Heavy Ion Physics at the LHC

• QCD at high temperature: the quark-gluon plasma• Probes of ultradense matter • Structure of nuclei at small x• Matter formation and breakup• Insights from the first 3 years of RHIC • The LHC heavy ion programme

Scottish Universities' Summer School 57

St. Andrews August 18 – 29, 2003

Part I

QCD at high temperature:

The quark-gluon plasma (QGP)

Matter under extreme conditions

1. Squeeze slowly Cold, dense matter2. Squeeze fast Hot, “dense” matter

(1) is much more difficult to do than (2): Beyond nuclear matter density (?B > ?0 = 0.15 fm-3) only in the core of collapsed (neutron) stars.

(2) Happened once: t < 20 s after it all began.Can also be achieved by colliding nuclei at high energy. 20 years of history: Bevalac, AGS, SPS, RHIC LHC.Goal: energy density e » MN ?0 = 0.14 GeV/fm3.

The Big Bang “experiment”

Thermal history of the universe

The “Little Bang” experiment

Au+Au Collision at RHIC

The “Little Bang”

Quantum chromodynamics

1QCD 4

a

a

ff

a

a

a

a

f

G G

g

m

L

A t

Degrees of freedom

• At extreme (energy) density, particle masses can be neglected relative to the kinetic energy:

/2 2

3

3(t

2i

)w h

1E T

d pE

E

ep m

24 7 / 8(fermions)

with1 (bosons)30

aaT

2

Quarks:

Gluon

2 2 12

): 2 1s ( 16C F F

C

N N N

N

Hadrons or quarks & gluons?

If QCD had NF light quark flavors, there would be (NF

2-1) nearly massless Goldstone bosons (“pions”):

2 1FN

For large NF the pions win out over quarks, but for NF=2-3 the quarks and gluons win out:

at high T matter is composed of a colored plasma of quarks and gluons, not of hadrons!

From hadrons to QGP

2 430 T

QCD equation of state from lattice QCD

Hadron gas

0

QGP = quark-gluon plasma

0

Is there a phase transition?

Most likely: NOT

Crossover of phases

Susceptibilities peak at Tc, but do not diverge. Vacuum properties change smoothly, but rapidly “crossover”

A phase transition at high baryon density

Controls baryon density

First order phase transition line

( )c BT

Color screening

2 ( ) ( )a a b a bG Qg g

3 1( ) / 2

3Tr 1

(2 )

b ba a E g t T ad pt e

Induced color density

2 2 2 2( ) ,wit (6

h )FG Q

NgT gT

Static color charge (heavy quark) generates potentiala a rst e

r

Color screening (lattice)

Linear confining potential disappears above Tc 160 MeV

Perturbative screening

r in units of 0.45 fm

Screened potential

The perturbative QGP

At T > 2Tc the QGP looks perturbative (neglect mq):

2 24 4

2 2 2 2122

15 5016 211 1

4 30 21 30

2 31 ( )

s sF

sq q

q

T N T

T

Expansion in s does notconverge, rather one must include interactions into the particle modes (“quasiparticles”) as basis for the expansion.

Quasiparticles in the QGP

Physical excitation modes at high T are not elementary quarks and gluons, but “dressed” quarks and gluons:

( , )k

T

Propagator of transversely polarized gluons

1 2 2 21 1( , ) ( ) 1 ln

2 2

k kD k k gT

k k

Effective mass of gluon:

0*

0*

1

31

2

kG

kG

m gT

m gT

Compton scattering on a thermal gluon!

QCD phase diagram

LHC

LHCinitial

state

RHIC

Color super-conducting quark matter

Part II

Probes of ultra-dense matter

Signatures of a QCD phase change

• Effects of “latent heat” in (E,T) relation

• Effects of large CV on thermal fluctuations

• Net charge and baryon number fluctuations

• Enhancement of s-quark production

• Thermal l+l- and radiation

• Disappearance of light hadrons (?0)

• Dissolution of ? , Y bound states

• Large energy loss of fast partons (jet quenching)

• Bulk hadronization

• Collective vacuum excitations (DCC)

Thermodynamics near Tc

2 4DOF30 g T

Additional energy is used up to liberate new degrees of freedom (color!) in transition region

T

E

Hadrons at the boiling point ?

Plateau is an indicator of latent heat of phase transformation.

RHIC

SPS

AGS

Anisotropic or “elliptic” flow is defined for b > 0 collisions.

Elliptic Flow

Elliptic flow “measures” the transverse pressure at very early times ( < 3 fm/c).

More flow in collision plane than perpendicular to it.

Force P

• Reaction plane analysis

dN/d 1 + 2v2cos2( lab- plane)

• Two-particle correlationsdN/d( 1- 2)

1 + 2v22cos(2[ 1- 2])

• Four-particle correlations

exp[i2( 1+ 2- 3- 4)] = -v24

Strangeness enhancement…

1

10

100

1000

10000

100000

1000000

u d s c b t

Q CD mass

Higgs mass

Flavor

Mass (MeV)

(sss)

(qss)

(qqs)

NA57 data

…probes chiral symmetry restoration and deconfinement

Charmonium suppression…

VQQ(r) is screened at distance scales r > (gT)-1

heavy quark bound states dissolve above some Td: J/ suppression.

Karsch et al.

But: J/ may survive above Td as a narrow resonance, as recent lattice calculations of the spectral function suggest.

Or charmonium enhancement?

If more than one c-quark pair is formed within y 1, and if the c-quarks are thermalized, J/ may be formed by recombination:

J/

This could easily result in a large enhancement of J/ production under LHC conditions. Depends critically on the stopping power for c-quarks (less than for light quarks)

J/ suppression

Data are consistent with:Hadronic comover breakup w/o QGPLimiting suppression via surface emissionDissociation + thermal regeneration

Energy/Momentum

High-energy parton loses energy by

rescattering in dense, hot medium.q

q

Jet Quenching

Can be described as medium effect on parton fragmentation:

2 2 2

1 /( , ) ( , ) ,p h p h p h

E E

zD z Q D z Q D Q

Radiative energy loss:2/ TdE dx L k

q q

g

Scattering centers = color charges

L

Energy loss in QCD

Gluon radiation is suppressed due to multiple scattering by LPM effect. LPM suppression differs from QED due to rescattering of the radiated gluon. Critical frequency:

212

ˆc qL 2 22

ˆd

q q dqdq

with

Energy loss spectrum for a fast parton is

2 2

( ) exp2 2

c cD

Radiative energy loss is suppressed like ( c/E)1/2 overall, and more strongly at small (Landau-Pomeranchuk-Migdal effect).

2( 2 / ) :sC

Energy loss in QCD - II

For power law parton spectrum ( pT-v)

energy loss leads to an effective momentum shift for fast partons (BDMS):

2ˆ /T s Tp qL p

Including expansion: 2 2 00

ˆ2ˆ ˆ ( , )

( )eff

qqL q L d r

r

Scattering “power” of QCD medium:

22

2T

2ˆd

q q dqdq

k

Density of scattering centers

Property of medium (range of color force)

Quenching factor: T2 2T T

( )dN dN

Q pd p d p

Analytical model: Surface emission

2 2 2 2 2 2 2 232 max D2( / ) ( ) ln /s sq dq d dq C q

0.5 ln(…) for gluons; 0.25 ln(…) for quarks

( )AAQ R

partons hadrons

02( )( )

( 1)T

TTR

p pQ p

p

Volume / R = surface

= QCD energy loss parameter:

= final dN/dy / volume

Jet correlations

Quenching provides a mechanism for generating an anisotropy with respect to the collision plane for hadron production in non-central collisions. The predicted anisotropy is less than 10%.

E L

Away-side jet

Q R/R

2asj' ( / )Q R R Q Q

Back-to-back jets (leading hadrons) are quadratically suppressed!

Part III

The initial state:

Structure of nuclei at small x

Au+Au Collision at RHIC

Hard scattering

Space-time picture of a HI collision

Equilibration

Expansion

Hadronization

Initial state: The naïve picture

20

1

( , ) ( , , ) ( , )h

i i

NN N

a a ai

F r k P k P Q R r R

For partons of flavour a in a nucleus the distribution is given by:

2 2 20 0( , , ) ( , ) ? ( ) d( ) d ( )i iN N A

a a a zP k P Q F x Q g k P P P

with the initial momentum distribution:

(Q0: initial resolution scale, ?A optional shadowing, g: opt. primordial kT)

boosted( , ) d( ) ( ) ( )i i

i

N Na AB a NR r R R b h r H R

and the initial spatial distribution:

• HN: distribution of nucleons in nucleus (e.g. Fermi-Distribution)• ha: distribution of partons in hadron (based on elastic form factor)

Initial state II: Parton momenta

• flavour and x are sampled from PDFs at an initial scale Q0 and low x cut-off xmin

• initial kt is sampled from a Gaussian of width Q0 (case of no initial state radiation)

Initial State III: Spatial Distribution

/3

1( ) with 0.24 fm

8N rah r e

• partons are spatially distributed according to elastic form factor of nucleon:

• Lorentz contraction utilizing y*; on-shell rapidity of partons, or rz~1/pz

rest frame

Parton saturation at small x

~ 1/Q2

2 1/3

2 2 2

(parton density

, )= r 1

a ea sA

A

xG x Q A x

R Q Q

2 1/3satQ A x from HERA data

DGLAP splitting:

GLRMQ parton fusion:

Parton saturation II

Saturation suggests a picture of quasiclassical glue fields at small x, where gA k, and the perturbation expansion is in powers of s, but not in powers of gA. In the extreme limit (x 0) the probability distribution of classical color fields is random and completely determined by the saturation scale:

2 2 2 2sexp ( ) /P A d x g A x Q

This ensemble of fields is called color glass condensate.

Qs evolves with x and satisfies a nonlinear RG equation, generalizing the BFKL equation, which is universal in the limit x 0, i.e. independent of the hadron species (meson, baryon, or even nucleus).

Parton saturation III

How many of these partons are “liberated” due to interactions when two nuclei collide?

In the limiting case (x 0 and s ) all partons are liberated, but PCM calculations suggest that the liberation probability drops for partons at small xat fixed collision energy s.

Baryon “stopping”

• net baryon contribution in the initial state (valence quark distribution) extends to small x, and accounts for a net baryon density at mid-rapidity dN/dy 5

• parton rescattering in the PCM then fills up the mid-rapidity region to explain the net baryon density observed in Au+Au collisions at RHIC.• At the LHC, the midrapidityregion is almost completely net baryon free.

13( ) [ ( ) ( )]q q

q

B x f x f xNet baryon number content of a hadron or nucleus:

RHIC

LHC

Part IV

Matter formation and breakup

Hard scattering

Space-time picture of a HI collision

Equilibration

Expansion

Hadronization

Equilibration and expansion

* Hard scattering: Occurs on short time scale t 1/Q < 1/Qs

and is described by pQCD.

* Equilibration: Can be described by multiple parton scattering in the PCM or by chaotic dynamics of classical color fields. Characteristic time scale: t 1/g2T.

* Expansion of the QGP: Described by relativistic fluid dynamics. Simplest case = boost invariant longitudinal flow (Bjorken model) gives cooling like T(t) 1/t1/3.

* Hadronization: Slow or fast – that is the question!

Hadron formation

qq

q

Baryon1

Meson

Fragmentation

q q

q q q

Baryon1

Meson

Recombination

Assumptions:

• Quarks and antiquarks recombine into hadrons locally “at an instant”:

• Gluons get absorbed into valence quarks before hadronization

• Competition between fragmentation and recombination;

• Hadron momentum P much larger than internal momentum p2 of the quark wave function of the hadron;

• Parton spectrum has thermal part (valence quarks) and a power law tail(quarks and gluons) from pQCD.

Sudden recombination model

qq M qqq B

recombinationfragmentation

Recombination of thermal quarks

2M

M3 3,

2B

B3 3, ,

( , ) ( , (1 ) ) ( )(2 )

' ( , ) ( , ' ) ( , (1 ') ) ( , ')(2 )

dN P uE d dxw R xP w R x P x

d P

dN P uE d dxdx w R xP w R x P w R x x P x x

d p

( , )w r p Quark distribution function at “freeze-out”

Relativistic formulation using hadron light-cone frame:

For a thermal distribution ( , ) exp( / )w r p p u T

( , ) ( , (1 ) ) exp /

( , ) ( , ' ) ( , (1 ') ) exp /

w R xP w R x P P u T

w R xP w R x P w R x x P P u T

Meson

Baryon

Recombination vs. Fragmentation

1h 1

h3 3 30

( , ) ( )(2 ) z

dN P u dzE d w r P D z

d P zFragmentation:

… always wins over fragmentation for an exponential spectrum:

… but loses at large pT, where the spectrum is a power law ~ (pT)-b

expexp / )( / ) ( /P u zT w P zP u T

Recombination… ( , ) ( , (1 ) ) exp /

( , ) ( , ' ) ( , (1 ') ) exp /

w r xP w r x P P u T

w r xP w r x P w r x x P P u T

Meson

Baryon

Apparent paradox: At given value of pT …• The average hadron is produced by recombination• The average parton fragments

Model fit to hadron spectrum

Teff = 350 MeVfitted to spectrum

shifted pQCD spectrum

R.J. Fries, BM, C. Nonaka, S.A. Bass (PRL in print)

2.2 GeV

Part V

Insights:

The first 3 years of RHIC

RHIC & its detectors

STAR

CM energy500 GeV for p-p200 GeV (per N-N) for Au-Au

LuminosityAu-Au: 2 x 1026 cm-2 s-1

p-p : 2 x 1032 cm-2 s-1

The Solenoidal Tracker At RHIC

Endcap Calorimeter

ZCal

Time Projection Chamber

Magnet

Coils

RICH * yr.1 SVT ladder

TPC Endcap & MWPC

ZCal

Central Trigger Barrel

FTPCs

Silicon Vertex Tracker *

Vertex Position Detectors

2001

+ TOF patch

Barrel EM Calorimeter

20032000

PHENIX (central part)

Not showing the North and South muon arms

PHOBOS & BRAHHMS

Flavour equilibration

The statistical (thermal) model for hadron abundances works well with T Tc

Parametrization of transverse flow

Blast wave parametrizationfit for STAR data works well for ,K,P, . Multiply strange baryons , show less, but still substantial flow: These particles with smaller interaction cross section decouple earlier; much flow is generated before the hadronization.

,

,K,P,

STAR preliminary

tanh

0 spectra in peripheral AuAu and pp

Au+Au binary Au+Au

pp

Yield N

Yield

/R=

70-80% PeripheralNbin =12.3 ±4.0

Au+Au

Suppression of high-pT hadrons in Au+Au collisions

PHENIX Data: Identified 0

Same side jet

Away side jet

STAR

Charged hadron suppression

suppression increases with centrality

Suppression patterns: baryons vs. mesons

What makes baryons different from mesons ?

Central

Peripheral

p / ratioHIGH-ENERGY PHYSICS:Wayward Particles Collide With Physicists' Expectations

Charles Seife

EAST LANSING --At a meeting here last week, resear-chers announced results that, so far, nobody can explain. By slamming gold atoms together at nearly the speed of light, the physicists hoped to make gold nuclei melt into a novel phase of matter called a quark-gluon plasma. But al-though the experiment produced encoura-ging evidence that they had succeeded, it also left them struggling to account for the behavior of the particles that shoot away from the tremen-dously energetic smashups.

Hadron spectra I

Hadron spectra II

Hadron dependence of high-pt suppression

• R+F model describes different RAA behavior of protons and pions

• Jet quenching becomes universal in the fragmentation region

Azimuthal anisotropy v2

)(tan,2cos 12

x

y

p

pv

Coordinate space: initial asymmetry

Momentum space: final asymmetry

pxx

y

Semiperipheral collision

Collective flow behavior extends to higher pT for baryons (p, ) than mesons ( ,K)

Mesons and baryons behave differently

Does v2 reflect parton flow?

Recombination model suggests that hadronicflow reflects partonicflow (n = number of valence quarks):

2 2v vhad partn

had partT Tp np

Provides measurement of partonic v2 !

P. Sorensen (UCLA – STAR)

d+Au compared with Au+Au

Nucleus-nucleus

collision

Proton/deuteronnucleus

collision

“Centrality” Dependence

• Dramatically different and opposite centrality evolution of Au+Au experiment from d+Au control.

Au + Au Experiment d + Au Control Experiment

Preliminary DataFinal Data

Azimuthal distributions

pedestal and flow subtracted

No back-side jet in central Au+Au

CONCLUSION

The strong suppression of the inclusive yield and back-to-back correlations at high pT previously observed in central Au+Au collisions are due tofinal-state interactions with the dense mediumgenerated in such collisions.

Part VI

The LHC heavy ion programme

What’s different (better) at the LHC ?

• Higher energy density 0 at earlier time 0.• Jet physics can be probed to pT > 100 GeV.• b, c quarks are plentiful, good probes.• Increased lifetime of QGP phase (10-15 fm/c)

Initial state effects less important.• QGP more dominant over final-state hadron

interactions.

Much larger “dynamic range” compared to RHIC

ECM dependence of dN/dy, dE/dy

NLO pQCD with geometric parton saturation (Eskola et al. - EKRT)

Overestimate of growth of dN/dy, dE/dy with ECM ??

RHIC

LHC

RHIC

LHC

Jet quenching at the LHC

Hadron production at the LHC

r = 0.75

r = 0.85

r = 0,65

R.J. Fries et al.

Includes estimated parton energy loss

Photon tagged jets

High-energy photon defines energy of the jet, but remains unaffected by the hot medium.

qg

Parton energy loss is measured by the suppression of the fragmentation function D(z) near z 1 .

Measuring the density

2

2

s qed u s

dt s s u

R.J. Fries, BM, D.K. Srivastava, PRL 90 (2003) 132301

gq

q + g q +

q + q g +

Backscattering probes the plasma density and initial parton spectrum

One dedicated HI experiment: ALICE

One pp experiment with a HI program: CMS

One pp experiment considering HI: ATLAS

LHC running conditions for Pb+Pb

• CM energy: 5.5 TeV/NN

• Luminosity: Lmax = 1 1027 cm-2s-1

• Charged multiplicity– Estimates dN/dy = 2 – 3000– Design for dNch/dy|max = 8000

• Event rate:

– 8000 minimum bias coll./ s– 109 events/year– 1% recorded

x 200

The ALICE Experiment

ITSLow pt trackingVertexing

ITSLow pt trackingVertexing

TPCTracking, dEdxTPCTracking, dEdx

TRDElectron IDTRDElectron ID

TOFPIDTOFPID

HMPIDPID (RICH) @ high pt

HMPIDPID (RICH) @ high pt

PHOS, 0

PHOS, 0

MUONS MUONS

PMDmultiplicity

PMDmultiplicity

ALICE central detector acceptance

0

-1

1

-2

2

0 1 2 3 pt

PHOSHMPID

TRD TOF

TPC

ITS tracking

ITS multiplicity

20 100

Muon arm: 2.4< <4 , PMD: 2.3< <3.5 , FMD: -5.4< <-1.6, 1.6< <3

ALICE event display for Pb+Pb

TRDTRD

HMPIDHMPID

TOFTOF

TPCTPC

PHOSPHOS

2 slice of TPC2 slice of TPC full TPC volumefull TPC volume

Unstable particles: K*, D

M(K+ -) (GeV/c2)

K*0

D0

K*0 K+ -

D0 K- +Detection of unstable neutral hadrons via “V” decays in TPC.

Quarkonia in ALICE

• M =94.5 MeV/ c2

at t he • Separ at ion of , ’, “• Tot al ef f iciency ~ 75%• Expect ed st at ist ics (kevent s – 1 mont h):

central min. biasJ/ 310 574

’ 12 2339 69

‘ 19 35“ 12 22

Quarkonia in CMS

J / f amily

Yield/month (kevents, 50% eff)(including barrel and endcaps)

Pb+Pb, 1 month at L=10Pb+Pb, 1 month at L=102727

Pb+Pb Sn+Sn Kr+Kr Ar+Ar

L 1027 1.7 1028 6.6 1028 1030

J/ 28.7 210 470 2200

' 0.8 5.5 12 57

22.6 150 320 1400

' 12.4 80 180 770

'' 7 45 100 440

Jet Reconstruction in CMS

• Subtract average pileup• Find jets with sliding window• Build a cone around ET

max

• Recalculate pileup outside the cone

• Recalculate jet energy

WindowAlgorithm

Full jet reconstruction in Pb+Pb central collisions (dN/dy~8000)Efficiency Measured jet energy Jet energy resolution

Balancing or Z0 vs Jets: Quark Energy Loss

ETjet, >120 GeV in the barrel

Jet+ Z0

ET// 0-ET

Jet (GeV)

<E>=8 GeV<E>=4 GeV<E>=0 GeV

Background

Isol. 0+jet

, Z0

1 month at1027 cm-2s-1

Pb+Pb

Conclusions

• ALICE, CMS, (and ATLAS ?) are nicely complementary in their physics capabilities to study hot, ultradense matter created in nuclear collisions.

• Hard probes (jets, heavy quarkonia) extend the range of matter probes into regimes that allow for more reliable calculations.

• Hadrons containing b- and c-quarks will become abundant components in the final state.

• Soft probes are governed by quantitatively so different parameters that conclusions drawn from RHIC data can be put to a serious test.

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