The Physics of Relativistic Heavy Ion Collisions

Associate Professor Jamie NagleUniversity of Colorado, Boulder

18th National Nuclear Physics Summer SchoolLectures July 31-August 3, 2006

Lecture #2

Heavy Ion Experiments

Need 10,000,000,000,000 Kelvin Bunsen Burner

How to Access This Physics?

Neutron stars

Lattice QCD

RHIC

Big Bang

Only one chance…

Who wants to wait?…

Slide from Jeff Mitchell

Kinetic Energy Thermal Energy

Bevalac-LBL and SIS-GSI fixed target max. 2.2 GeV

AGS-BNL fixed targetmax. 4.8 GeV

SPS-CERN fixed targetmax. 17.3 GeV

TEVATRON-FNAL (fixed target p-A)max. 38.7 GeV

RHIC-BNL collidermax. 200.0 GeV

LHC-CERN collidermax. 2760.0 GeV

BRAHMS, PHENIX, PHOBOS, STAR

ALICE, ATLAS, CMS

NA35/49, NA44, NA38/50/51, NA45,NA52, NA57, WA80/98, WA97, …

E864/941, E802/859/866/917, E814/877,E858/878, E810/891, E896, E910 …

1992Au-Au

1994Pb-Pb

2000Au-Au

2007?Pb-Pb

Energy Frontier History

Bevalac-LBL2.2 GeV

AGS-BNL4.8 GeV

SPS-CERN17.3 GeV

TEVATRON-FNAL38.7 GeV

RHIC-BNL200.0 GeV

LHC-CERN 2760.0 GeV

Net Baryon Density ~ Potential B [MeV]

Tem

per

atu

re T

ch [

Me

V]

0

200

250

150

100

50

0 200 400 600 800 1000 1200

AGS

LBL/SIS

SPS

RHIC/LHCquark-gluon plasma

hadron gas

atomic nuclei

Many basic goals of the field have remained the same over the last 20 years. However, the character of the system created is a strong function of energy.Many new probes and theoretical handles are available at higher energies.

Nuclear FragmentationResonance ProductionStrangeness Near Threshold

Resonances DominateLarge Net Baryon DensityStrangeness Important

Charm Production Starts

Low Net Baryon DensityHard Parton Scattering

Beauty Production

Why Energy Matters?

RHIC is doing great !

STARHadronic Observables over a Large

AcceptanceEvent-by-Event Capabilities

Solenoidal magnetic fieldLarge coverage Time-Projection

ChamberSilicon Tracking, RICH, EMC, TOF

PHENIXElectrons, Muons, Photons and Hadrons

Measurement CapabilitiesFocus on Rare Probes: J/, high-pT

Two central spectrometers with tracking and electron/photon PID

Two forward muon spectrometers

BRAHMSHadron PID over broad rapidity

acceptance

Two conventional beam line spectrometers

Magnets, Tracking Chambers, TOF, RICH

PHOBOSCharged Hadrons in Central

SpectrometerNearly 4 coverage multiplicity counters

Silicon Multiplicity RingsMagnetic field, Silicon Strips, TOF

Ring Counters

Paddle Trigger Counter

Spectrometer

TOF

Octagon+Vertex

What Are Protons and Nuclei?

Structure of the Proton

Momentum transfer QQ22 = 0.1 GeV = 0.1 GeV22

QQ22 = 1.0 GeV = 1.0 GeV22

QQ22 = 20.0 GeV = 20.0 GeV22

Wavelength Wavelength = h/p = h/p

See the whole protonSee the whole proton

See the quark substructureSee the quark substructure

See many partons (quarks and gluons)See many partons (quarks and gluons)

Parton Distribution Functions

• Structure functions rise rapidly at low-x• More rapid for gluons than quarks

30!

valence

sea

Quarks Gluons

When protons are viewed at short wavelength, there is a large increase in low x gluons.

Is there a limit to the low x gluon density?

Limitless Gluons?

Gluon Saturation

Wavefunction of low x gluons overlap and the self-coupling gluons fuse, thus saturating the density of gluons in the initial state

probe rest frame

r/ggg

1 J.P Blaizot, A.H. Mueller, Nucl. Phys. B289, 847 (1987).

target rest frame

c ~1/x

Fluctuations from dipole increase and the unitary limit of the photon cross section in deep inelastic scattering is the equivalent to saturation.

Transverse size of the quark-antiquark cloudis determined by r ~ 1/Q ~ 2 10-14cm/ Q (GeV)

Saturation in the ProtonHERA deep inelastic scattering data has been interpreted in the context of gluon saturation models.

Lowest x data is at modest Q2 (should QCD+DGLAP work?)

Recent HERA running may not resolve these issues since machine changes limit the coverage at low-x.

Future Electron-Ion Collider at RHIC or HERA upgrade may be necessary.

K. Golec-Biernat, Wuesthoff, others

What about Nuclei?

x .1x .1

210T2px

s

Nucleon structure functions are known to be modified in nuclei.

Can be modeled as recombination effect due to high gluon density at low x (in the frame where the nucleus is moving fast).

x

Saturation?

shadowing

enhancement

EMC effect

Fermi Effect

RHIC probes

Gluon Number Density

Gluon number density:

g = A xGN(x,Q2)/R2

Gluon density depends on the nuclear overlap area

(R2 A2/3) and the momentum scale (Q2) since DGLAP evolution requires:

G(x, Q2) ~ ln (Q2 / QCD2)

HERA tests gluon density in the proton at very low x. RHIC can test similar gluon density at significantly higher x values. LHC heavy ion collisions probe even higher gluon densities.

Color Glass Condensate

Put many nucleons into a nucleus and Lorentz boost to the infinite momentum frame

Creates a 2-dimensional sheet of very high density color charges set by a saturation scale.

High density of gluons (saturation) allows for the simplification of Quantum Chromodynamics

Color fields can be described as classical wave solutions to the Yang-Mills equation

Experimental ComparisonsIn this saturation regime (sometimes termed the Color Glass Condensate), with one parameter (saturation scale Qs) defines the physics. In this classical approximation one can calculate the collision output distribution of gluons. If one assumes a mapping of partons to hadrons, one can compare with data.

42/

2

22

22211ln

sinh

cosh ys

QCD

ysy

opart

TT

es

Qy

eQe

s

scN

ypm

y

d

dN

Saturation Regime?

The agreement appears impressive, but at the lowest energy one is no where near the saturation condition. Also, when the particle yield is matched, the transverse energy per particle is a factor of 2 too large. Perhaps this is longitudinal work, but no detailed calculation accounts for this yet.

Lower x?For a 2 2 parton scattering process (LO), if both partons scatter at 90 degrees, then x1=x2= 2pT/Ecm

x1

x2 pT ~ 2 GeVEcm ~ 200 GeVx ~ 0.04

x1

x2

One can probe lower x values if x1 >> x2 and look at particles away from 90 degrees (forward rapidity).

Rapidity y=0 (x~0.01), y=2.0 (x~0.001), y=4.0 (x~0.0001) for pT ~ 2 GeV.

Suppression Factor R

In deuteron-Gold collisions, forward rapidity probes low x in the Gold nucleus. BRAHMS observes a suppression of particles that could be related to saturation of the gluon density in the Gold nucleus.

ddpdT

ddpNdpR

TNN

AA

TAA

TAA /

/)(

2

2

b

Participant

BinaryCollisions

R = 1 (binary collision scaling)

Suppression of forward hadrons generically consistent with saturation of low-x gluons.

Aud

AuAu

dAuAu

dAu

x ~ 10-3x ~ 10-2x ~ 10-1

Sup

pres

sion

Fac

tor

d+Gold Probes

Tagged photons and jets at forward angles will give precise information on x dependence of saturation effect.

PT is balanced by many gluons

“Mono-jet”

Dilute parton system

(deuteron)

Dense gluon field (Au)

MonoJets?

STAR Experiment

No MonoJets at y=2?

PHENIX has measured the correlation between y=2 hadrons and y=0 hadrons.

There appears to be no decrease in away side partners as predicted by saturation models.

However, these predictions were for more forward rapidity (probing lower x) regions.

What do they have in common?

x

1. Scaling of the total p-p cross section

2. Growth of low x gluons in the proton

3. Shadowing of structurefunctions in nuclei

4. Particle production in nucleus-nucleus reactions

Saturation SummaryInteresting hints at non-linear saturation effects of partons in protons at HERA. Current HERA running does not focus on this physics, and facility will soon be shut down.Interesting hints in proton (deuteron) nucleus reactions at RHIC, but at a rather soft scale. Photon Jet or Jet Jet correlations that pin down x1 and x2 may shed more light.Key future is much larger x reach at high Q2 at the LHC, or with Deep Inelastic Scattering at future electron ion collider (EIC or eRHIC).

Collision Dynamics

RHIC = Gluon Collider

10,000 gluons, quarks, and antiquarks are made physical in the laboratory !

What is the nature of this ensemble of partons?

Can be dismissed with some basic General Relativity

metersc

GMRS49

2 102

metersR 1510

much less than

Planck length !

Even if it could form, it would evaporate by

Hawking Radiation in 10-83 seconds !

End of the World!

Start with Simpler SystemOPAL Event Display

Electron-Positron Annihilation

(Mueller 1983)

)/exp( sAsch BN

e+ e-

q

q

Quark radiates gluons and eventually forms hadrons in a jet cone.

QCD calculation of gluon multiplicity times a hadron scale factor gives excellent agreement with data.

e+e- qq hadron jets

Becattini et al., hep-ph/9701275

If we assume everything is produced statistically (phase space) or from thermal equilibrium, we get a reasonable description too.

Key feature is that strangeness is suppressed relative to its mass and energy.

Thermal / Statistical Model

pQCD versus Statistical ModelsEvent to Event fluctuations or within Event fluctuations can be discriminating. For example, some events have quark jets and some also have gluon jets.

Bjorken speculated that in the “interiors of large fireballs produced in very high-energy pp collisions, vacuum states of the strong interactions are produced with anomalous chiral order parameters.”

Tim

e

“Baked Alaska”

QGP in Proton Proton Reactions?

“High Energy Nuclear Events”, Prog. Theor. Phys. 5, 570 (1950)

Groundwork for statistical approach to particle production in strong interactions:

“Since the interactions of the pion field are strong, we may expect that rapidly this energy will be distributed among the various degrees of freedom present in this volume according to statistical laws.”

Fermi (1950)

Significant extension of Fermi’s approach

Considers fundamental roles of– Hydrodynamic evolution– Entropy

“The defects of Fermi’s theory arise mainly because the expansion of the compound system is not correctly taken into account…(The) expansion of the system can be considered on the basis of relativistic hydrodynamics.”

Landau (1955)

Experiments (E735, UA1, others) observe substantially larger source volumes in high multiplicity pp (pp) events via particle correlations and boosted pt spectra.

Rad

i us

( fm

)

dNch/d (charged) dNch/d (charged)<

p t>

(G

e V/ c

)

k

p

QGP Signatures?

Strangeness is enhanced in high multiplicity pp events, but not up to statistical equilibrium.

Watch out for autocorrelations. Higher multiplicity events have gluon jets which have higher strangeness!

RHIC experiments can add a lot to these measurements.

Nch

pt (GeV/c)

dNch/dR

ati o

Rat

i o

K/

Experiment E735

Strangeness Enhancement

Thermal / Statistical Model

Again, the statistical model works, with a remaining strangeness suppression.

Multiplicity Scaling

Both the Landau model (thermal fireball) and the pQCD (radiated gluon counting) give very similar scaling of multiplicity versus energy (?)

• Higher energy density may be achieved in proton-proton, but the partonic re-interaction time scale of order 1 fm/c.

• It is difficult to select events with different geometries and avoid autocorrelations.

• We will see that probes with long paths through the medium are key.

We should not rule out pp reactions, but rather study the similarities and differences with AA reactions.

Why Heavy Ions?

1. Initial Nuclei Collide

2. Partons are Freed from Nuclear Wavefunction

3. Partons interact and potentially form a Quark-Gluon Plasma

4. System expands and cools off

5. System Hadronizes and further Re-Scatters

6. Hadrons and Leptons stream towards our detectors

Heavy Ion Time Evolution

0 fm/c

2 fm/c

7 fm/c

>7 fm/c

Diagram from Peter Steinberg

Collision Characterization

Zero Degree Calorimeter

Spectators

Binary collisions

The impact parameter determines the number of nucleons that participate in the collision.

Participants = 2 x 197 - Spectators

Spectators

Participating nucleons

nn

np

pp

Participants

Out of a maximum energy of 39.4 TeV in central Gold Gold reactions, 26 TeV is made available for heating the system.

26 TeV of Available Energy !

Bjorken Energy Density• At t=tform, the hatched volume contains all particles w/ b<dz/tform:

• At y=b||=0, E=mT, thus:

• We can equate dN<mT> & dET and have:

Two nuclei pass through one another leaving a region of produced particles

between them.

)0@(; ||||

yddydy

dN

t

dz

d

dN

t

dzdN

formform

At

m

dy

tdN

Adz

mdN

V

Et

form

TformTform

)(

)(

dy

tdE

Att formT

formformBJ

)(1)(

Energy Density

R2

2c

dy

dE

cRT

Bj 22

112

PHENIX: Central Au-Au yields

GeVd

dET 25030

Energy density far above transition value predicted by lattice.

We start out with a system completely out of equilibrium and lots of kinetic energy.

We can try to use the Grand Canonical Ensemble to calculate the abundances of all the final measured particles.

1

1/)(

kTs sen

Depends on Temperature and Chemical Potential.

Fermions or Bosons

Grand Canonical Ensemble

2 2

3

3 ( ) /

1

2 1Bi i p m T

d pN g V

e

My system.

Infinite heat bath with which my system can exchange energy and particles, hence we have a temperature and chemical potential.

Grand Canonical Ensemble

Heavy Ions GCE

Works very well again, but now almost no additional suppression of strangeness.

Consider canonical ensemble in smaller systems?

Statistical Model using Grand Canonical Ensemble

One can use the GCE even when energy and other quantum numbers are conserved. The temperature and chemical potentials simply reflect characteristics of the system. Fluctuation calculations are not valid.

If the volume of the system is large, GCE is appropriate. For small volumes, you must conserve quantum numbers (for example strangeness) in every event !

Thus the Canonical Ensemble is relevant. In the CE, strangeness is suppressed for very small volumes and reaches the GCE limit for large volumes. Volume (fm3)

Canonical Ensemble

Hadronic rescattering can equilibrate overall strangeness (ie. K+, K-, ) in 10-100 fm/c and strange antibaryons () in over 1000 fm/c !

Heavy Ion collision lifetime is of order 10-15 fm/c before free streaming.

Quark-gluon plasma may equilibrate all strange particles in 3-6 fm/c !

Strangeness Enhancement

“A particularly striking aspect of this apparent ‘chemical equilibrium’ at the quark-hadron transition temperature is the observed enhancement of hadrons containing strange quark relative to proton-included collisions.

Since the hadron abundances appear to be frozen in at the point of hadron formation, this enhancement signals a new and faster strangeness-producing process before or during hadronization, involving intense rescattering among quarks and gluons.”

Becattini et al hep-ph/0011322, hep-ph/0002267

RHIC

dduu

sss

2

factor ~2

Strangeness Suppression

The enhancement of total strangeness appears quite similar at AGS, SPS, and now RHIC !

This challenges any model QGP model for enhancement. All systems are approaching something that looks statistically equilibrated, and we already see this trend in proton induced collisions.

Strange Patterns

Strangeness Enhancement

NA57 (open)STAR (filled)

Collision Dynamic Summary

- Depositing majority of kinetic energy into new medium

- Energy density appears above phase transition value

- Energy is distributed into particle production statistically including equivalent strangeness production

- No sharp global feature distinct from smaller hadron collisions, but instead gradual changes