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Heavy Ions and Quark-Gluon Plasma…. XXV SEMINARIO NAZIONALE di FISICA NUCLEARE e SUBNUCLEARE "Francesco Romano" EDIZIONE SPECIALE: IL BOSONE DI HIGGS. E. Scomparin INFN Torino (Italy). …to LHC!. From SPS…. …to RHIC…. Highlights from a 25 year-old story . Before starting….

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Heavy Ions and Quark-Gluon Plasma…


E. Scomparin

INFN Torino (Italy)

…to LHC!

From SPS…

…to RHIC…

Highlights from a

25 year-old story

Before starting….

  • Many thanks to all of my colleagues who produced many of the

  • plots/slides I will show you in these three lectures…..

…and in particular to my Torino colleagues Massimo Masera

and Francesco Prino. We hold together a university course on these

topics and several slides come from there

Why heavy ions ?

  • Heavy-ion interactions represent by far the most complex collision

  • system studied in particle physics labs around the world

  • So why people are attracted to the study of such a complex system ?

  • Because they can offer a unique view to understand

  • The nature of confinement

  • The Universe a few micro-seconds after the Big-Bang,

  • when the temperature was ~1012 K

  • Let’s briefly recall the properties of strong interaction…..

Strong interaction

  • Stable hadrons, and in particular protons and neutrons, which build up

  • our world, can be understood as composite objects, made of quarks

  • and gluons, bound by the strong interaction (colour charge)

  • 3 colour charge states (R,B,G) are

  • postulated in order to explain the

  • composition of baryons (3 quarks or

  • antiquarks) and mesons (quark-antiquark pair)

  • as color singlets in SU(3) symmetry

  • Colour interaction through 8 massless vector

  • bosons gluons

  • The theory describing the interactions of quarks and gluons was

  • formulated in analogy to QED and is called Quantum

  • Chromodynamics (QCD)

Coupling constant

  • Contrary to QED, in QCD the coupling constant decreases when

  • the momentum transferred in the interaction increases or, in other

  • words, at short distances

  • Express S as a function of

  • its value estimated at a certain

  • momentum transfer 

  • Consequences

  •  asymptotic freedom (i.e. perturbative calculations possible

  • mainly for hard processes)

  •  interaction grows stronger as distance increases

From a confined world….

  • The increase of the interaction strength, when for example a quark and

  • an antiquark in a heavy meson are pulled apart can be approximately

  • expressed by the potential

where the confinement term Kr parametrizes the effects

of confinement

  • When r increases, the colour field can be seen as a tube connecting the quarks

  • At large r, it becomes energetically favourable to convert

  • the (increasing) energy stored in the color tube to a

  • new qqbar pair

  • This kind of processes (and in general the phenomenology

  • of confinement) CANNOT be described by perturbative QCD,

but rather through lattice calculations or bag models, inspired to QCD

…to deconfinement

  • Since the interactions between quarks and gluons become weaker

  • at small distances, it might be possible, by creating a high

  • density/temperature extended system composed by a large number of

  • quarks and gluons, to create a “deconfined” phase of matter

  • First ideas in that sense date back to the ‘70s

”Experimental hadronic spectrum

and quark liberation”

Cabibbo and ParisiPhys. Lett. 59B, 67 (1975)

Phase transition at large T and/or B

Becoming more quantitative…

  • MIT bag model: a simple, phenomenological approach which contains

  • a description of deconfinement

  • Quarks are considered as massless particles contained in a finite-size bag

  • Confinement comes from the balancing of the pression from the quark

  • kinetic energy and an ad-hoc external pressure

Kinetic term

Bag energy

  • Bag pressure can be estimated by considering the typical hadron size

  • If the pression inside the bag increases in such a way that it exceeds the

  • external pressure  deconfined phase, or Quark-Gluon Plasma (QGP)

  • How to increase pressure ?

    • Temperature increase  increases kinetic energy associated to quarks

    • Baryon density increase  compression

High-temperature QGP

  • Pressure of an ideal QGP is given by

  • with gtot(total number of degrees of freedom relative to quark, antiquark

  • and gluons) given by gtot = gg + 7/8  (gq + gqbar) = 37, since

gg = 8  2 (eight gluons with two possible polarizations)

gq = gqbar = Ncolor Nspin Nflavour= 3  2  2

  • The critical temperature where QGP pressure is equal to the bag

  • pressure is given by

and the corresponding energy density =3P is given by

High-density QGP

  • Number of quarks with momenta between p and p+dp is (Fermi-Dirac)

where q is the chemical potential, related

to the energy needed to add one quark to

the system

  • The pressure of a compressed system of quarks is

  • Imposing also in this case the bag pressure to be equal to the pressure

  • of the system of quarks, one has

  • which gives q = 434 MeV

  • In terms of baryon density this corresponds to nB = 0.72 fm-3, which is

  • about 5 times larger than the normal nuclear density!

Lattice QCD approach

  • The approach of the previous slides can be considered useful only

  • for what concerns the order of magnitude of the estimated parameters

  • Lattice gauge theory is a non-perturbative QCD approach based on a

  • discretization of the space-time coordinates (lattice) and on the

  • evaluation of path integrals, which is able to give more quantitative

  • results on the occurrence of the phase transition

  • In the end one evaluates the partition function and consequently

    • The thermodynamic quantities

    • The “order parameters” sensitive to the phase transition

  • This computation technique requires intensive use of computing resources

  • “Jump” corresponding to the

  • increase in the number of degrees

  • of freedom in the QGP

  • (pion gas, just 3 degrees of freedom,

  • corresponding to +, -, 0)

  • Ideal (i.e., non-interacting) gas

  • limit not reached even at high

  • temperatures

Phase diagram of strongly interacting matter

  • The present knowledge of the phase diagram of strongly interacting

  • matter can be qualitatively summarized by the following plot

  • How can one “explore” this phase diagram ?

  • By creating extended systems of quarks and gluons at

  • high temperature and/or baryon density  heavy-ion collisions!


Facilities for HI collisions

  • The study of the phase transition requires center-of-mass energies of

  • the collision of several GeV/nucleon

  • First results date back to the 80’s when existing accelerators and

  • experiments at BNL and CERN were modified in order to be able to

  • accelerate ion beams and to detect the particles emitted in the collisions

From fixed-target…

  • SPS at CERN

  • p beams up to 450 GeV

  • O, S, In, Pb up to 200 A GeV

  • AGS at BNL

  • p beams up to 33 GeV

  • Si and Au beams up to 14.6 A GeV

Remember Z/A rule !

… to colliders!

  • RHIC: the first dedicated machine for HI collisions (Au-Au, Cu-Cu)

    • Maximum sNN = 200 GeV

  • 2 main experiments : STAR and PHENIX

  • 2 small(er) experiments: PHOBOS and BRAHMS

… to colliders!

  • LHC: the most powerful machine for HI collisions

    • sNN = 2760 GeV(for the moment!)

  • 3 experiments studying HI collisions: ALICE, ATLAS and CMS

How does a collision look like ?

  • A very large number of secondary particles is produced

    • How many ?

    • Which is their kinematical distribution ?

Kinematical variables

  • The kinematical distribution of the produced particles are usually

  • expressed as a function of rapidity (y) and transverse momentum (pT)

  • pT:Lorentz-invariant with respect to a boost in the beam direction

  • y: no Lorentz-invariant but additive transformation law  y’=y-y

  • (where y is the rapidity of the ref. system boosted by a velocity )

  • y measurement needs particle ID (measure momentum and energy)

  • Practical alternative: pseudorapidity ()

y~ for relativistic particles

  • Alternative variable to pT: transverse mass mT

Typical rapidity distributions

Fixed target: SPS

  • pBEAM=158 GeV/c, bBEAM=0.999982

  • pTARGET=0 , bTARGET=0


largest density of

produced particle

Collider: RHIC

  • pBEAM=100 GeV/c

  • b=0.999956, gBEAM≈100


Multiplicity at midrapidity

SPS energy

RHIC energy

LHC energy (ALICE)

  • Strong increase in the number of produced particles with s

  • In principle more favourable conditions at large s for the creation of an

  • extended strongly interacting system

Multiplicity and energy density

  • Can we estimate the energy density reached in the collision ?

  • Important quantity: directly related to the possibility of observing

  • the deconfinement transition (foreseen for   1 GeV/fm3)

  • If we consider two colliding nuclei with Lorentz-factor , in the instant

  • of total superposition one could have

 at RHIC energies 


  • But the moment of total overlap is very short!

    •  Need a more realistic approach

  • Consider colliding nuclei as thin pancakes (Lorentz-contraction)

  • which, after crossing, leave an initial volume with a limited longitudinal

  • extension, where the secondary particles are produced

Multiplicity and energy density

  • Calculate energy density at the time f (formation time) when the

  • secondary particles are produced

  • Let’s consider a slice of thickness z and transverse area A. It will

  • contain all particles with a velocity

(y~ when

y is small)

The number of particles

will be given by

Multiplicity and energy density

  • The average energy of these particles is close to their average

  • transverse mass since E=mTcosh y ~ mT when y0

  • Therefore the energy density at formation time can be obtained as



  • Assuming f ~ 1 fm/c one gets

  • values larger than 1 GeV/fm3!

  • Compatible with phase transition

  • With LHC data one gets Bj ~ 15 GeV/fm3

  • Warning: f is expected to decrease when increasing s

  • For example, at RHIC energies a more realistic value is f~0.35-0.5 fm/c

Time evolution of energy density

  • One should take into account that the system created in heavy-ion

  • collisions undergoes a fast evolution

  • This is a more realistic evaluation (RHIC energies)

Peak energy density

Energy density at


Late evolution:

model dependent

Time evolution of the collision

  • More in general, the space-time evolution of the collision is not trivial

  • In particular we will see that different observables can give us

  • information on different stages in the history of the collision

  • Soft processes:

  • High cross section

  • Decouple late

     indirect signals for QGP

EM probes (real and virtual photons): insensitive to the hadronization phase

  • Hard processes:

  • Low cross section

  • Probe the whole

    evolution of the collision

High- vs low-energy collisions

  • Clearly, high-energy collisions should create more favourable

  • conditions for the observation of the deconfinement transition

  • However, moderate-energy collisions have interesting features

  • Let’s compare the net baryon rapidity distributions at various s

  • Starting at top SPS energy, we observe

  • a depletion in the rapidity distribution

  • of baryons (B-Bbar compensates for

  • baryon-antibaryon production)

  • Corresponds to two different regimes:

    • baryon stopping at low s

    • nuclear transparency at high s

Explore different regions

of the phase diagram

Mapping the phase diagram





  • High-energy experiments  create conditions similar to Early Universe

  • Low-energy experiments  create dense baryonic system

Characterizing heavy-ion collisions

  • The experimental characterization of the collisions is an essential

  • prerequisite for any detailed study

  • In particular, the centrality of the collision is one of the most important

  • parameters, and it can be quantified by the impact parameter (b)

  • Small b  central collisions

    • Many nucleons involved

    • Many nucleon-nucleon collisions

    • Large interaction volume

    • Many produced particles

  • Large b  peripheral collisions

    • Few nucleons involved

    • Few nucleon-nucleon collisions

    • Small interaction volume

    • Few produced particles


Hadronic cross section

  • Hadronicpp cross section grows logarithmically with s

Mean free



RHIC (top)



  •  ~ 0.17 fm-3

  • ~70 mb

  • = 7 fm2

 ~ 1 fm

  • is small with

  • respect to

  • the nucleus size

  •  opacity

Laboratory beam momentum (GeV/c)

  • Nucleus-nucleus hadronic cross section can be approximated

  • by the geometric cross section

hadPbPb = 640 fm2 = 6.4 barn

(r0 = 1.35 fm,  = 1.1 fm)

Glauber model

  • Geometrical features of the collision determines its global characteristics

  • Usually calculated using the Glauber model, a semiclassical approach

  • Nucleus-nucleus interaction  incoherent superposition of

  • nucleon-nucleon collisions calculated in a probabilistic approach

  • Quantities that can be calculated

    • Interaction probability

    • Number of elementary nucleon-nucleon

    • collisions (Ncoll)

    • Number of participant nucleons (Npart)

    • Number of spectator nucleons

    • Size of the overlap region

    • ….

  • Nucleons in nuclei considered as point-like and non-interacting

  • (good approx, already at SPS energy =h/2p ~10-3 fm)

  • Nucleus (and nucleons) have straight-line trajectories (no deflection)

  • Physical inputs

    • Nucleon-nucleon inelastic cross section (see previous slide)

    • Nuclear density distribution

Nuclear densities

Core density

“skin depth”

Nuclear radius

Interaction probability and hadronic cross sections

  • Glauber model results confirm the “opacity” of the interacting nuclei,

  • over a large range of input nucleon-nucleon cross sections

  • Only for very peripheral collisions (corona-corona) some transparency

  • can be seen

Nucleon-nucleon collisions vs b

  • Although the interaction probability practically does not depend on

  • the nucleon-nucleon cross section, the total number of nucleon-nucleon

  • collisions does

inel corresponding to

the main ion-ion


Number of participants vs b

  • With respect to Ncoll, the dependence on the nucleon-nucleon cross

  • section is much weaker

  • When inel > 30 mb, practically all the nucleons in the overlap region

  • have at least one interaction and therefore participate in the collisions

inel corresponding to

the main ion-ion



Centrality – how to access experimentally

  • Two main strategies to evaluate the impact parameter in

  • heavy-ion collisions

    • Measure observables related to the energy deposited in the

    • interaction region charged particle multiplicity, transverse

    • energy ( Npart)

    • Measure energy of hadrons emitted in the beam direction

    •  zero degree energy ( Nspect)

…and now to some results…

  • Can we understand quantitatively the evolution of the fireball ?

Chemical composition ofthe fireball

  • It is extremely interesting to measure the multiplicity of the various

  • particles produced in the collision  chemical composition

  • The chemical composition of the fireball is sensitive to

    • Degree of equilibrium of the fireball at (chemical) freeze-out

    • Temperature Tchat chemical freeze-out

    • Baryonic content of the fireball

  • This information is obtained through the use of statistical models

    • Thermal and chemical equilibrium at chemical freeze-out assumed

    • Write partition function and use statistical mechanics

  • (grand-canonical ensemble)  assume hadron production is a

  • statistical process

    • System described as an ideal gas of hadrons and resonances

    • Follows original ideas by Fermi (1950s) and Hagedorn (1960s)

Hadron multiplicities vss

  • Baryons from colliding

  • nuclei dominate at low s

  • (stopping vs transparency)

  • Pions are the most

  • abundant mesons (low

  • mass and production

  • threshold)

  • Isospin effects at low s

  • pbar/p tends to 1 at

  • high s

  • K+ and  more produced

  • than their anti-particles

  • (light quarks present in

  • colliding nuclei)

Statistical models

  • In statistical models of hadronization

    • Hadron and resonance gas with baryons and mesons

    • having m  2 GeV/c2

      • Well known hadronic spectrum

      • Well known decay chains

  • These models have in principle 5 free parameters:

    • T : temperature

    • mB : baryochemical potential

    • mS : strangeness chemical potential

    • mI3 : isospin chemical potential

    • V : fireball volume

    • But three relations based on the knowledge of the initial state

    • (NS neutrons and ZS “stopped” protons) allow us to reduce the

    • number of free parameters to 2

Only 2 free parameters remain: T and mB

Particle ratios at AGS

  • Results on ratios: cancel a significant fraction of systematic uncertainties

  • AuAu - Ebeam=10.7 GeV/nucleon - s=4.85 GeV

  • Minimum c2 for: T=124±3 MeV mB=537±10 MeV

c2 contour lines

Particle ratios at SPS

  • PbPb - Ebeam=40 GeV/ nucleon - s=8.77 GeV

  • Minimum c2 for: T=156±3 MeV mB=403±18 MeV

c2 contour lines

Particle ratios at RHIC

  • AuAu - s=130 GeV

  • Valore minimo di c2 per: T=166±5 MeV mB=38±11 MeV

c2 contour lines

Thermal model parameters vs. s

  • The temperature Tch quickly

  • increases with s up to ~170 MeV

  • (close to critical temperature for the

  • phase transition!) at s ~ 7-8 GeV

  • and then stays constant

  • The chemical potential B decreases

  • with s in all the energy range

  • explored from AGS to RHIC

Chemical freeze-out and phase diagram

  • Compare the evolution vss of the (T,B) pairs with the QCD phase

  • diagram

  • The points approach the phase transition region already at SPS energy

  • The hadronic system reaches chemical equilibrium immediately after

  • the transition QGPhadronstakes place

News from LHC

  • Thermal model fits for yields

  • and particle ratios

  • T=164 MeV, excluding protons

  • Unexpected results for protons: abundances below thermal model

  • predictions  work in progress to understand this new feature!

Chemical freeze-out

  • Fits to particle abundances

  • or particle ratios in

  • thermal models

  • These models assume

  • chemical and thermal

  • equilibrium and describe

  • very well the data

  • The chemical freeze-out

  • temperature saturates

  • at around 170 MeV, while

  • B approaches zero at

  • high energy

  • New LHC data still

  • challenging

Collective motion in heavy-ion collisions (FLOW)

Radial flow  connection with thermal freeze-out

Elliptic flow connection with thermalization of the system

Let’s start from pT distributions in pp and AA collisions


  • Transverse momentum distributions of produced particles can provide important information on the system created in the collisions

  • Low pT(<~1 GeV/c)

  • Soft production

  • mechanisms

  • 1/pTdN/dpT ~exponential,

  • Boltzmann-like and almost

  • independent on s

  • High pT (>>1 GeV/c)

  • Hard production

  • mechanisms

  • Deviation from exponential

  • behaviour towards

  • power-law

Let’s concentrate on low pT

  • In pp collisions at low pT

    • Exponential behaviour, identical for

    • all hadrons (mTscaling)

  • Tslope~ 167 MeV for all particles

  • These distribution look like thermal spectra and Tslope can be seen as

  • the temperature corresponding to the emission of the particles, when

  • interactions between particles stop (freeze-out temperature, Tfo)


pTand mTspectra

  • Slightly different shape of spectra,

  • when plotted as a function of pTor mT

Evolution of pT spectra vsTslope,

higher T implies “flatter” spectra

Breaking of mT scaling in AA

  • Harder spectra (i.e. larger Tslope)

  • for larger mass particles

  • Consistent with a shift towards

  • larger pTof heavier particles

Breaking of mT scaling in AA

  • Tslopedepends linearly

  • on particle mass

  • Interpretation:

  • there is a collective

  • motion of all particles

  • in the transverse plane

  • with velocity v,

  • superimposed to

  • thermal motion,

  • which gives

Such a collective transverse expansion is called radial flow

(also known as “Little Bang”!)





Flow in heavy-ion collisions

  • Flow: collective motion of particles superimposed to thermal motion

  • Due to the high pressures generated when nuclear matter is heated

  • and compressed

  • Flux velocity of an element of the system is given by the sum of the

  • velocities of the particles in that element

  • Collective flow is a correlation between the velocity v of a volume

  • element and its space-time position

Radial flow at SPS



  • Radial flow breaks mT

  • scaling at low pT

  • With a fit to identified

  • particle spectra one can

  • separate thermal and

  • collective components

  • At top SPS energy

  • (s=17 GeV):

  • Tfo= 120 MeV

  •  = 0.50


Radial flow at RHIC



  • Radial flow breaks mT

  • scaling at low pT

  • With a fit to identified

  • particle spectra one can

  • separate thermal and

  • collective components

  • At RHIC energy

  • (s=200 GeV):

  • Tfo~ 100 MeV

  •  ~ 0.6


Radial flow at LHC

  • Pion, proton and kaon spectra

  • for central events (0-5%)

  • LHC spectra are harder than

  • those measured at RHIC

  • Tfo= 95  10 MeV

  •  = 0.65  0.02

Clear increase of radial flow at LHC,

compared to RHIC (same centrality)


Thermal freeze-out

  • Fits to pT spectra allow

  • us to extract the

  • temperature Tfoand the

  • radial expansion velocity

  • at the thermal freeze-out

  • The fireball created in

  • heavy-ion collisions

  • crosses thermal

  • freeze-out at 90-130

  • MeV, depending on

  • centrality and s

  • At thermal freeze-out the

  • fireball has a collective

  • radial expansion, with a

  • velocity 0.5-0.7 c




Anisotropic transverse flow

  • In heavy-ion collisions the impact parameter creates a “preferred”

  • direction in the transverse plane

  • The “reaction plane” is the plane defined by the impact parameter and

  • the beam direction





Anisotropic transverse flow

  • In collisions with b  0 (non central) the fireball has a geometric

  • anisotropy, with the overlap region being an ellipsoid

  • Macroscopically (hydrodynamic description)

    • The pressure gradients, i.e. the forces “pushing” the particles are

  • anisotropic (-dependent), and larger in the x-z plane

    • -dependent velocity  anisotropic azimuthal distribution of particles

  • Microscopically

  • Interactions between produced

  • particles (if strong enough!) can

  • convert theinitial geometric

  • anisotropy in an anisotropy in

  • the momentum distributions

  • of particles, which can be

  • measured

Reaction plane

Anisotropic transverse flow

  • Starting from the azimuthal distributions of the produced particles with

  • respect to the reaction plane RP, one can use a Fourier decomposition

  • and write

  • The terms in sin(-RP) are not present since the particle distributions

  • need to be symmetric with respect to RP

  • The coefficients of the various harmonics describe the deviations with

  • respect to an isotropic distribution

  • From the properties of Fourier’s series one has

v2 coefficient: elliptic flow

Elliptic flow

  • v2 0 means that there is a

  • difference between the

  • number of particles directed

  • parallel (00 and 1800) and

  • perpendicular (900 and 2700)

  • to the impact parameter

  • It is the effect that one may

  • expect from a difference of

  • pressure gradients parallel

  • and orthogonal to the impact

  • parameter



v2 > 0  in-plane flow, v2 < 0 out-of-plane flow

Elliptic flow - characteristics

  • The geometrical anisotropy which

  • gives rise to the elliptic flow

  • becomes weaker with the evolution

  • of the system

  • Pressure gradients are stronger in

  • the first stages of the collision

  • Elliptic flow is therefore an observable

  • particularly sensitive to the first stages

  • (QGP)

Elliptic flow - characteristics

  • The geometric anisotropy (X= elliptic deformation of the fireball)

  • decreases with time

  • The momentum anisotropy (p , which is the real observable), according

  • to hydrodynamic models:

    • grows quickly in the QGP state ( < 2-3 fm/c)

    • remains constant during the phase transition (2<<5 fm/c), which in

    • the models is assumed to be first-order

  • Increases slightly in the hadronic phase ( > 5 fm/c)

Results on elliptic flow: RHIC

  • Elliptic flow depends on

    • Eccentricity of the overlap region, which decreases for central events

    • Number of interactions suffered by particles, which increases for

    • central events

  • Very peripheral collisions:

    • large eccentricity

    • few re-interactions

    • small v2

  • Semi-peripheral collisions:

    • large eccentricity

    • several re-interactions

    • large v2

  • Semi-central collisions:

    • no eccentricity

    • many re-interactions

    • v2 small (=0 for b=0)


Hydrodynamic limit




v2vs centrality at RHIC

  • Measured v2 values are in good agreement with ideal hydrodynamics

  • (no viscosity) for central and semi-central collisions, using parameters

  • (e.g. fo) extracted from pT spectra

  • Models, such as RQMD, based on a hadronic cascade, do not

  • reproduce the observed elliptic flow, which is therefore likely

  • to come from a partonic(i.e. deconfined) phase

Hydrodynamic limit




v2vs centrality at RHIC

  • Interpretation

    • In semi-central collisions there is a fast thermalization and the

    • produced system is an ideal fluid

    • When collisions become peripheral thermalization is incomplete

    • or slower

  • Hydro limit corresponds to a perfect fluid, the effect of viscosity is

  • to reduce the elliptic flow

v2 vs transverse momentum

  • At low pThydrodynamics reproduces data

  • At high pT significant deviations are observed

  • Natural explanation: high-pTparticles quickly escape the fireball

  • without enough rescattering no thermalization, hydrodynamics

  • not applicable

v2vspTfor identified particles

  • Hydrodynamics can reproduce rather well also the dependence of

  • v2 on particle mass, at low pT

Elliptic flow, from RHIC to LHC

  • Elliptic flow, integrated over pT, increases by 30% from RHIC to LHC

In-plane v2 (>0) for very low √s: projectile and target form a rotating system

In-plane v2 (>0) at relativistic energies (AGS and above) driven by pressure gradients (collective hydrodynamics)

Out-of-plane v2 (<0) for low √s, due to absorption by spectator nucleons

Elliptic flow at LHC

  • The difference in the pT

  • dependence of v2 between

  • kaons, protons and pions (mass

  • splitting) is larger at LHC

  • v2 as a function of pTdoes not

  • change between RHIC and LHC

  • The 30% increase of integrated

  • elliptic flow is then due to the

  • larger pT at LHC coming from

  • the larger radial flow

  • This is another consequence of

  • the larger radial flow which

  • pushes protons (comparatively)

  • to larger pT

Conclusions on elliptic flow

  • In heavy-ion collisions at RHIC and LHC one observes

    • Strong elliptic flow

    • Hydrodynamic evolution of an ideal fluid (including a QGP phase)

    • reproduces the observed values of the elliptic flow and their

    • dependence on the particle masses

    • Main characteristics

      • Fireball quickly reaches thermal equilibrium (equ~ 0.6 – 1 fm/c)

      • The system behaves as a perfect fluid (viscosity ~0)

  • Increase of the elliptic flow at LHC by ~30%, mainly due to larger

  • transverse momenta of the particles

The dilepton invariant mass spectrum

“low” s version

“high” s version

  • The study of lepton (e+e-, +-) pairs is one of the most important tools

  • to extract information on the early stages of the collision

  • Dileptonsdo not interact strongly, once produced can cross the system

  • without significant re-interactions (not altered by later stages)

  • Several resonances can be “easily” accessed through the dilepton spectrum

Heavy quarkonium states

Quarkonium is a bound state of and



Several quarkonium states exists,

distinguished by their quantum numbers (JPC)


Bottomonium () family

Charmonium () family

Colour Screening

At T=0, the binding of the and quarks can be expressed using the Cornell potential:



Coulombian contribution, induced by gluonicexchange between and

Confinement term

What happens to a pair placed in the QGP?

The QGP consists of deconfinedcolourcharges

 the binding of a pair is subject to the effects of colour screening



  • The “confinement” contribution disappears

  • The high color density induces a screening of the coulombian term of the potential


..and QGP temperature

Screening of

strong interactionsin a QGP

  • Screening stronger at high T

  • D maximum size of a bound

  • state, decreases when T increases

  • Different states, different sizes

Resonance melting

QGP thermometer










Feed-down and suppression pattern

  • Feed-down process: charmonium (bottomonium) “ground state”

  • resonances can be produced through decay of larger mass quarkonia

  • Effect : ~30-40% for J/, ~50% for (1S)

  • Due to different dissociation temperature for each resonance, one should

  • observe «steps» in the suppression pattern of measured J/ or (1S)

Digal et al.,

Phys.Rev. D64(2001)



  • Ideally, one could vary T

    • by studying the same system (e.g. Pb-Pb) at various s

    • by studying the same system for various centrality classes

From suppression to (re)generation

At sufficiently high energy, the cc pair multiplicity becomes large

  • Statistical approach:

  • Charmoniumfully melted in QGP

  • Charmoniumproduced, together

  • with all other hadrons, at chemical freeze-out,

  • according to statistical weights

  • Kinetic recombination:

  • Continuous dissociation/regeneration over

  • QGP lifetime

Contrary to the suppression scenarii described before,

these approaches may lead to a J/ enhancement

How quantifying suppression ?

  • High temperature should indeed induce a suppression of the

  • charmonia and bottomonia states

  • How can we quantify the suppression ?

  • Low energy (SPS)

    • Normalize the charmonia yield to another hard process

    • (Drell-Yan) not sensitive to QGP

  • At RHIC, LHC Drell-Yan is no more “visible” in the dilepton

  • mass spectrum  overwhelmed by semi-leptonic decays of

  • charm/beauty pairs

  • Solution: directly normalize to elementary collisions (pp), via

  • nuclear modification factor RAA


RAA<1 suppression

RAA>1 enhancement

If no nuclear effects  NPAA=Ncoll NPNN (binary scaling)

Results: cold nuclear matter also matters….

  • pA collisions  no QGP formation. What is observed ?

Drell-Yan used

as a reference here!

NA50, pA 450 GeV

  • There is suppression of the J/ already in pA! This effect can mask a

  • genuine QGP signal. Needs to be calibrated and factorized out

  • Commonly known as Cold Nuclear Matter Effects (CNM)

  • Effective quantities are used for their parameterization (, abs, …)

B. Alessandro et al., EPJC39 (2005) 335

R. Arnaldi et al., Nucl. Phys. A (2009) 345

SPS: the anomalous J/ suppression

  • Results from NA50 (Pb-Pb) and NA60 (In-In)

In-In 158 GeV (NA60)

Pb-Pb 158 GeV (NA50)

Drell-Yan used

as a reference here!



  • In semi-central and central Pb-Pb collisions there is suppression

  • beyond CNM  anomalous J/ suppression

After correction for EKS98 shadowing

  • Maximum suppression ~ 30%. Could be consistent with suppression

  • of J/ from c and (2S) decays (sequential suppression)

RHIC: first surprises

  • Let’s simply compare RAA

  • (i.e. no cold nuclear effects taken into account)

  • Qualitatively, very similar

  • behaviour at SPS and

  • RHIC !

  • Do we see (as at SPS)

  • suppression of (2S) and

  • c ?

  • Or does (re)generation

  • counterbalance a larger

  • suppression at RHIC ?

  • RHIC: larger suppression

  • at forward rapidity:

  • favours a regeneration

  • scenario

Answer: go to LHC

Two main improvements:

1) Evidence for charmonia

(re)combination:now or never!






2) A detailed study (for the first time)

of bottomonium suppression



Yes, we can!


  • Even at the LHC, NO rise of J/ yield for central events, but….

  • Compare with PHENIX

    • Stronger centrality dependence at lower energy

    • Systematically larger RAA values for central events in ALICE

First possible evidence for (re)combination

 results

  • (2S), (3S) much less bound than (1S)

  • Striking suppression effect seen when comparing Pb-Pb and pp !

Conclusions on quarkonia

  • Verystrong sensitivity of quarkonium states to the medium

  • created in heavy-ion collisions

  • Two main mechanisms at play in AA collisions

    • Suppression by color screening/partonic dissociation

    • Re-generation(for charmonium only!) at high s

  • can qualitativelyexplainthe main features of the results

  • Cold nuclear matter effects are an important issue (almost

  • not covered here and in these lectures): interesting physics in

  • itself and necessary for precision studies study pA at the LHC

High pT particles (and jet!)suppression, open heavy quark particles

  • Other hard probes

    • High pThadrons and jets

    • Mesons and baryons containing heavy quarks (charm+beauty)

  • Theirproduction cross section can be calculated via

  • perturbative QCD approaches

  • Such hard probes come from high pTpartonsproduced on a

    • short timescale (tform ≈ 1/Q2)

  • Sensitive to the whole history of the collisions

  • Can be considered as probes of the medium

  • But what is the effect of the medium on such hard probes ?



s /2





s /2



pp and “normal” AA production

  • In pp collisions, the following factorized approach holds

Parton Distribution Functions

xa , xb= momentum fractions of

partons a, b in their hadrons

Cross section for hadronic collisions (hh)

Fragmentation of

quark q in the hadron H


cross section

In AA collisions, in absence of

nuclear and/or QGP effects

one should observe binary scaling


RAA = 1

RAA < 1

Breaking of binary scaling (1)

  • Binary scaling for high pTparticles

  • can be broken by

    • Initial state effects (active both in pA and AA)

      • Cronin effect

      • PDF modifications in nuclei

    • (shadowing)

E - DE

Spectrum in pp

Quenched spectrum

Breaking of binary scaling (3)

  • Final state effects  change in the fragmentation functions due

  • to the presence of the medium: energy loss/jet quenching

  • Parton crossing the medium looses

  • energy via

    • scattering with partons in the

    • medium (collisional energy loss)

    • gluon radiation (gluonstrahlung)

  • The net effect is a decrease of the

  • pT of fast partons (produced on short

  • timescales)

  • Quenching of the high-pT spectrum

  • Radiative mechanism dominant at

  • high energy

Radiative energy loss (BDMPS approach)

Energy loss

Distance travelled in medium

Casimir factor

Transport coefficient

  • aS = QCD coupling constant

  • (running)

  • CR = Casimir coupling factor

    • Equal to 4/3 for

    • quark-gluon coupling and 3 for

    • gluon-gluon coupling

  • q = Transport coefficient

    • Related to the properties

    • (opacity) of the medium,

    • proportional to gluon density and

    • momenta


  • L2 dependence related to the fact that

  • radiated gluons interact with the medium

Transport coefficient

  • The transport coefficient is related

  • to the gluon density and therefore

  • to the energy density of the

  • produced medium


  • From the measured energy loss

  • one can therefore obtain an indirect

  • measurement of the energy density

  • of the system

Pion gas

Cold nuclear matter

  • Typical (RHIC) values

  • qhat= 5 GeV2/fm

  • aS= 0.2  value corresponding to a process with Q2= 10 GeV

  • CR = 4/3

  • L = 5 fm

Enormous! Only very

high-pTpartons can survive

(or those produced close to

the surface of the fireball)

Results for charged hadrons and 0

factor ~5 suppression

  • Is this striking result due to a final state effect ?

    • Control experiments

      • pA collisions

      • AA collisions, with particles not interacting strongly (e.g., photons)

d-Au collisions and photon RAA

  • Both control experiments confirm that we observe a final state effect

    • d-Au collisions  observe Cronin enhancement

    • Direct photons medium-blind probe

Angular correlations

  • qqbar pairs produced inside fireball: both partonshadronize to low pT particles

  • qqbar pairs produced in the corona: one parton (outward going) gives a high pThadron (jet), the other (inward going) looses energy and hadronizes to low pThadron

Near-side peak

Away-side peak

  • Study azimuthal angle

  • correlations between a “trigger”

  • particle (the one with largest pT)

  • and the other high-pTparticles in

  • the event

  • At LO, hard particles come from

  • back-to-back jet fragmentation:

  • two peaks at 00 and 1800

Results on angular correlations

  • Suppression of back-to-back jet

  • emission in central Au-Au collisions

  • Another evidence for parton

  • energyloss

  • d-Au results confirm this is a final

  • state effect

High-pTparticles: results from LHC (1)

  • Comparison RHIC vs LHC

  • In the common pT region, similar

  • shape of the suppression

  • (minimum suppression at

  • pT~ 2 GeV/c)

  • Larger suppression at LHC!

  • Possibly due to higher energy

  • density (take also into account

  • that pTspectra are harder at the

  • LHC and should give a larger

  • RAAfor the same energy loss)

High-pTparticles: results from LHC (2)

  • Good discriminating power between models at very high pT

Dijet imbalance: clear signal at LHC

  • Significant imbalance of jet energies for central PbPb events!

  • Jet studies should tell us more about the parton energy loss and

  • its dynamics (leading hadrons biased towards jets with little interaction)

Pushing to very high pT

  • Strong jet suppression at LHC, extending to pT = 200 GeV!

  • Radiation is not captured inside the jet cone R

  • But where does the energy go ?

Where does energy go? (1)

  • Calculate projection of pT on leading jet axis and average over

  • selected tracks with pT > 0.5 GeV/c and |η| < 2.4

Define missing pT//

  • Integrating over the whole event final state

  • the momentum balance is restored

Leading jet



0-30% Central PbPb

excess away from leading jet

excess towards leading jet

balanced jets

unbalanced jets



Where does energy go? (2)

  • Calculate missing pTin ranges

  • of track pT

  • The momentum difference in

  • the leading jet is compensated

  • by low pT particles at large

  • angles with respect to the jet

  • axis

Energy loss of (open) heavy quarkmesons/baryons

  • The study of open heavy quark particles in AA collisions is a crucial

  • test of our understanding of the energy loss approach

  • A different energy loss for charmed and beauty hadrons is expected

  • In particular, at LHC energy

    • Heavy flavoursmainly come from quark fragmentation, light flavours

    • from gluons smaller Casimirfactor, smaller energy loss

    • Dead cone effect: suppression of gluon radiation at small angles,

    • depending on quark mass

  • Suppression for

  • q< MQ/EQ

Should lead to

a suppression


Eg > Echarm > Ebeauty

RAA (light hadrons) < RAA (D) < RAA (B)


p0 gee

h gee, 3p0

w ee, p0ee

f ee, hee

r ee

h’  gee

Heavy-flavor measurements: NPE

  • Non-photonic electrons

  • (pioneered at RHIC), based

  • on semi-leptonic decays of

  • heavy quark mesons

  • Electron identification

  • Subtract electrons not coming

  • from heavy-flavour decays

    • e+e- (main bckgr. source)

    • 0, , ’ Dalitz decays

    • , ,  decays

  • Sophisticated background

  • subtraction techniques

    • Converter method

    • Vertex detectors…

  • Indirect measurement, expect non-negligible systematic uncertainties

Non-photonic electrons - RHIC

  • RAA values for non-photonic

  • electronssimilar to those for

  • hadrons no dead cone ?

  • No separation of charm and

  • beauty, adds difficulty in the

  • interpretation

  • Results difficult to explain by

  • theoretical models, even

  • including high qvalues and

  • collisional energy loss


  • Fair agreement with models including only charm, but clearly not

  • a realistic description

Various techniques forheavy-flavor measurements

  • Direct reconstruction of hadronicdecay

  • Pioneered at RHIC, fully exploited at the LHC

    • Fully combinatorial analysis (build all pairs, triplets,…) prohibitive

    • Use

      • Invariant mass analysis of decay topologies separated from

    • the interaction vertex (need ~100 m resolution)

    • K identification (time of flight, dE/dx)

LHC results – D-mesons

  • Similar trend vs. pT for D,

  • charged particles andp±

  • Good compatibility between various

  • charmed mesons

  • Large suppression! (factor~5)

  • Hint of RAAD > RAAπ at low pT?

 Look at beauty

Beauty via displaced J/

  • Fraction of non-prompt J/yfrom

  • simultaneous fit to m+m- invariant mass

  • spectrum and pseudo-proper decay length

  • distributions(pioneered by CDF)

  • LHC results from CMS

  • Background from sideways (sum of 3 exp.)

  • Signal and prompt from MC template

Non-prompt J/ suppression

Suppression hierarchy (b vs c)

observed, at least for central

collisions (note different y range)

Larger suppression at high pT ?

Heavy quark v2 at the LHC

  • A non-zero elliptic flow for heavy quark would imply that also heavy

  • quark thermalize and participate in the collective expansion


Indication of non-zero D meson v2(3s effect) in 2<pT<6 GeV/c

Data vs models: D-mesons

Consistent description of charm RAA and v2

very challenging for models,

can bring insight on the medium transport properties,

also with more precise data from future LHC runs

Heavy quark – where are we ?

  • Studies pioneered at RHIC

  • Abundant heavy flavour production at the LHC

    • Allow for precision measurements

  • Can separate charm and beauty (vertex detectors!)

    • Indication for RAAbeauty>RAAcharmand RAAbeauty>RAAlight

    • More statistics needed to conclude on RAAcharm vs. RAAlight

  • Indication (3s) for non-zero charm elliptic flow at low pT

At the end of the journey…..

…let’s try to summarize the main findings

  • Heavy-ion collisions are our door to the study of the properties of

  • strong interaction at very high energy densities

  •  A system close to the first instants of the Universe

  • Years of experiments at various facilities from a few GeV to a few

  • TeVcenter-of-mass energies provided a lot of results which shows

  • a strong sensitivity to the properties of the medium

  • This medium behaves like a perfect fluid, has spectacular effects

  • on hard probes (quarkonia, jet,…) and has the characteristics

  • foreseen for a Quark-Gluon Plasma

  • Even if many aspects are understood, with the advent of LHC we are

  • answering long-standing questions but we face new challenges….

  • …so QGP physics might be waiting for you!

Also because….

…sagas never end!

Other topics

Low-mass resonances anddilepton continuum

  • Study of low-mass region:

  • investigate observables related

  • to QCD chiral symmetry

  • restoration

  • Conceptual difference between

  • study of heavy quarkonia and

  • low-mass resonances

  •  (,  to a lesser extent)

    • Short-lived meson ( = 149 MeV)

    • Decays to e+e- (+ -) inside the

    • reaction zone

    • QGP directly influences spectral

  • characteristics  may expect

  • mass, width modifications

  • J/

    • Long-lived meson ( = 93 keV)

  • Decays outside reaction region

  • QGP may influence production

  • cross section but not its spectral

  • characteristics (mass, width)

  • Chiral symmetry(1)

    • The QCD lagrangianfor two light massless quarks is


    • The quark fields can be decomposed into a left-handed and a

    • right-handed component

    • The Lagrangian is unchanged under a rotation of Lby any 2 x 2 unitary

    • matrix L, and Rby any 2 x 2 unitary matrix R

    • This symmetry of the lagrangian is called chiral symmetry

    • It turns out that the non-zero mass for hadrons is generated by a

    • spontaneous breaking of the chiral symmetry (i.e. the ground state does

    • not have the symmetry of the lagrangian)

    Chiral symmetry(2)

    • In our world, therefore, the QCD vacuum corresponds to a situation

    • where the scalar field qq (quark condensate) has a non-zero

    • expectation value

    • The massless Goldstone bosons

    • associated with the symmetry

    • breaking are the pions

    • Contrary to the expectations m 0,

    • due to the non-zero (but very small)

    • bare mass of u,d quarks

    • Pion mass is anyway much smaller

    • than that of other hadrons

    • Lattice QCD calculations predict that , close to the deconfinement

    • transition, chiral symmetry is (approximately) restored, i.e. qq0

    • with consequences on the spectral properties of hadrons

    Chiral symmetry restoration and QCD phase diagram

    • Even in cold nuclear matter effects one could observe effects due to

    • partial restoration of chiral symmetry

    • Strong sensitivity to baryon density too  study collisions far from

    • transparency regime

    • Stronger effect in AA than in pA, but interpretation more difficult

    • need to understand the fireball evolution, mesons emitted along

    • the whole history of the collision

    rB /r0





    Effects on vector mesons

    • Dilepton spectrum study vector mesons (JPC=1--)

    • In the vector meson sector, predictions around TC are model dependent

    • Some degree of degeneracy between vector and pseudovector states,

    •  and a1 mesons

    • Rapp-Wambach broadening scenario

    • Brown-Rho scaling hypothesis,

    • hadron masses directly related to

    • quark condensate


    Results at SPS energy: NA60

    In-In collisions, s=17 GeV

    • Highest-quality data on the market

    •  ~  ~ 20 MeV

    • Subtract contributions of

    • resonance decays, both 2-body

    • and Dalitz, except 

    • Investigate the evolution of the

    • resulting dilepton spectrum,

    • which includes  meson plus

    • a continuum possibly due to

    • thermal production

    Centrality dependence of  spectral function

    12 centrality


    Comparison data vs

    expected spectrum

    A clear broadening of

    the -meson is

    observed, but without

    any mass shift

    Brown-Rho scaling clearly disfavored

    Theory comparisons

    • Good agreement with broadening models

    • Direct contribution from QGP phase is not dominant

    • 4 interaction sensitive to -a1 mixing and therefore to chiral

    • symmetry restoration

    Dilepton studies at RHIC

    • Clear signal in the low-mass region ! But discrepancy between

    • experiments, not easy to explain…

    • STAR and NA60 results can be described in the broadening approach

    Conclusions on low-mass dileptons

    • Chiral symmetry is a property of the QCD lagrangian, when neglecting

    • the (small) light quark mass terms

    • A spontaneous breaking of the chiral symmetry is believed to be

    • responsible for the generation of the hadron masses, and leads to

    • having a non-zero value for the quark-condensate in the vacuum

    • At high temperature and baryon density chiral symmetry is

    • gradually restored, leading to qq = 0

    • Chiral symmetry restoration effects can influence spectral

    • properties of light vector mesons

    • Several interesting effects observed, clear connection with

    • chiral symmetry still being worked out

    • Collisioni nucleo-nucleo ultrarelativistiche hanno mostrato effetti molto

    • forti sulla larghezza della  (non sulla massa), legati probabilmente al

    • ripristino della simmetria chirale nella regione prossima a Tc


    Breaking of mT scaling in AA

    200 GeV

    200 GeV

    130 GeV

    130 GeV

    • Average pT increases with particle mass

    • (as a consequence of the increase of Tslope with particle mass)


    Directed flow

    v1 coefficient: directed flow

    • v1 0 means that there is a

    • difference between the number

    • of particles emitted parallel (00)

    • and anti-parallel (180 0) with

    • respect to the impact

    • parameter

    • Directed flow represents

    • therefore a preferential

    • emission direction of particles

    Probes of the QGP

    • One of the best way to study QGP is via probes, created early in

    • the history of the collision, which are sensitive to the

    • short-lived QGP phase

    • Ideal properties of a QGP probe

    • Production in elementary NN collisions

  • under control





    • Interaction with cold nuclear matter

  • under control

    • Not (or slightly) sensitive to the final-state

  • hadronic phase

    • High sensitivity to the properties of the

  • QGP phase

  • Why are heavy quarkonia sensitive to the QGP phase ?

    RHIC: forward vs central y

    Comparison of results obtained at different rapidities



    Stronger suppression at forward rapidities

    • Not expected if suppression

    • increases with energy density

    • (which should be larger at

    • central rapidity)

    • Are we seeing a hint of

    • (re)generation, since there are

    • more pairs at y=0?

    • Comparisons with theoretical models tend to confirm this interpretation,

    • but not in a clear enough way. How to solve the issue ?

    pT dependence of the suppression

    Large pT: compare CMS with STAR

    Small pT: compare ALICE with models

    (comparison with PHENIX in prev. slide)

    • At high pTno regeneration expected: more suppression at LHC energies

    • At small pT~ 50% of the J/ should come from regeneration

    What happens to (1S)?

    • (2S) and (3S) are suppressed

    • with respect to (1S). But what

    • about (1S) itself ?

    • Also a large suppression

    • for (1S),increasing with

    • centrality

    • (1S) compatible with only

    • feed-down suppression ?

    • Complete suppression of 2S

    • and 3S states would imply

    • 50% suppression on 1S

     Probably yes, also taking into

    account the normalization


    Possibly (1S) dissoc. threshold still beyond LHC reach ?  Full energy

    Cronin enhancement

    RpA > 1


    RpA = 1

    pp spectrum

    pA spectrum normalized to Ncoll≈ A

    • Cronin effect

      • Multiple

      • scattering

    • of initial

    • state partons

      • pT kick

      • Increase

      • final state pT

    Breaking of binary scaling (2)

    • Shadowing

    • Parton densities for nucleons inside a nucleus are different from those

    • in free nucleons (seen for the first time by EMC collaboration, 1983)

    • Non–perturbative effect, parameterized by fitting simultaneously

    • various sets of data. Still large uncertainties are present

    • These initial state effects are not related to QGP formation!

    The new frontier: b-jet tagging

    • Jets are taggedby cutting on

    • discriminating variables based

    • on the flight distance of the

    • secondary vertex

    •  enrich the sample with b-jets

    Factor 100 light-jet rejection

    for 45% b-jet efficiency

    • b-quark contribution extracted using template fits to

    • secondary vertex invariant mass distributions

    Beauty vs light: high vs low pT

    Fill the gap!

    • LowpT: different suppression

    • for beauty and light flavours,

    • but:

      • Different centrality

      • Decay kinematics

    • HighpT: similar suppression

    • for light flavour and b-tagged

    • jets

    Before starting….

    CERN Summer Student Official Photo


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