistic gas! Sound velocity cs2 = P/ << 1/3.

## Lattice - susceptibilities

- Eijiri Karsch Redlich

- QCD matter above Tc may be a highly correlated system, but what is correlated are quarks and not hadrons!  (What about gluons?)

## Part 2...

- The 6 Stages of the Collision

## A multi-stage reaction

## Stage 1

- Decoherence of
- the initial state

## The initial state

- The Color Glass Condensate model is based on a brilliant idea:

- What applies to the proton (at high energy!), applies much better to a large nucleus, and at lower energy, because the gluon density per area is enhanced by a factor *A*1/3.

## Gluon saturation

- Universal saturated state at small *x*:   *Q*s >> QCD

- Gribov, Levin, Ryskin ’83
- Blaizot, A. Mueller ’87
- McLerran, Venugopalan ‘94

- “Color glass condensate” (CGC)

- Evolution in *x* is described by BK or JIMWLK equations*. *Location of the onset of saturation is determined by fluctuations (Iancu, Peschanski,...)

- p

- A

## CGC: Gluon production

- Fields carried by moving sources interact non-linearly and generate classical spectrum of gluonic modes. This requires numerical solution of YM eqs. with CGC initial cond’s.

- Krasnitz-Nara-Venugopalan, Lappi, Gelis

- Simulation of *T*(*x*,*t*) possible.

- Classical 2-particle rapidity correlations
- (Dumitru et al. ‘08)

## Stage 2

- Entropy:
- From 0 to (dS/dy=) 5000 in
- 0.000 000 000 000 000 000 000 002 seconds

## Final entropy

- Bjorken’s formula

- Assuming isentropic expansion up to *T*ch, averaging over *R*2 with *R* = 7 fm, and using lattice EOS:

- Phase space analysis (Pal & Pratt):

- Chemical analysis (BM & Rajagopal):

- How is this entropy produced?

## Decoherence

- Coherent state:

- Counting causally disconnected transverse domains:

- In D dimensions after equilibration:

- Clearly, fully 3-dimensional equilibration is essential - how and when?

## From 2D to 3D

- Nielsen-Olesen instability of
- longitudinal color-magnetic field
- (Itakura & Fujii, Iwazaki)

## Weibel instability

## Color “turbulence”

*Mrowczynski *
*Rebhan,Romatschke, Strickland*
*Arnold, Moore, Yaffe*
*Dumitru, Schenke*

- Wavelength and growth rate of unstable modes can be calculated perturbatively:
-      kz ~ gQs ,    ~ gQs < kz

## Turbulent color fields

**M. Strickland, hep-ph/0511212**

- Extended domains of coherent color field can create “anomalous” contributions to transport coefficients and accelerate equilibration (as in EM plasmas).

## Stage 3

- The (almost) perfect liquid

## Collision Geometry: Elliptic Flow

- Bulk evolution described by relativistic fluid dynamics,
- assumes that the medium is in local thermal equilibrium,
- but no details of how equilibrium was reached.
**Input: ********(x,********i****), P(********), (********,etc.).**

## v2(pT) vs. hydrodynamics

## Elliptic flow “measures”QGP

- Boost invariant hydrodynamics with T00 ~ 1 requires /s ≤ 0.1

- Relativistic viscous hydrodynamics:

- Small shear viscosity implies:
- The QGP is an almost perfect liquid

- Romatschke & Romatschke

## String theory weighs in

- General argument [Kovtun, Son & Starinets, PRL 94 (2005) 111601] based on duality between thermal QFT and string theory on curved background with the “black-brane” metric:

- Dominated by absorption of (thermal) gravitons by the black hole:

- horizon

- (3+1)-D world

*r*0

- (*t*,*x*)

- (0,0)

## An age-old problem solved!

- Unfortunately, this renders relativistic viscous hydrodynamics a-causal !
- Solution, in principle: include time derivatives (Israel,Stewart, Müller - 1960s).
- Full second-order expression for shear stress in conformal limit finally given by Baier, Romatschke, Son, Starinets & Stephanov (arXiv:0712.2451):

## Viscosity of RHIC

- R.J.Fries, BM, A. Schäfer, tbp

## Stage 4

- Hadronizing the
- Quark-Gluon Plasma

## v2(pT) vs. hydrodynamics

## Quark number scaling of v2

- In the recombination regime, meson and baryon v2 can be obtained from the quark v2 :

**Emitting medium is composed of  unconfined, flowing quarks.**

## CEP Observables

-  Observables that are not be sensitive to final state interactions

- Chemical Freeze-out

-  usually assumed to be
-      momentum independent

-  but this is not right

- chemical freeze-out time
- is pT (or yT) dependent

-  Larger pT (or yT),
-       earlier ch. Freeze-out

- Critical fluctuations, the primary signature of the CEP, are modified
- During expansion until chemical or kinetic freeze-out, in addition to being suppressed near CEP by critical slowing down.

## Emission Time Distribution

- Emission Time

-  Larger yT, earlier emission

-  To minimize resonance effect,
-   yT is used instead of pT

-  No CEP effect (UrQMD)

## Focus on chemistry

- Tc

- Tc

- Asakawa, Bass, BM, Nonaka ‘08

## RHIC can do it! 

- RHIC can do it!

## Part 3...

- Probing the structure
- of the Quark-Gluon Plasma

## Energy loss in QCD

- Radiative energy loss:

- Density of scattering centers

- Range of color force

- Nonradiative energy loss:

## Towards q-hat

- 3-D ideal hydrodynamics with
- radiative energy loss only

- Bass, Majumder, Qin, Renk et al. (tbp)

- Numbers change by up to factor of 2, depending on whether q-hat is scaled with *T*3, *s,* or **3/4 !

- Other unresolved issues:
- Consistent treatment of virtuality of parton created by hard scattering;
- Nature of scattering centers

## Closing in on q-hat

- Zhang et al. (using higher twist energy loss theory + back-to-back coincidences)

- Bass et al.

- More differential measurements of jet quenching with very high statistics are needed, as well as consistent theories of jet quenching for these observables.

## Collisions + radiation

- Qin, Ruppert, Gale, Jeon, Moore & Mustafa, PRL 100,072301 (2007)

- Inclusion of collisional energy
- loss leads to reduction of s
- from 0.33 to 0.27, corresponding
- to a reduction of extracted value
- of q-hat by 33%.

- Contributions from collisional and radiative energy loss may be separated due to their
- different fluctuations (Poisson vs. intermittent) by comparing singles quenching (RAA)
- with coincident back-to-back quenching (IAA), and by their different quark mass
- dependence by comparing with charm RAA.

## Connecting jets with the medium

- Hard partons probe the medium via the density of colored scattering centers:

- If kinetic theory applies, thermal gluons are quasi-particles that experience the same medium. Then the shear viscosity is:

- In QCD, small angle scattering dominates:

## An interesting question

- How does a fast parton interact with the quark- gluon plasma ?
- What happens to the energy and momentum lost by a fast parton on its passage through the hot medium ?
- How does the energy and momentum perturbation of the medium propagate ?

- Trigger jet

- Back jet

- Thanks to: E. Wenger (PHOBOS)

- Hard scattering

## Parton-medium coupling

- Space-time distribution of collisional eneregy loss

## Unscreened source

- For an unscreened color charge, an analytical result is obtained in *u*1 limit:

- Spatial integral over deposited energy and momentum distribution equals collisional energy loss; radiated gluons increase effective color charge.

- R.B. Neufeld

## Linearized hydro

- Linearize hydro eqs. for a weak source:  *T*00   + ,  *T*0i  *g*i .

- Solve in Fourier space for longitudinal sound:

- ... and dissipative transverse perturbation:

- See: J. Casalderrey-Solana, E.V. Shuryak and D. Teaney, arXiv:hep-ph/0602183

## pQCD vs. N=4 SYM

- Chesler & Yaffe arXiv:0712.0050

- Neufeld et al. arXiv:0802.2254

*u* = 0.99955 *c*

*u* = 0.75 *c*

-    (*z - ut*)

**

## Mach cone: cs and η

## RHIC data

- Technique: Measure 2- and 3- particle correlations on the away-side triggered by “high” *p*T hadron in central coll’s. Cone-shaped emission should show up in 3-particle correlations as signal on both sides of backward direction.

## Summary 1

**The RHIC program has shown that **
** ****equilibrated matter**** is rapidly formed in heavy ion collisions;**
** ****new, powerful probes**** become available at collider energies;**
** ****systematic study**** of matter properties is possible.**
**QGP appears to be a ****strongly coupled****, maybe ****turbulent**** color liquid with novel and unanticipated transport properties.**
**Experimental and theoretical surprises**** have opened a ****gold mine**** for theorists:**
** ****extreme opaqueness of matter to colored probes;**
** ****collective flow phenomena;**
** ****collective medium response to jets;**
** ****large enhancement of baryon production;**
** ****connection to string theory and AdS/CFT duality.**

## Summary 2

**Ultimate success of the RHIC program requires****:**
** ****precision data for key (often rare) observables;**
** ****continued progress of our understanding of thermal QCD;**
** ****sustained collaboration between theorists and experimentalists on precision data interpretation.**
**Superficially different observables (flow, jet quenching, two-particle correlations) are connected at a deep level.**
**Their exploration in a comprehensive framework will lead to deep insights into how bulk QCD matter behaves and, ultimately, to the fulfillment of the scientific promise of RHIC. **
**The LHC heavy ion program will help resolve ambiguities, due to its extended kinematic range for critical observables.**

## Summary 3

**Experimental and theoretical surprises**** have opened a ****gold mine**** for theorists, but to extract the gold,  painstaking work will be required in collaboration between theorists and experimentalists.**
**The first steps have been taken:**

- For report and details see:
**https://wiki.bnl.gov/TECHQM/index.php/Main_Page**

## THE   END