The Physics of Relativistic Heavy Ion Collisions

Lecture #2

18 th National Nuclear Physics Summer School Lectures July 31-August 3, 2006 Associate Professor Jamie Nagle University of Colorado, Boulder

Heavy Ion Experiments

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

How to Access This Physics?

Big Bang Only one chance… Who wants to wait?… Lattice QCD RHIC Neutron stars Slide from Jeff Mitchell

Kinetic Energy



Thermal Energy

Energy Frontier History

1992 Au-Au 1994 Pb-Pb 2000 Au-Au 2007?

Pb-Pb Bevalac-LBL and SIS-GSI fixed target max.

2.2 GeV

AGS-BNL fixed target max.

4.8 GeV

E864/941, E802/859/866/917, E814/877, E858/878, E810/891, E896, E910 … SPS-CERN fixed target max.

17.3 GeV

NA35/49, NA44, NA38/50/51, NA45, NA52, NA57, WA80/98, WA97, … TEVATRON-FNAL (fixed target p-A) max.

38.7 GeV

RHIC-BNL collider max.

200.0 GeV

LHC-CERN collider max.

2760.0 GeV

BRAHMS, PHENIX, PHOBOS, STAR ALICE, ATLAS, CMS

Why Energy Matters?

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.

250 200 RHIC/LHC

quark-gluon plasma

Bevalac-LBL 2.2 GeV AGS-BNL 4.8 GeV SPS-CERN 17.3 GeV Nuclear Fragmentation Resonance Production Strangeness Near Threshold Resonances Dominate Large Net Baryon Density Strangeness Important Charm Production Starts TEVATRON-FNAL 38.7 GeV 150 SPS AGS 100

LBL/SIS

50

hadron gas atomic nuclei

0 0 200 400 600 800 1000 1200 Net Baryon Density ~ Potential  B [MeV]

RHIC-BNL

200.0 GeV LHC-CERN 2760.0 GeV Low Net Baryon Density Hard Parton Scattering Beauty Production

RHIC is doing great !

STAR

Hadronic Observables over a Large Acceptance Event-by-Event Capabilities Solenoidal magnetic field Large coverage Time-Projection Chamber Silicon Tracking, RICH, EMC, TOF

PHENIX

Electrons, Muons, Photons and Hadrons Measurement Capabilities Focus on Rare Probes: J/ y , high-p T Two central spectrometers with tracking and electron/photon PID Two forward muon spectrometers

BRAHMS

Hadron PID over broad rapidity acceptance Two conventional beam line spectrometers Magnets, Tracking Chambers, TOF, RICH

PHOBOS

Charged Hadrons in Central Spectrometer Nearly 4 p coverage multiplicity counters Silicon Multiplicity Rings Magnetic field, Silicon Strips, TOF Paddle Trigger Counter TOF Spectrometer Octagon+Vertex Ring Counters

What Are Protons and Nuclei?

Structure of the Proton

See the whole proton Momentum transfer

Q 2 = 0.1 GeV 2

Wavelength l = h/p See the quark substructure

Q 2 = 1.0 GeV 2

See many partons (quarks and gluons)

Q 2 = 20.0 GeV 2

Parton Distribution Functions

Quarks Gluons

30!

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

Limitless 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?

Gluon Saturation

probe rest frame target rest frame

gg



g

r/  Wavefunction of low x gluons overlap and the self coupling gluons fuse, thus saturating the density of gluons in the initial state l

c ~1/x

-14 cm/ Q (GeV) Fluctuations from dipole increase and the unitary limit of the photon cross section in deep inelastic scattering is the equivalent to saturation.

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

Saturation in the Proton

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

Lowest x data is at modest Q 2 (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?

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).

Fermi Effect enhancement Saturation?

shadowin g EMC effect x  .1

x  .1

RHIC probes

x



2p T s

 10  2 x

Gluon Number Density

Gluon number density:  g = A xG N (x,Q 2 )/ p R 2 Gluon density depends on the nuclear overlap area ( p R 2 a A 2/3 ) and the momentum scale (Q 2 ) since DGLAP evolution requires: G(x, Q 2 ) ~ ln (Q 2 / L QCD 2 ) 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 Comparisons

In this saturation regime (sometimes termed the Color Glass Condensate), with one parameter (saturation scale Q s ) 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.

dN d

 

m T

2 cosh

y p T

2  sinh 2

y



cN part

 

s s o

  l 2 

e

 l

y

ln

Q s

2

e

 l L 2

QCD y

    1  l

y

  1 

Q s s e

l

y

/ 2   4   

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 x 1 =x 2 = 2p T /E cm x 1 x 2 p T E cm ~ 2 GeV ~ 200 GeV x ~ 0.04

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.

x 2 x 1

Suppression Factor R

R AA

(

p T

) 

d

2

N T AA d

2 

AA NN

/

dp T

/

d



dp T d



b Binary Collisions

R = 1 (binary collision scaling)

Participant

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.

d+Gold Probes

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

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

“Mono-jet”

Dilute parton system (deuteron)

MonoJets?

p 0

P T is balanced by many gluons

Dense gluon field (Au) STAR Experiment Tagged photons and jets at forward angles will give precise information on x dependence of saturation effect.

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?

1. Scaling of the total p-p cross section 3. Shadowing of structure functions in nuclei 2. Growth of low x gluons in the proton x 4. Particle production in nucleus-nucleus reactions

Saturation Summary

Interesting 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 x 1 may shed more light.

Key future is much larger x reach at high Q 2 and x at the LHC, or with Deep 2 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?

End of the World!

Can be dismissed with some basic General Relativity

R S

 2

GM c

2  10  49

meters

much less than Planck length !

R

 10  15

meters

Even if it could form, it would evaporate by Hawking Radiation in 10 -83 seconds !

Start with Simpler System

OPAL Event Display Electron-Positron Annihilation

e +

e+e-



qq



hadron jets

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

e -

N ch

 a

s A

exp(

B

/ a

s

)

(Mueller 1983)

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

Thermal / Statistical Model

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.

Becattini et al., hep-ph/9701275

pQCD versus Statistical Models

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

QGP in Proton Proton Reactions?

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.” “Baked Alaska”

Fermi (1950)

“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.”

Landau (1955)

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

.”

QGP Signatures?

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

Strangeness Enhancement

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

Experiment E735 Watch out for autocorrelations. Higher multiplicity events have gluon jets which have higher strangeness!

RHIC experiments can add a lot to these measurements.

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 (?)

Why Heavy Ions?

• 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 .

Heavy Ion Time Evolution

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

Diagram from Peter Steinberg >7 fm/c 0 fm/c 2 fm/c 7 fm/c

Collision Characterization

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

Binary collisions Participating nucleons Spectators

Participants = 2 x 197 - Spectators n n n p p p Zero Degree Calorimeter

Participants Spectators

26 TeV of Available Energy !

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

Bjorken Energy Density

• At t=t form , the hatched volume contains all particles w/ b

dN



dz t form dN d

 || 

dz t form dN

; (

dy dy



d

 || @

y

 0 ) • At y=b || =0, E=m T , thus:  (

t form

) 

E V



dN



dz



m T A

 

dN

(

t form

)

dy t



m T



form



A

 • We can equate dN & dE T and have: 

BJ

(

t form

)  1

t form



A dE T

(

t form

)

dy

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

Energy Density

Energy density far above transition value predicted by lattice.



Bj

 1 p

R

2 1 2

c

t   2

dE T dy

  p R 2 2c t PHENIX: Central Au-Au yields

dE T d

   0  503  2

GeV

Grand Canonical Ensemble

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.

n s

 1

e

( 

s

  ) /

kT

 1 Fermions or Bosons Depends on Temperature and Chemical Potential.

Grand Canonical Ensemble

My system.

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

N i



g V i

 3

d p

  3

e

( 1

p

2 

m

2  

B

) /

T

 1

Heavy Ions GCE

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

Consider canonical ensemble in smaller systems?

Canonical Ensemble

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.

Strangeness Enhancement

Hadronic rescattering can equilibrate overall strangeness (ie. K + , K , L ) in

10-100 fm/c

and strange antibaryons ( L, X, W ) in over

1000 fm/c

!

Quark-gluon plasma may equilibrate all strange particles in

3-6 fm/c

!

Heavy Ion collision lifetime is of order

10-15 fm/c

before free streaming.

“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 .

”

Strangeness Suppression

l

s



u u

2

s s



d d

factor ~2 RHIC

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

Strange Patterns

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.

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