A NEARLY PERFECT INK:The quest for the quark-gluon plasma at

the Relativistic Heavy Ion Collider

Berndt Mueller (Duke University)LANL Theory Colloquium

2 June 2005

The Road to the Quark-Gluon Plasma…

STAR

…Is Hexagonal and 2.4 Miles Long

Insights and Scientific Challenges from the RHIC Experiments

The quest for simplicity

• Before the 1975, matter at high energy density was considered a real mess!

• QCD predicts that hot matter becomes simple – the QGP (not necessarily weakly interacting!).

• Characteristic features: deconfinement and chiral symmetry restoration.

The equation of state of strongly interacting matter according to lattice QCD

Quark-gluon plasma

Tc ≈ 160 MeV

The QCD phase diagram

B

Hadronicmatter

Critical endpoint

?Plasma

Nuclei

Chiral symmetrybroken

Chiral symmetryrestored

Colour superconductor

Neutron stars

T

1st order line ?

Quark-Gluon

RHIC

Tc

Space-time picture of a r.h.i.c.

Equilibration

Hadronization

Thermal freeze-out

RHIC data gathering

RHIC has had runs with:

• Au+Au at 200, 130, 62 GeV

• Cu+Cu at 200, 62 GeV

• d+Au at 200 GeV

• p+p at 200, 130 GeV

Charged particle tracks from a central Au+Au collision

Frequently Asked Questions

• How do we know that we have produced equilibrated matter, not just a huge bunch of particles ?

• What makes this matter special ?• How do we measure its properties ?• Which evidence do we have that quarks are deconfined for

a brief moment (about 10-23 s) ?• Which evidence do we have for temporary chiral

symmetry restoration ?• What do we still need to learn ?

– Translation: When can RHIC be closed down ?

FAQ #1

How do we know that we produced equilibrated matter, not just a bunch of particles ?

Answer:

Particles are thermally distributed and flow collectively !

9

Chemical equilibrium

• Chemical equilibrium fits work, except where they should not (resonances with large rescattering).

RHIC Au+Au @ 200 GeV

– Tch = 160 10 MeV

– µB = 24 5 MeV

STAR PreliminaryCentral Au-Au √s=200 GeV

Elliptic flow

Coordinate space: initial

asymmetry

Momentum space: final

asymmetrypyPressure

gradient

collective flow

pxx

y

Two-particle correlationsdN/d(1- 2) 1 + 2v2

2cos(2[1- 2])

FAQ #2

What makes this matter special ?

Answer:

It flows astonishingly smoothly !“The least viscous non-superfluid ever seen”

v2 requires low viscosity

( )

0 with

( trace)P u

T

uT uu Pg

Relativistic viscous fluid dynamics:

Shear viscosity tends to smear out the effects of sharp gradients

3

2 1

43 ln

ss

Tp

But what is s ?pQCD:

Dimensionless quantity 2 1

shear viscosityentropy

115densi ly nt

sss

Viscosity must be ultra-low

D. Teaney Quantum lower bound on /s :

/s = 1/4 (Kovtun, Son, Starinets)

Realized in strongly coupled (g1) N = 4 SUSY YM theory, also in QCD ?

/s = 1/4 implies f ≈ (5 T)-1 ≈ 0.3 dQGP(T≈Tc) =

sQGP

v2 data comparison with (2D) relativistic hydrodynamics results suggests /s 0.1

Recent excitement:

FAQ #3

How do we measure its properties ?

Answer:

With hard QCD probes, such as jets, photons, or heavy quarks

High-energy parton loses energy byrescattering in dense, hot medium.

qq

Radiative energy loss: 2/ TdE dx L k

“Jet quenching” = Parton energy loss

q qg

Scattering centers = color chargesL

Scattering power of the QCD medium:

22 2 2

2 Tˆ dq q dqdq

k

Density of scattering centers

Range of color force

Suppression of fast pions (0)

Phenix preliminary

Central collisons

Peripheral collisons

AAAA

coll pp

NRN N

Energy loss at RHIC

• Data are described by a very large loss parameter for central collisions:2ˆ 5 10 GeV /fmq

pT = 4.5 – 10 GeV/c

(Dainese, Loizides, Paic, hep-ph/0406201)

Larger than expected from perturbation theory ?

Pion gas

QGP

Cold nuclear matter

RHIC data

sQGP

R. Baier

Does QCD perturbation theory work?

I. Vitev (JRO Fellow – LANL)

d+Au

Au+Au

→ What is the appropriate value of QCD coupling s ?

0

FAQ #4

Which evidence do we have that quarks are deconfined for a brief moment (about 10-23 s) ?

Answer:

Baryons and mesons are formed from independently flowing quarks

Suppression Patterns: Baryons vs. Mesons

What makes baryons different from mesons ?

Hadronization Mechanisms

qq

q

Baryon 1Meson

Fragmentation

q q

q q q

Baryon 1Meson

Recombination

M Q B Q2 3p p p p

This is not coalescence

from a dilute medium !

Recombination “wins” …

… always for a thermal source

Baryons compete with mesons

Fragmentation still wins for a power law tail

Recombination vs. Fragmentation

Teff = 350 MeV blue-shifted temperature T = 180 MeV

pQCD spectrum shifted by 2.2 GeV

R.J. Fries, BM, C. Nonaka, S.A. BassBaryon enhancement

Hadron v2 reflects quark flow !

Recombination model suggests that hadronic flow reflects partonic flow (n = number of valence quarks):

2 2v vhad partn

had partT Tp np

Provides measurement of partonic v2 !

FAQ #5

Which evidence do we have for temporary chiral symmetry restoration ?

Strangeness in Au+Au at RHIC

(sss)

(qss)

(qqs)

1

10

100

1000

10000

100000

1000000

u d s c b t

Q CD mass

Higgs mass

Flavor

Mass (MeV)

QCD mass disappears

FAQ #6: What do we still need to (or want to) learn ?

• Number of degrees of freedom:– via energy density – entropy relation.

• Color screening: – via dissolution of heavy quark bound states (J/).

• Chiral symmetry restoration:– modification of hadron masses via e+e- spectroscopy.

• Quantitative determination of transport properties:– viscosity, stopping power, sound velocity, etc.

• What exactly is the “s”QGP ?

QCD equation of state

24

30T 20%

Challenge: Devise method for determining from data

Alternative method

24

23

30245

T

s T

4 4

2 3 3

1215 0.96128

s s

Eliminate T from and s :

Lower limit on requires lower limit on s and upper limit on .

BM & K. Rajagopal, hep-ph/0502174

Eur. J. Phys. C (in print)

Measuring and s

• Entropy is related to produced particle number and is conserved in the expansion of the (nearly) ideal fluid: dN/dy → S → s = S/V.

• Energy density is more difficult to determine:

– Energy contained in transverse degrees of freedom is not conserved during hydrodynamical expansion.

– Focus in the past has been on obtaining a lower limit on ; here we need an upper limit.

– New aspect at RHIC: parton energy loss. dE/dx is telling us something important – but what exactly?

Entropy

• Two approaches:1) Use inferred particle numbers at chemical freeze-out from statistical model

fits of hadron yields;2) Use measured hadron yields and HBT system size parameters as kinetic

freeze-out (Pratt & Pal).

• Method 2 is closer to data, but requires more assumptions (HBT radii = geometric radii, isentropic expansion of hadronic gas).

• Good news: results agree within errors: – dS/dy = 5100 ± 400 for Au+Au (6% central, 200 GeV/NN)

State of the art

• 6% central sNN1/2 = 200 GeV Au+Au collisions (0 = 1 fm/c):

– dS/dy = 5100 ± 400 → s = (dS/dy)/(R20) = 33 ± 3 fm-3

– dET/dy = 650 GeV/fm3 → Bj = (dET/dy)/(R20) = 4.2 GeV/fm3

> Bj due to longitudinal hydrodynamic work done. PHOBOS estimate is > 5 GeV/fm3 at 0 = 1 fm/c. Some examples: = 5 GeV/fm3 → = 71 ± 22 = 7 GeV/fm3 → = 26 ± 8 = 9 GeV/fm3 → = 12 ± 4

– Improved determination of must be an immediate goal.

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;

D-, B-mesons as probes of collective flow.

RHIC program: c-quarks and J/;

LHC-HI program: b-quarks and .

RHIC data for J/ are forthcoming (Runs 4 & 5).

The Baier plot - again

• 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.

Better calculations are needed.

One approach (Turbide et al.) based on complete LO HTL transport theory, gets RAA right (hep-ph/0502248)

q̂

q̂

q̂

Pion gas

QGP

Cold nuclear matter

RHIC data

sQGP

J/ suppression ?

Vqq is screened at scale (gT)-1 heavy quark bound states dissolve above some Td.

Karsch et al.

Color singlet free energy

Quenched lattice simulations, with analytic continuation to real time, suggest Td 2Tc !

S. Datta et al. (PRD 69, 094507)

Challenge: Compute J/ spectral function in unquenched QCD

Di-hadron correlations

STAR Data

Away-side jet: Q’(R/R)2

QR/R

Correlations depend on selected momentum windows

“Waking” the sQGP

v=0.55c v=0.99c

Outlook

• The “discovery phase” of RHIC is just hitting its full stride.

• Several important observables still waiting to be explored.

• Run-4 and -5 data are eagerly anticipated.• More than 109 events will provide many answers

and help us to refine the questions.• Many well defined theoretical challenges.