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
Feb 22, 2016
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….
2
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
27
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)
28
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
31
/)(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
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
..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!)