Hot and Dense Nuclear Matter - Department of Physics and Astronomy

Hot and Dense Nuclear Matter 

Soren Sorensen 

Department of Physics 

University of Tennessee 

UTK, October, 2006 

Sources: 

Bill Zajc 

Tom Hemmick 

Ken Read 

Quark Matter 2005 Presentations 

All of PHENIX

The Standard Model 

Hot and Dense Nuclear matter 2

Quark Confinement 

What happens if we try to “free” a quark from it’s partner? 

A typical meson 

The meson is being 

stretched to separate the 

quarks. 

The “spring” energy between 

the quarks is eventually so 

high that a new quark pair is 

created -> two new mesons 

are formed. 

No free quarks. The quarks are confined to be inside hadrons. 


Is there another way we can “free” 

the quarks? 

Normal Nuclear Matter 

Quark Gluon Plasma 

Increasing density or temperature 

This figure and several others in this talk are copied from 

“Gauge Field Theories” by Mike Guidry 


Phase Diagram for Nuclear Matter 

Partonic Matter 


What kind of phase transition? 



QGP connection to the Big Bang 


How to create a Quark Gluon Plasma in the lab? 

A Little “Big Bang” 

Our best guess: Collisions between large atomic nuclei at the highest possible energies 

Low energy collisions create no QG plasma (we have tried!) 

High energy collisions will. 

Animation by Jeffery Mitchell. VNI model by Klaus Kinder-Geiger and Ron Longacre, Brookhaven National Laboratory 


RHIC’s Experiments 

STA 

R 


Evolution of Heavy Ion Collisions 

Preequilibrium 

Thermalization 

QGP 

phase? 

Mixed 

Phase 

Hadronization 

Expansion 

T < 0 

0.1 fm/c 

~ 1 fm/c 

3-4 fm/c 

8–10 fm/c 

10 – 20 fm/c 

γ, γ∗→ e + e - , μ + μ − 

Hard processes (early 

stages): Real and virtual 

photons, leptons, high p T 

particles. 

π, K, p, n, φ, Λ, Δ, Ξ, Ω, d,… 

Soft hadrons reflect 

medium properties later 

in the collision after 

hadronization (chemical 

freeze-out). 


Late Stage Hadro-Chemistry 


Therma- 

Lization 

QGP 

phase? 

Mixed 

Phase 

Hadronization 

Expansion 

T = 

0.1 fm/c 

~ 1 fm/c 

3-4 fm/c 

8–10 fm/c 

10 – 20 fm/c 

π, K, p, n, φ, Λ, Δ, Ξ, Ω, d,… 

Relative Hadron 

Abundances – 

Hadro Chemistry 


Late stage hadrochemistry 

• Assume all distributions described by one temperature T and one 

(baryon) chemical potential μ 

(Chemical Equilibrium): 

• One ratio (e.g., ⎯p-bar / p ) determines μ / T : 

• A second ratio (e.g., K / π ) provides T μ 

• Then predict all other hadronic yields and ratios: 

−( E −μ)/ T 3 

dn ~ e d p 

− ( E + μ)/ 

T 

p e 

= = e 

−( E −μ)/ 

T 

p e 

−2 μ / T 


• 

What do we learn from 

Hadro Chemical Thermodynamics 

– Beautiful systematics from many 

energies of freeze-out conditions 

– Does not necessarily indicate 

• QGP formation and Deconfinement 

– But … 

• Relaxation time of Ω (sss) 

– Hadronic state: Ω (sss) reaches 

chemical equilibrium only after 40-50 

fm/c 

RHIC 

– Partonic state: (sss) reaches chemical 

equilibrium in 1-2 fm/c 

– Freeze-out happens after max 10-20 

fm/c 

– Indication that the chemical equilibrium 

is reached in a partonic phase. 


Signals from High Density State 


Therma- 

Lization 

QGP 

phase? 

Mixed 

Phase 

Hadronization 

Expansion 

T = 

0.1 fm/c 

~ 1 fm/c 

3-4 fm/c 

8–10 fm/c 

10 – 20 fm/c 

High Density Partonic 

State Signatures: 

Jet Quenching 


Transverse Dynamics 

p 

p T 

θ 

Q. How to probe the deep interior and the earliest phases of the collision? 

A. By measuring “hard scatterings” at large p T 

“transverse momenta” 


Hard Scattered Partons (= Probes) 

• Hard scatterings in nucleonnucleon 

collisions produce 

jets of particles. 

schematic view of jet production 

hadrons 

leading 

particle 

q 

jet 

• In particular, the jets are 

great probes of the medium 

they traverse 

hadrons 

jet 

leading particle 

q 


Calibrated Probes 

• Extensive in situ measurements in (simple) p+p collisions at RHIC 

– Calibrated probes 

– Supported by well-established theory (perturbative Quantum Chromo 

Dynamics - pQCD) 

Produced pions 

Produced photons 


Schematically (Photons) 

The scattered direct photons always emerge undisturbed, 

because they do not interact via Nuclear Forces (Strong 

Interactions) 


Direct Photon Spectra in Au+Au 

• Now have a calibrated 

probe (note agreement 

of data and theory) 

• that works in the 

complex environment of 

two nuclei (Au+Au ) 

colliding at high energies 

• N binary or N collision scaling 

works! 


Jet Quenching 

The jet has to make its way out through the hot and dense medium 

Energy loss (stopping power) depends 

critically on type of medium: 

Hadronic Medium: ~ 0.2 - 0.4 GeV/fm 

Partonic Medium: ~ 2 – 3 GeV/fm 


Discovery of Strong Suppression 

peripheral 

N coll 

= 12.3 ± 4.0 

central 

N coll 

= 975 ± 94 

→ 

Scaling of calibrated probe works in peripheral Au+Au, 

but strong suppression in central Au+Au 


Nuclear Modification Factor: R AA 

• We define the nuclear modification 

factor as: 

R 

• R AA is what we get divided by what we 

2 A+ 

A 

expect. 

1 d N 

Nevt 

dpT 

dη 

• By definition, processes that scale 

AA( pT ) = < N 

2 N + N 

binary > d σ 

N + N 

σinel 

dpT 

d η 

with the number of underlying nucleonnucleon 

collisions (N binary ) will produce 

R AA = 1 . 


Photons shine, Pions don’t 

• Direct photons are not inhibited by hot/dense medium 

• Pions (all hadrons) are inhibited by hot/dense medium 


What about the “far-side” jet 


Far Side Jet Disapperance 

Pedestal&flow subtracted 

Δφ 

“partner” in hard scattering is absorbed 

in the dense medium 

• Strong absorption and jet quenching 

require high gluon densities 


Collective Flow 


Therma- 

Lization 

QGP 

phase? 

Mixed 

Phase 

Hadronization 

Expansion 

T = 

0.1 fm/c 

~ 1 fm/c 

3-4 fm/c 

8–10 fm/c 

10 – 20 fm/c 

Collective flow due to 

very early pressure 

gradients 

Recombination of 

quarks into hadrons 

(hadronization) 


Motion Is Hydrodynamic 

• When does thermalization occur? 

– Strong evidence that final state bulk behavior 

reflects the initial state geometry 

• Because the initial azimuthal asymmetry 

persists in the final state 

dn/dφ ~ 1 + 2 v 2 (p T ) cos (2 φ) + ... 

y 

z 

x 


The “Flow” Is Large 

• Value of v 2 in 

dn/dφ ~ 1 + 2 v 2 cos (2 φ) + .. 

saturates at ~ 0.2 

• Hydrodynamic calculations 

show this collective flow is 

– characteristic of 

a strongly interacting 

state of matter with 

very low viscosity 

10 

5 

0 

−5 

−10 

−10 −5 0 5 10 

10 

5 

10 

5 

0 

−5 

−10 

−10 −5 0 5 10 

10 

5 

– established in the 

earliest (geometrically 

asymmetric) stage 

of the collision 

– The flow is as strong as it 

can be 

0 

−5 

−10 

−10 −5 0 5 10 

0 

−5 

−10 

−10 −5 0 5 10

Hot and Dense Nuclear Matter - Department of Physics and Astronomy

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