Heavy Ions and Quark-Gluon Plasma…

1

Highlights from a 25 year-old story

From SPS…

…to RHIC…

…to LHC!

E. Scomparin INFN Torino (Italy)

XXV SEMINARIO NAZIONALE di FISICA NUCLEARE e SUBNUCLEARE

"Francesco Romano" EDIZIONE SPECIALE: IL BOSONE DI HIGGS

Before starting….

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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 Maseraand Francesco Prino. We hold together a university course on thesetopics and several slides come from there

Why heavy ions ?

3

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

4

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)

The theory describing the interactions of quarks and gluons was formulated in analogy to QED and is called Quantum Chromodynamics (QCD)

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

Coupling constant

5

Contrary to QED, in QCD the coupling constant decreases when the momentum transferred in the interaction increases or, in other words, at short distances

Consequences asymptotic freedom (i.e. perturbative calculations possible

mainly for hard processes) interaction grows stronger as distance increases

Express S as a function of its value estimated at a certain momentum transfer

From a confined world….

6

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

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,

where the confinement term Kr parametrizes the effectsof confinement

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

Cabibbo and Parisi Phys. Lett. 59B, 67 (1975)

”Experimental hadronic spectrumand quark liberation”

Phase transition at large T and/or B

Becoming more quantitative…

8

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

9

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

3

34

2

7.0130

37 fmGeVc

T

MeVBTBTP cc 1453790

9037 4

24

2

42

90 ctot TgP

High-density QGP

10

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

where q is the chemical potential, relatedto the energy needed to add one quark tothe 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!

Tpq

q qe

dppVgdN /3

2

11

24

42243 q

qqq

gP

41

224

qq g

B

Lattice QCD approach

11

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

12

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

13

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…

14

AGS at BNL p beams up to 33 GeV Si and Au beams up to 14.6 A GeV

Remember Z/A rule !

SPS at CERN p beams up to 450 GeV O, S, In, Pb up to 200 A GeV

… to colliders!

15

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!

16

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 ?

17

A very large number of secondary particles is produced How many ? Which is their kinematical distribution ?

Kinematical variables

18

z

z

pEpEy ln

21

The kinematical distribution of the produced particles are usually expressed as a function of rapidity (y) and transverse momentum (pT)

22yxT ppp

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 ( )

2

tanloglog21

z

z

pppp

y~ for relativistic particles

Alternative variable to pT: transverse mass mT22TT pmm

Typical rapidity distributions

1919

Fixed target: SPS

Collider: RHIC

pBEAM=158 GeV/c, BEAM=0.999982pTARGET=0 , TARGET=0

91.22

01ln21

82.511ln

21

TARGPROJTARGMID

TARG

PROJ

yyyy

y

y

02

8.10

36.511ln

21

TARGPROJTARGMID

TARGETPROJ

TARGETPROJ

yyyy

yyy

yy

pBEAM=100 GeV/c=0.999956, gBEAM≈100

Midrapidity:largest density ofproduced particle

Multiplicity at midrapidity

20

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

LHC energy (ALICE)RHIC energySPS energy

Multiplicity and energy density

21

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 g, in the instant of total superposition one could have

at RHIC energies (enormous!)

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

22

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

The number of particleswill be given by

(y~ when y is small)

Multiplicity and energy density

23

The average energy of these particles is close to their average transverse mass since E=mTcosh y ~ mT when y0 Therefore the energy density at formation time can be obtained as

Bjorken formula

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

24

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 thermalization

Late evolution:model dependent

Time evolution of the collision

25

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

Hard processes:• Low cross section• Probe the whole evolution of the collision

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

Soft processes: • High cross section• Decouple late indirect signals for QGP

High- vs low-energy collisions

26

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

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High-energyexperiments

Low-energyexperiments

High-energy experiments create conditions similar to Early Universe Low-energy experiments create dense baryonic system

Characterizing heavy-ion collisions

28

In particular, the centrality of the collision is one of the most important parameters, and it can be quantified by the impact parameter (b)

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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

The experimental characterization of the collisions is an essential prerequisite for any detailed study

Hadronic cross section

29

SPSRHIC (top) LHC(Pb)

LHC(p)

Laboratory beam momentum (GeV/c)

Hadronic pp cross section grows logarithmically with sMean free

path

/1 ~ 0.17 fm-3

~ 70 mb = 7 fm2

~ 1 fm

is small with respect to

the nucleus size opacity

21/3b

1/3a

20in δ)A(Aπrσ

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

30

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/2p ~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

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/)(0

01)( rrer

Core density

Nuclear radius

“skin depth”

Interaction probability and hadronic cross sections

32

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

33

Although the interaction probability practically does not depend on the nucleon-nucleon cross section, the total number of nucleon-nucleon collisions does

Accel. √s (GeV)

total (mb)

inel (mb

)AGS 3-5 40 21

SPS 17 40 33

RHIC 200 50 42

LHC(Pb)

5500 90 60

inel corresponding tothe main ion-ion

facilities

Number of participants vs b

34

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

34

Accel. √s (GeV)

total (mb)

inel (mb

)AGS 3-5 40 21

SPS 17 40 33

RHIC 200 50 42

LHC(Pb)

5500 90 60

inel corresponding tothe main ion-ion

facilities

Centrality – how to access experimentally

35

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…

36 Can we understand quantitatively the evolution of the fireball ?

Chemical composition ofthe fireball

37

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 Tch at 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

38

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

39

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 B : baryochemical potential S : strangeness chemical potential I3 : 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 B

023

i

iiSSi

iiSS

ii SnVNZBnV

NZInV

i

40

Particle ratios at AGS

• AuAu - Ebeam=10.7 GeV/nucleon - s=4.85 GeV• Minimum c2 for: T=124±3 MeV B=537±10 MeV

c2 contour lines

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

41

Particle ratios at SPS• PbPb - Ebeam=40 GeV/ nucleon - s=8.77 GeV• Minimum c2 for: T=156±3 MeV B=403±18 MeV

c2 contour lines

42

Particle ratios at RHIC• AuAu - s=130 GeV• Valore minimo di c2 per: T=166±5 MeV B=38±11 MeV

c2 contour lines

43

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

44

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 QGPhadrons takes place

News from LHC

45

Thermal model fits for yields and particle ratios T=164 MeV, excluding protons

Unexpected results for protons: abundances below thermal modelpredictions work in progress to understand this new feature!

Chemical freeze-out

46

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)

47

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

pT distributions

48

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/pT dN/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

49

In pp collisions at low pT Exponential behaviour, identical for all hadrons (mT scaling)

slope

T

slope

T

Tm

TT

Tm

TT

emdmdNe

dmmdN

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)

pT and mT spectra

50

slope

T

slope

T

Tpm

Tm

TTTT

eedmmdN

dppdN

22

Evolution of pT spectra vs Tslope,higher T implies “flatter” spectra

Slightly different shape of spectra, when plotted as a function of pT or mT

Breaking of mT scaling in AA

51

Harder spectra (i.e. larger Tslope) for larger mass particles

Consistent with a shift towards larger pT of heavier particles

Breaking of mT scaling in AA

52

2

21

mvTT foslope

Tslope depends 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

53

x

y v

v

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

54

x

y

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

55

x

y

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

5656

Pion, proton and kaon spectra for central events (0-5%) LHC spectra are harder than those measured at RHIC

Clear increase of radial flow at LHC, compared to RHIC (same centrality)

Tfo= 95 10 MeV = 0.65 0.02

Thermal freeze-out

57

Fits to pT spectra allow us to extract the temperature Tfo and 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

x

y

YRP

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

x

y z

Reaction plane

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 the initial geometric anisotropy in an anisotropy in the momentum distributions of particles, which can be measured

Anisotropic transverse flow

60

....2cos2)cos(212)( 21

0 YYY RPRP

RP

vvNd

dN

RPn nv Y cos

Starting from the azimuthal distributions of the produced particles with respect to the reaction plane YRP, one can use a Fourier decomposition and write

The terms in sin(-YRP) are not present since the particle distributions need to be symmetric with respect to YRP 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

61

....2cos2)cos(212)( 21

0 YYY RPRP

RP

vvNd

dN

Elliptic flow

RPv Y 2cos2

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

OUT OF PLANE

IN P

LANE

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

Elliptic flow - characteristics

62

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

63

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

6464

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)

v2 vs centrality at RHIC

65

Hydrodynamic limit

STAR PHOBOS

RQMD

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

v2 vs centrality at RHIC

66

Hydrodynamic limit

STAR PHOBOS

RQMD

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

67

At low pT hydrodynamics reproduces data At high pT significant deviations are observed

Natural explanation: high-pT particles quickly escape the fireball without enough rescattering no thermalization, hydrodynamics not applicable

v2 vs pT for identified particles

68

Hydrodynamics can reproduce rather well also the dependence of v2 on particle mass, at low pT

Elliptic flow, from RHIC to LHC

69

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

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

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

Elliptic flow at LHC

70

v2 as a function of pT does 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

The difference in the pT dependence of v2 between kaons, protons and pions (mass splitting) is larger at LHC This is another consequence of the larger radial flow which pushes protons (comparatively) to larger pT

Conclusions on elliptic flow

71

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

72

The study of lepton (e+e-, + -) pairs is one of the most important tools to extract information on the early stages of the collision Dileptons do 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

“low” s version

“high” s version

Heavy quarkonium states

73

Quarkonium is a bound state of and q

qwith

Charmonium () family Bottomonium () family

Several quarkonium states exists,distinguished by their quantum numbers (JPC)

Colour Screening

74

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

krr

rV )(

Coulombian contribution, induced by gluonic exchange between and

Confinement term

qq

74

The QGP consists of deconfined colour charges the binding of a pair is subject to the effects of colour screening

What happens to a pair placed in the QGP?

krr

rV )( Dre

rrV /)(

• The “confinement” contribution disappears• The high color density induces a screening of the coulombian term of the potential

qq

..and QGP temperature

Perturbative Vacuum

cc

Color Screening

ccScreening of

strong interactionsin a QGP

• Screening stronger at high T• D maximum size of a bound state, decreases when T increases

Resonance melting

QGP thermometer

• Different states, different sizes

Feed-down and suppression pattern

J/

(3S) cb(2P)(2S)

cb(1P)

(1S)

(2S)cc(1P)

J/

Digal et al., Phys.Rev. D64(2001)

094015

• Due to different dissociation temperature for each resonance, one should observe «steps» in the suppression pattern of measured J/ or (1S)

• 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

Yiel

d(T)

/Yie

ld(T

=0)

• 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)

From suppression to (re)generation At sufficiently high energy, the cc pair multiplicity becomes large

Contrary to the suppression scenarii described before,these approaches may lead to a J/ enhancement

Statistical approach: Charmonium fully melted in QGP Charmonium produced, together with all other hadrons, at chemical freeze-out, according to statistical weightsKinetic recombination: Continuous dissociation/regeneration over QGP lifetime

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

= If no nuclear effects NP

AA=Ncoll NPNN (binary scaling)

RAA<1 suppressionRAA>1 enhancement

Results: cold nuclear matter also matters….

pA collisions no QGP formation. What is observed ?

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, …)

Drell-Yan usedas a reference here!

SPS: the anomalous J/ suppression

After correction for EKS98 shadowing

In-In 158 GeV (NA60)Pb-Pb 158 GeV (NA50)

Results from NA50 (Pb-Pb) and NA60 (In-In) B. Alessandro et al., EPJC39 (2005) 335R. Arnaldi et al., Nucl. Phys. A (2009) 345

Anomaloussuppression

In semi-central and central Pb-Pb collisions there is suppression beyond CNM anomalous J/ suppression

Drell-Yan usedas a reference here!

Maximum suppression ~ 30%. Could be consistent with suppressionof 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 !

RHIC: larger suppression at forward rapidity: favours a regeneration scenario

Do we see (as at SPS) suppression of (2S) and cc ? Or does (re)generation counterbalance a larger suppression at RHIC ?

Answer: go to LHC

82

Two main improvements:

1) Evidence for charmonia (re)combination: now or never!

Yes, we can!

(3S) cb(2P)(2S)

cb(1P)

(1S)

2) A detailed study (for the first time) of bottomonium suppression

Massr0

J/, ALICE vs PHENIX

83

Compare with PHENIX Stronger centrality dependence at lower energy Systematically larger RAA values for central events in ALICE

First possible evidence for (re)combination

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

results

84

(2S), (3S) much less bound than (1S) Striking suppression effect seen when comparing Pb-Pb and pp !

Conclusions on quarkonia Very strong sensitivity of quarkonium states to the medium created in heavy-ion collisions

Two main mechanisms at play in AA collisions

1) Suppression by color screening/partonic dissociation2) Re-generation (for charmonium only!) at high s

can qualitatively explain the 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

Their production cross section can be calculated via perturbative QCD approaches

Other hard probes High pT hadrons and jets Mesons and baryons containing heavy quarks (charm+beauty)

Such hard probes come from high pT partons produced on a short timescale (form ≈ 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 ?

pp and “normal” AA production

)Q(zDQxPDFQxPDF qHqqqabbaHxhh222 ,),(),(

Partoniccross section

Parton Distribution Functionsxa , xb= momentum fractions ofpartons a, b in their hadrons

Cross section for hadronic collisions (hh)

s /2

q

q

H

xa

xb

Q2

s /2

Jet-

Fragmentation ofquark q in the hadron H

In pp collisions, the following factorized approach holds

In AA collisions, in absence of nuclear and/or QGP effects

one should observe binary scalingTppcollTAA pNNpN d/dd/d

Breaking of binary scaling (1)

RAA < 1

RAA = 1

RA

A

Binary scaling for high pT particles can be broken by

Initial state effects (active both in pA and AA) Cronin effect PDF modifications in nuclei

(shadowing)

Breaking of binary scaling (3) Final state effects change in the fragmentation functions due to the presence of the medium: energy loss/jet quenching

E - E

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

Quenched spectrum

Spectrum in pp

Radiative energy loss (BDMPS approach)

2 ˆ LqCE Rs

Casimir factorTransport coefficient

Energy loss Distance travelled in medium

S = 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

Pion gas

Cold nuclear matter

QGP

4/3 ˆ q

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

Typical (RHIC) values qhat = 5 GeV2/fm S = 0.2 value corresponding to

a process with Q2 = 10 GeV CR = 4/3 L = 5 fm

GeV40E

Enormous! Only veryhigh-pT partons can survive(or those produced close tothe surface of the fireball)

Results for charged hadrons and 0

Tpp

TAA

collTAA dpdN

dpdNN

pR//1)(

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 partons

hadronize to low pT particles

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

Study azimuthal angle correlations between a “trigger” particle (the one with largest pT) and the other high-pT particles in the event

At LO, hard particles come from back-to-back jet fragmentation: two peaks at 00 and 1800

94

Near-side peak

Away-side peak

Results on angular correlations

95

Suppression of back-to-back jet emission in central Au-Au collisions Another evidence for parton energy loss

d-Au results confirm this is a final state effect

High-pT particles: 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 pT spectra are harder at the LHC and should give a larger RAA

for the same energy loss)

High-pT particles: results from LHC (2)

Good discriminating power between models at very high pT

Dijet imbalance: clear signal at LHC

2, 12

21

21

TT

TTJ EE

EEA

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//

Leading jet definesdirection

0-30% Central PbPb

balanced jets unbalanced jets

excess away from leading

jet

excess towards leading jet

Integrating over the whole event final state the momentum balance is restored

Where does energy go? (2) Calculate missing pT in 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

in-cone

out-of-cone

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 flavours mainly come from quark fragmentation, light flavours from gluons smaller Casimir factor, smaller energy loss Dead cone effect: suppression of gluon radiation at small angles, depending on quark mass

Suppression for < MQ/EQ

Eg > Echarm > Ebeauty

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

Should lead toa suppression

hierarchy

Heavy-flavor measurements: NPE

g conversion

0 gee

gee, 30

w ee, 0ee

f ee, ee

ee

’ gee

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

ge+e- (main bckgr. source) 0 , , ’ Dalitz decays , w, f decays

Indirect measurement, expect non-negligible systematic uncertainties

Sophisticated background subtraction techniques

Converter method Vertex detectors…

Non-photonic electrons - RHIC

RAA values for non-photonic electrons similar to those for hadrons no dead cone ?

No separation of charm and beauty, adds difficulty in the interpretation

Results difficult to explain bytheoretical models, even including high q values andcollisional energy loss

Fair agreement with models including only charm, but clearly not a realistic description

^

Various techniques forheavy-flavor measurements

Direct reconstruction of hadronic decay 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

Good compatibility between various charmed mesons Large suppression! (factor~5)

106

Similar trend vs. pT for D, charged particles and ±

Hint of RAAD > RAA

π at low pT ? Look at beauty

Beauty via displaced J/

107

Fraction of non-prompt J/ from simultaneous fit to +- 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

108

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

109109

OUTIN

OUTIN

NNNN

Rv

4

1

22

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

A non-zero elliptic flow for heavy quark would imply that also heavy quark thermalize and participate in the collective expansion

Data vs models: D-mesons

110

Consistent description of charm RAA and v2very 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 ?

111

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>RAA

charm and RAAbeauty>RAA

light

More statistics needed to conclude on RAAcharm vs. RAA

light

Indication (3) 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 TeV center-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

Conceptual difference between study of heavy quarkonia and low-mass resonances

Study of low-mass region: investigate observables related to QCD chiral symmetry restoration

J/ Long-lived meson ( = 93 keV) Decays outside reaction region QGP may influence production

cross section but not its spectral characteristics (mass, width)

(w, f 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

Chiral symmetry(1) The QCD lagrangian for two light massless quarks is

jjiL g where du

The Lagrangian is unchanged under a rotation of L by any 2 x 2 unitary matrix L, and R by any 2 x 2 unitary matrix R This symmetry of the lagrangian is called chiral symmetry

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

g2

1 5L g

21 5

R

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

Effects on vector mesons In the vector meson sector, predictions around TC are model dependent Some degree of degeneracy between vector and pseudovector states, and a1 mesons

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

Brown-Rho scaling hypothesis, hadron masses directly related to quark condensate

qqqq

mm

mm

mm

N

N

****

Rapp-Wambach broadening scenario

B /0 0 0.1 0.7 2.6

Results at SPS energy: NA60

wf

In-In collisions, s=17 GeV Highest-quality data on the market w ~ f ~ 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

A clear broadening ofthe -meson is

observed, but withoutany mass shift

Brown-Rho scaling clearly disfavored

12 centrality bins

Comparison data vsexpected spectrum

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

Minbias (value ± stat ± sys) Central (value ± stat ± sys)

STAR 1.53 ± 0.07 ± 0.41 (w/o ρ) 1.40 ± 0.06 ± 0.38 (w/ ρ)

1.72 ± 0.10 ± 0.50 (w/o ρ) 1.54 ± 0.09 ± 0.45 (w/ ρ)

PHENIX 4.7 ± 0.4 ± 1.5 7.6 ± 0.5 ± 1.3Difference 2.0 σ 4.2 σ

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

Backup

Breaking of mT scaling in AA

126

200 GeV130 GeV130 GeV200 GeV

Average pT increases with particle mass (as a consequence of the increase of Tslope with particle mass)

v1 coefficient: directed flow

127

....2cos2)cos(212)( 21

0 YYY RPRP

RP

vvNd

dN

Directed flow

RPv Y cos1 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

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 ?

Interaction with cold nuclear matter under control

VACUUM

HADRONICMATTER

QGP

RHIC: forward vs central y

129

Comparison of results obtained at different rapidities

Stronger suppression at forward rapidities

Mid-rapidity

Forward-rapidity

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 suppressionLarge pT: compare CMS with STAR Small pT: compare ALICE with models

(comparison with PHENIX in prev. slide)

At high pT no regeneration expected: more suppression at LHC energies At small pT ~ 50% of the J/ should come from regeneration

What happens to (1S)?

131

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 uncertainty

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

(2S) and (3S) are suppressed with respect to (1S). But what about (1S) itself ?

RpA = 1RpA

RpA > 1Cronin

enhancement

TdpdN

Tp

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)

These initial state effects are not related to QGP formation!

Non–perturbative effect, parameterized by fitting simultaneously various sets of data. Still large uncertainties are present

),(),(),( 2

22

QxfQxfQxR p

i

AiA

i

The new frontier: b-jet tagging

134

Jets are tagged by cutting on discriminating variables based on the flight distance of the secondary vertex enrich the sample with b-jets

b-quark contribution extracted using template fits to secondary vertex invariant mass distributions

Factor 100 light-jet rejectionfor 45% b-jet efficiency

Beauty vs light: high vs low pT

135

Low pT: different suppression for beauty and light flavours, but:

Different centrality Decay kinematics

High pT: similar suppression for light flavour and b-tagged jets

Fill the gap!

Before starting….

136

CERN Summer Student Official Photo(1988!)