# Presentation: 542578

## Using Lattice QCD to UnderstandData from RHIC

- 	        LLNL - 9 February 2006
**Modeling the QCD Equation of State at RHIC**

- Berndt Mueller (Duke University)

## QCD phase diagram

## The QGP

- Original conception of the QGP as the “hadronic plasma” (Shuryak 1978).
- Followed by 2 decades of conceptualization as “gaseous” medium with self-energies and vertex corrections.
- The “surprise” (as of 2003-06): The QGP is a plasma!
- Color forces as Debye screened
- Its equilibration is influenced (governed?) by plasma instabilities
- Energy deposition may be dominated by collective modes
- Main open issues:
- Is it a “liquid” plasma?
- Is it a plasma of complex bound states – polymeric plasma?

## Collective modes

## HTL formalism

- Nonabelian Vlasov equations generalizing “hard-thermal loop” effective theory:
- Soft fields are large initially and can continue to regenerate via plasma instabilities.

***k ~ gT *****(*****gQ******s*****)**

***k ~ T *****(*****Q******s*****)**

**Challenge: Full (3+1) dimensional simulation of HTL dynamics with back reaction**

## Investigative tools

- Detectors

- Connecting the two worlds

- Computers

- BG/L

## Lattice - EOS

- F. Karsch et al.

**Indication of weak or strong coupling?**

## Lattice – Critical end point

- Z. Fodor & S. Katz

- R. Gavai & S. Gupta

- Is the critical end point (Tc,c) reachable by RHIC?

## Lattice - susceptibilities

- R. Gavai & S. Gupta, hep-lat/0510044

## Heavy quark potentials

- Effective coupling s(r,T)
- Kaczmarek et al.

- Color singlet potential
- Kaczmarek & Zantow

- Important for insight into medium effects on J/, 

## Lattice – spectral functions

- Spectral functions via analytic continuation using the maximum entropy method:  J/ .
- (At present only for quenched QCD.)

- Karsch et al.

- Asakawa & Hatsuda

## The road to the quark-gluon plasma

- ...Is hexagonal and 2.4 miles long

## Bridging the gap

- LGT

- TRANSPORT

- DATA

## Space-time picture

- Pre-equil. phase

- Bjorken formula

## Stages of a relat. HI collision

- Initial collision ≈ break-up of the coherent gluon field (“color glass condensate”)
- Pre-equilibrium: the most puzzling stage
- Equilibrium (T > Tc): hydrodynamic expansion in longitudinal and transverse directions
- Hadronization: Are there theoretically accessible domains in pT ?
- Hadronic stage (T < Tc): Boltzmann transport of the hadronic resonance gas

## Transport theory for RHIC

**hadronization**

**initial state**

**pre-equilibrium**

**QGP and**
**hydrodynamic expansion**

**hadronic phase**
**and freeze-out**

## LGT  Transport

- Equation of state
- Susceptibilities
- Spectral functions
- Transport coefficients

- (Ideal) hydrodynamics
- Mean fields
- E-by-E fluctuations
- Models of QGP phase
- Hadronization models
- J/ transport models
- Dileptons
- Viscous hydrodynamics
- Jet quenching
- ..........

## Initial state: Gluon saturation

- Details of space-time picture depend on gauge!

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

- “Color glass condensate (CGC)”

## Classical glue dynamics

- Initial state occupation numbers ~ 1/****s  1 → classical fields generated by random color sources on light cone:

- Boost invariance → Hamiltonian gauge field dynamics in transverse plane (x,). 2-dim lattice simulation shows rapid equipartitioning of energy (eq ~ *Q*s-1).  Doorway to equilibration?

- Equilibration / isotropization via Weibel-type plasma instabilities?

## QGP molecular dynamics?

- Wong
- Heinz

- Reproduces HTL perturbation theory at weak coupling
- Lattice/particle formulation (with certain flaws) exists (Hu, BM, Moore)

- Well suited for studies of equilibrium properties.

## After thermalization...

- ... matter is described by (relativistic) hydrodynamics !
- Requires f  L _and_ small shear viscosity .

**Large v****2**** signals early equilibration **
**(*****t*****eq**** ******** 0.6 fm/c)**
**& small shear viscosity ******

## v2 vs. hydro

## Bounds on

**D. Teaney**

- Boost invariant hydro with T00 ~ 1 requires /s ~ 0.1.

- N=4 SUSY YM theory (g2*N**c** * 1):
- /s = 1/4(**Kovtun, Son, Starinets**).
- Absolute lower bound on /s ?

- /s = 1/4 implies  f ≈ 0.3 d !

**Challenge: (3+1) dim. relativistic viscous fluid dynamics**

- QGP(T≈Tc) = sQGP

## From QGP to hadrons

## Measuring 

- Measure   and *T,*  or  *s* and *T.*
-  and *s* from global observables (dN/dy, dET/dy), jets and hydro,
*T* from penetrating probes (photons).

## Entropy

- Two approaches:
- Use inferred particle numbers at chemical freeze-out from statistical model fits of hadron yields;
- Use measured hadron yields and HBT system size parameters as kinetic freeze-out (Pratt & Pal).
- Good news: results agree within errors:
- dS/dy = 5100 ± 400  for Au+Au (6% central, 200 GeV/NN)
-     → *s* = (d*S*/dy)/(R20) = 33 ± 3 fm-3
- For n ≈ 30 degrees of freedom, this results corresponds to  *T *(1 fm/c) ≈ 275 MeV.

## “Jet quenching” = parton energy loss

- Radiative energy loss:

- “Jet quenching” = parton energy loss

- q

- q

- g

- Scattering centers = color charges

***L***

- Density of scattering centers

- Range of color force

## Jet quenching in Au+Au

## 0 vs.   -  d+Au vs. Au+Au

- No suppression for photons

- Suppression of hadrons

## Energy loss at RHIC

- Present calculations use simplified geometry and evolution models. Flow, space-time dependence are essential for a reliable analysis.

## Stopping power

- Plotted against ,    is the same for a  gas and for a perturbative QGP.
- Suggests that    is really a measure of the energy density.
- Data suggest that    may be larger than compatible with Baier plot.
- Improved calculations of transport needed.

- Cold nuclear matter

**Challenge: *****Ab initio***** calculation of gluon radiation in medium**

## Where does Eloss go?

- STAR

- p+p

- Au+Au

- Lost energy of away-side jet is redistributed to rather large angles!

**Trigger jet**

**Away-side jet**

## Wakes in the QGP

**Mach cone requires **
**collective mode with ********(k) < k****:**

- J. Ruppert and B. Müller, Phys. Lett. B 618 (2005) 123

** ****Colorless sound**
**  ****Colored sound = longitudinal gluons**
**  ****Transverse gluons**

## Heavy quarks

- Heavy quarks* *(*c*, *b*) provide a hard scale via their mass. Three ways to make use of this:
-  Color screening of (Q-Qbar) bound states;
-  Energy loss of “slow” heavy quarks (suppressed by 	“dead-cone” effect for  < M/E);
-  D-, B-mesons as probes of collective flow.
- RHIC program: *c*-quarks and J/(and some *b*);
- LH”I”C program: *b*-quarks and .

## Charm energy loss

- Teaney & Moore

## J/ suppression

***V*****QQ**** is screened at scale (*****gT*****)****-1 **
********
**heavy quark bound states  dissolve above *****some***** *****T*****d****.**

**Challenge: Compute J/******** spectral function in unquenched QCD**

## Hadronization

## Quark number scaling of v2

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

## LGT  Transport

- Equation of state
- Susceptibilities
- Spectral functions
- Transport coefficients

- (Ideal) hydrodynamics
- Mean fields
- E-by-E fluctuations
- Models of QGP phase
- Hadronization models
- J/ transport models
- Dileptons
- Viscous hydrodynamics
- Jet quenching
- ..........

## LQCD  RHIC Data 

- Systematic effort needed to obtain precision data on:
- QCD equation of state,
- T- dependence of potentials, susceptibilities, etc.
- Spatial correlators and structure factors,
- T- dependence of spectral functions,
- Transport coefficients (?), light-cone correlators (?)
- Systematic effort needed to develop a suite of transport codes, which use the LQCD information as input:
**3-D relativistic viscous fluid dynamics,**
**Parton and hadron cascade codes with mean field,**
**3-D classical Yang-Mills simulations with HTL interactions.**

## Back-up slides

## Eikonal formalism

- Gluon radiation:

- x = 0

- x

- Kovner, Wiedemann

## Eikonal form. II

**Challenge: Compute **F+i(x)F+i(0) for x2 = 0 **on the lattice**

- Not unlike calculation of gluon structure function, maybe moments are calculable using euclidean techniques.