Heavy Ions and Quark-Gluon Plasma…

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…. 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 Parisi Phys. 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 BNL

From fixed-target… SPS at CERN AGS at BNL 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= pTARGET=0 , bTARGET=0 Collider: RHIC Midrapidity: largest density of produced particle pBEAM=100 GeV/c b= , gBEAM≈100 19

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  (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

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 particles will be given by (y~ when y is small)

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 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~ 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 thermalization 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 Low-energy experiments 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 28

Hadronic cross section
Hadronic pp cross section grows logarithmically with s SPS RHIC (top) LHC(Pb) LHC(p) Laboratory beam momentum (GeV/c) Mean free path  ~ 0.17 fm-3 ~ 70 mb = 7 fm2  ~ 1 fm is small with respect to the nucleus size  opacity 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 facilities Accel. √s (GeV) stotal (mb) sinel (mb) AGS 3-5 40 21 SPS 17 33 RHIC 200 50 42 LHC(Pb) 5500 90 60

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 facilities Accel. √s (GeV) stotal (mb) sinel (mb) AGS 3-5 40 21 SPS 17 33 RHIC 200 50 42 LHC(Pb) 5500 90 60 34

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 of the 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 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
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 AuAu - Ebeam=10.7 GeV/nucleon - s=4.85 GeV
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hadrons takes 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

pT distributions 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
In pp collisions at low pT Exponential behaviour, identical for all hadrons (mT scaling) 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) 49

pT and mT spectra Slightly different shape of spectra,
when plotted as a function of pT or mT Evolution of pT spectra vs Tslope, 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 pT of heavier particles

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
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 x y v

Radial flow at SPS y x 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 54

Radial flow at RHIC y x 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 55

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) 56

Thermal freeze-out 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 MeV, depending on centrality and s At thermal freeze-out the fireball has a collective radial expansion, with a velocity 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 58

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 x y z 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 Reaction plane

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
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 IN PLANE OUT OF PLANE 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) 64

v2 vs centrality at RHIC RQMD
Hydrodynamic limit STAR PHOBOS RQMD Parameters for hydro: initial state via Glauber equilibration time, freeze-out time 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 RQMD Interpretation
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
Increase of v2 with pT: larger pT is generated by more rescattering so it is naturally connected to a larger v2 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
Consequence of radial flow which pushes proton at higher pT 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 v2 as a function of pT does not
change between RHIC and LHC The difference in the pT dependence of v2 between kaons, protons and pions (mass splitting) is larger at 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 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

Heavy quarkonium states
Quarkonium is a bound state of 𝑞 and 𝑞 q with 𝑚 𝑞 𝑞 <2𝑚𝐷(𝑚𝐵) Several quarkonium states exists, distinguished by their quantum numbers (JPC) Charmonium (𝑐 𝑐 ) family Bottomonium (𝑏 𝑏 ) family

Colour Screening q q The “confinement” contribution disappears
At T=0, the binding of the 𝑞 and 𝑞 quarks can be expressed using the Cornell potential: q Coulombian contribution, induced by gluonic exchange between 𝑞 and 𝑞 Confinement term What happens to a 𝑞 𝑞 pair placed in the QGP? q The QGP consists of deconfined colour charges  the binding of a 𝑞 𝑞 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 74

strong interactions in a QGP
..and QGP temperature Screening of strong interactions in 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) J/  (3S) b(2P) (2S) b(1P) (1S) (2S) c(1P) Digal et al., Phys.Rev. D64(2001) 094015 Yield(T)/Yield(T=0) 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: Charmonium fully melted in QGP Charmonium produced, 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 𝑅 𝐴𝐴 = 𝑑𝑁𝑃 𝐴𝐴 𝑁𝐶𝑜𝑙𝑙 𝑑𝑁𝑃𝑁𝑁 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 ? NA50, pA 450 GeV Drell-Yan used as a reference here! N.B.: J/pA/(A J/pp ) is equivalent to RpA 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, …)

SPS: the anomalous J/ suppression
Results from NA50 (Pb-Pb) and NA60 (In-In) B. Alessandro et al., EPJC39 (2005) 335 R. Arnaldi et al., Nucl. Phys. A (2009) 345 After correction for EKS98 shadowing In-In 158 GeV (NA60) Pb-Pb 158 GeV (NA50) Drell-Yan used as a reference here! Anomalous suppression In semi-central and central Pb-Pb collisions there is suppression beyond CNM  anomalous J/ suppression 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  (3S) b(2P) (2S) b(1P) (1S) Mass r0 Yes, we can!

J/, ALICE vs PHENIX 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
Very strong 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 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
Other hard probes High pT hadrons and jets Mesons and baryons containing heavy quarks (charm+beauty) Their production cross section can be calculated via perturbative QCD approaches Such hard probes come from high pT partons produced 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 ?

pp and “normal” AA production
In pp collisions, the following factorized approach holds Cross section for hadronic collisions (hh) Parton Distribution Functions xa , xb= momentum fractions of partons a, b in their hadrons Fragmentation of quark q in the hadron H Partonic cross section s /2 q H xa xb Q2 Jet - In AA collisions, in absence of nuclear and/or QGP effects one should observe binary scaling

Breaking of binary scaling (1)
RAA < 1 RAA = 1 RAA 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)

Final state effects  change in the fragmentation functions due to the presence of the medium: energy loss/jet quenching E - DE Parton crossing the medium looses energy via scattering with partons in the medium (collisional energy loss) gluon radiation (gluonstrahlung) Quenched spectrum Spectrum in pp 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)
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 QGP 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-pT partons 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 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 Near-side peak Away-side peak 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

Results on angular correlations
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
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 defines direction 0-30% Central PbPb excess away from leading jet excess towards leading jet balanced jets unbalanced jets

Where does energy go? (2) Calculate missing pT in ranges of track pT
in-cone out-of-cone 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 quark mesons/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 q < MQ/EQ Should lead to a suppression hierarchy Eg > Echarm > Ebeauty RAA (light hadrons) < RAA (D) < RAA (B)

Heavy-flavor measurements: NPE
Non-photonic electrons (pioneered at RHIC), based on semi-leptonic decays of heavy quark mesons g conversion p0  gee h  gee, 3p0 w  ee, p0ee f  ee, hee r  ee h’  gee 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 electrons similar 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 q values and collisional energy loss ^ Fair agreement with models including only charm, but clearly not a realistic description

Various techniques for heavy-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 Similar trend vs. pT for D,
charged particles and p± 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/y from 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 109

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>RAAcharm and RAAbeauty>RAAlight More statistics needed to conclude on RAAcharm vs. RAAlight Indication (3s) for non-zero charm elliptic flow at low pT Angular correlation: radiative vs collisional energy loss

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!

Heavy Ions and Quark-Gluon Plasma…

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Heavy Ions and Quark-Gluon Plasma…

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