From Heavy-Ion Collisions to Quark Matter
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From Heavy-Ion Collisions to Quark Matter
Constantin Loizides(LBNL)
Lecture 2
CERN summer student programme 2014
2Study QCD bulk matter at high temperature
Momentum transfer
Transverse size of collision region
Bulk QCDmatter at hightemperature
0.2 GeV/c
>10 GeV/c
~1fm ~10fm
Nebula M1-67(see hubblesite.org)
3External parameters: Collision energy
Collision energy
Drees, QM 01
Ratio of “soft” to “hard” processes
μB (MeV)
Initial conditions and freeze-out paths
4External parameters: Collision centrality
Collision centrality
Collision energy
Nuclear cross-section classes(by slicing in bins of multiplicity)
Cross-section percentile (in %)
5External parameters: Collision centrality
Collision centrality
Collision energy
Nuclear cross-section classes(by slicing in bins of multiplicity)
Glauber model
Number of participants (collisions) Cross-section percentile (in %)Via model
6External parameters: Transverse geometry
Center of mass energy
Collision centrality
x
y Nucleus 2Nucleus 1
Overlap (participant) region is asymmetric in azimuthal angle
φ
PHOBOS Glauber MC
Number of participants
Eccentricity
ϵstd=σ y
2−σ x2
σ y2 +σ x
2
Initial state eccentricity
7
The “fireball” evolution:• Starts with a “pre-equilibrium state”
• Forms a QGP phase (if T is larger than Tc)
• At chemical freeze-out, Tch, hadrons stop being produced
• At kinetic freeze-out, Tfo, hadrons stop scattering
Time evolution in heavy-ion collisions
8Time evolution in heavy-ion collisions
Experimental approach is to study various observables with different sensitivity to the different stages of the collision
MultiplicityThermal photonsHBTParticle yieldsParticle spectra
Transverse flow
Hard probes(jets, heavy flavor)
Observables
9Energy dependence of dN/dη and dET/dη
Central collisions
Central collisions
arXiv:1202.3233
PRL 109 (2012) 152303
CMS
Use these measurements to get an estimate of the energy density
10Estimate of energy density
● Consider two nuclei contracted with Lorentz factor γ. In the moment of total overlap one gets
● For RHIC 200 AGeV collisions
Huge!
11Estimate of energy density
● Consider two nuclei contracted with Lorentz factor γ. In the moment of total overlap one gets
● For RHIC 200 AGeV collisions
● Need to account for the formation time needed to produce particles
● Imagine colliding nuclei as thin pancakes (Lorentz-contraction) which, after crossing, leave an initial volume with a limited longitudinal extension, where the particles are produced
Bjorken, PRD 27 (1983) 140
Huge!
12Energy dependence of dN/dη and dET/dη
Central collisions
Central collisions
arXiv:1202.3233
PRL 109 (2012) 152303
CMS
● Take into account that the system undergoes a rapid evolution● Using 1 fm/c as an upper limit
for the time needed to thermalization● Leads to densities far above the
transition region (except for AGS)
13Initial temperature at RHIC
Direct photons: No charge, no color, ie. they do not interact after Use (at low pT) to extract temperature of the system.
14Initial temperature at RHIC
Direct photons: No charge, no color, ie. they do not interact after Use (at low pT) to extract temperature of the system.
Excess
QGP dominated
PRC 87 (2013) 054907
PRL 104 (2010) 132301
PHENIX
PRL 94 (2005) 232301
● Different measurements performed using real and virtual photons
● Exponential (thermal) shape with inverse slope of T~200 MeV in excess region
● No excess seen in d+Au (or pp)
15Initial temperature at RHIC
Direct photons: No charge, no color, ie. they do not interact after Use (at low pT) to extract temperature of the system.
● Different measurements performed using real and virtual photons
● Exponential (thermal) shape with inverse slope ofT~220 MeV in excess region
● No excess seen in d+Au (or pp)
● Emission rate and shape consistent with that from equilibrated matter
● From models: Tinit = 300 - 600 MeV (> 2 Tc)
First experimental observation of T>Tc
Models
PRC 81 (2010) 034911
16Intensity interferometry (HBT)
● Two particles whose production or propagation are correlated in any way exhibit wave properties in their relative momentum difference
● First used with photons by Hanbury Brown and Twiss to measure size of star Sirius
● Quantum statistics effect: Enhancement of correlation for identical bosons
● From uncertainty principle● Δq Δx ~ 1 ● Use to extract source size
from correlation function● Need Δq ~ 200 MeV to be
sensitive to fm scale
1
2
q=p 1− p2 r=r1−r2
HBT, Nature 178 (1956) 1046
17Intensity interferometry (HBT)
● In LCMS (pL,1+pL,2=0), can decompose correlation function in three directions
● Longitudinal direction
● Outward (along kT direction)● Sideward (orthogonal) direction
● Assuming Gaussian
● Three components of C(q)for pairs of identical pions in 8 intervals of the pair transverse momentum
18Intensity interferometry (HBT)From RHIC to LHC
● Increase of radii in all directions– Out, side and long
PLB 696 (2011) 328
19Intensity interferometry (HBT)From RHIC to LHC
● Increase of radii in all directions– Out, side and long
● “Homogeneity” volume: 2x RHIC
● Substantial expansion– For comparison: R(Pb) ~ 7fm →V~1500fm3
– Lifetime (extr. from Rlong) ~ 10fm/c
PLB 696 (2011) 328
20Thermal equilibrium● In HI usually two aspects of thermal equilibrium are considered
● Kinetic Equilibrium
– Are the pT distributions of particle species at low pT described by a thermal distribution?
● Chemical Equilibrium– Are all particle species produced at the right relative abundances?
21Statistical models● Statistical models of hadronization
● Hadron and resonances gas with masses < 2 GeV/c– Well known hadronic spectrum– Well known decay chains
● The formula for the yield per species
● Here, Ei is the energy and gi is the degeneracy of the species i, and μB, μS, μ3 are baryon, strangeness and isospin chemical potentials, respectively
● In principle, 5 unknowns but also have information from initial state about Ns neutron and Zs stopped protons
● Only two parameters remain: μB and T ● Typically use ratio of particle yields between
various species to determine μB and T
22Particle ratios at the AGS
c2 contour lines
Au+Au: Ebeam = 10.7 GeV/nucleon ↔ √sNN=4.85 GeVMinimum χ2 for : Tch = 124±3 MeV and μB = 537±10 MeV
NPA 772 (2006) 167
23Particle ratios at the SPS
c2 contour lines
Pb+Pb: Ebeam = 40 GeV/nucleon ↔ √sNN=8.77 GeVMinimum χ2 for : Tch = 156±3 MeV and μB = 403±18 MeV
NPA 772 (2006) 167
24Particle ratios at RHIC
c2 contour lines
Au+Au: √sNN=130 GeVMinimum χ2 for : Tch = 166±5 MeV and μB = 38±11 MeV
NPA 772 (2006) 167
25Particle ratios at the LHC
Pb+Pb: √sNN=2.76 TeVMinimum χ2 for : Tch = 156±2 MeV and μB = 0 MeV (fixed)
arXiv:1407.5003
χ2/dof = 17.4/9
● Ratios except p/π well described
● Disagreement for p/π may point to the relevance of other effects at LHC like
● Rescattering in hadronic phase
● Non-equilibrium effects● Flavor-dependent
freeze-out
26Statistical model parameters vs √sNN
arXiv:1407.5003
Chemical freeze-out points
27Transverse momentum distributions
To address the question of kinetic equilibrium, inspect pT distributions
● Low pT (<~1 GeV/c)
● “Soft” (ie. non-perturbative) production mechanisms
● 1/pT dN/pT ~ exponential i.e. Boltzmann-like
● Almost independent of √s
● High pT (>>1 GeV/c)
● “Hard” (ie. perturbative) production mechanisms
● Deviation from exponential towards power-law
28Transverse mass (mT) scaling in pp collisions
● Exponential behaviorat low pT, in pp collisions
● Identical for all hadrons
● Transverse mass (mT) scaling
● Tslope ~ 170 MeV for all particles
● These distributions look like thermal spectra
● Tslope can be interpreted as the temperature at the timewhen kinetic interactions between particles ended
● Kinetic freeze-out temperature (Tfo)
29Breaking of mT scaling in A+A collisions
● Harder spectra (i.e. larger Tslope) for larger masses
● Consistent with a shift towards larger pT for heavier particles
● Remember pT = m0vT
30
x
yv
v
Flow in A+A collisions
Radial flow first mentioned:Shuryak, PLB 89 (1980) 253
● Interpretation in the flow picture:Collective motion of particles superimposed to thermal motion
● For any interacting system of particles expanding into vacuum, radial flow is a natural consequence
● During the cascade process, one naturally develops an ordering of particles with the highest common underlying velocity at the outer edge
● This motion complicates the interpretation of the momentum of particles at kinetic freeze-out and should be subtracted
31Decoupling motion: Blast wave description
● Consider a thermal Boltzman source
Schnedermann et al., PRC 48 (1993) 2462
● Boost source radially with a velocity β and evaluate at y=0
with
Three parameters: T,βs and n(sometimes n=2 is fixed)
● Simple assumption: Consider uniform sphere of radius R
and parametrize surface velocity as
32Radial flow and kinetic freeze-outPRL 109 (2012) 252301
● Strong radial flow up to βLHC,central = 0.65c
● βLHC,central = 1.1 βRHIC,central
● Similar kinetic freeze-out Tkin≈100 MeV
LHC
RHIC
33Thermal equilibrium vs √sNN
arXiv:1407.5003
34
Non-interacting particles Collective expansion
What happens to the shape (eccentricity) information during the expansion?
How do we prove that we make “matter”?
35How do we prove that we make “matter”?
4
1
2
3
Non-interacting particles Collective expansionNon-interacting particles Collective
Eccentricity information is not transferred to momentum space
Eccentricity information does get transferred to momentum space
dN/dφ
Flat azimuthal distribution
dN/dφ
cos 2φ modulation
1
2 4
13
36Initial and final state anisotropy
Initial spatial anisotropy:Eccentricity
Momentum space anisotropy:Elliptic flow
v 2=⟨ cos ( 2 ϕ − 2 Ψ R )⟩
Interactions present early
x
y Nucleus 2Nucleus 1
φ
dNd ϕ
∼1+2 v2 cos [2(ϕ−ψR)]+…
std= y
2− x2
y2 x
2
cos 2φ modulation
dN/dφ
37Elliptic flow: Self quenching
● 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 early stages of the system
38Elliptic flow: Self quenching
Kolb, Heinz, nucl-th/0305084● The picture is supported by a
hydrodynamical calculation using two different equations of state
● The momentum anisotropy is dominantly built up in the QGP (τ<2-3fm/c) phase and stays constant in the (first-order) phase transition, and only slightly rises in the hadronic phase
39Measuring the v2 coefficient
v 2=⟨ cos ( 2 ϕ − 2 Ψ R )⟩
Needs to deal with the reaction plane angle: Either use differences or reconstruct it
tan 2A=⟨sin 2⟩A⟨cos2⟩A
v 2obs= ⟨ cos 2 − 2 A ⟩B
v 2=⟨v 2
obs ⟩events⟨cos 2 A−2B ⟩events
Estimate reaction plane angle using two sub-events. Then correlateparticles of interest, and correct for event plane resolution.
Poskanzer, Voloshin, nucl-ex/9805001
v {2 }=√ ⟨ cos (2 ϕ 1− 2 ϕ 2 )⟩
Two-particle correlations
Can suppress “non-flow” by employing cuts in |Δη|
40Measuring the v2 coefficient
Minbias Au+Au, √sNN=130 GeV
STAR, PRL 86 (2001) 402
Huge elliptic flow coefficients!dNd ϕ
∼1+ 2 v2 cos [2(ϕ−ψR)]+ …
At 1 GeV: 20% modulation
41Results on integrated elliptic flow (RHIC)
Hydrodynamic limit
RQMD
√sNN=130 GeV
Nch/Nmax
v2
STAR
PHOBOS
● Elliptic flow depends on● Eccentricity of overlap
region, which decreaseswith increasing centrality
● Number of interactions, which increases with increasing centrality
● At RHIC● Models based on hadronic cascades, such as RQMD, fail.
Hence, v2 is likely to be built up in the partonic (deconfined) phase
42Results on integrated elliptic flow (RHIC)
Hydrodynamic limit
RQMD
√sNN=130 GeV
Nch/Nmax
v2
STAR
PHOBOS
● Elliptic flow depends on● Eccentricity of overlap
region, which decreaseswith increasing centrality
● Number of interactions, which increases with increasing centrality
● At RHIC● Models based on hadronic cascades, such as RQMD, fail.
Hence, v2 is likely to be built up in the partonic (deconfined) phase
● Measured v2 found for the first time in agreement with ideal hydrodynamical calculations (for central and mid-central collisions)
– Fast (<1fm/c) thermalization with matter (close to) an ideal fluid– In more peripheral collisions thermalization is incomplete or slower– Hydro limit is done for perfect fluid, the effect of viscosity would reduce
the elliptic flow
43Hydrodynamical model calculations
Today even second order calculations (full Israel-Stewart) calculations done.
Heinz, arXiv:0901.4355
+ freeze-outconditions
44Effect of viscosity
Heinz, arXiv:0901.4355
Early calculations at RHIC used η/s=0. Today small values between (1-3)/4π used.
45Results on elliptic flow vs pT (RHIC)
● At low pT the data is described by hydrodynamics
● At high pT, significant deviations are observed. Natural explanation:
● High-pT particles are produced early and quickly escape the fireball without (enough) rescattering and no thermalization
● Hydrodynamics not expected to be applicable
46What's needed partonically to get v2?
Need large opacity to describe elliptic flow, ie elastic parton cross sections as large as inelastic the proton cross-section
Transverse momentum [GeV]
v2
Parton transport model:Bolzmann equation with2-to-2 gluon processes
HUGE (almost hadronic!!!) cross sections needed to describe v2
D.Molnar, M.Gyulassy NPA 697 (2002)
47Change of paradigm
RHIC whitepapers: NPA 757 1-283 (2005)
● Manifestation of strongly coupled QGP
● Not a gas of free quarks and gluons
● Instead, strongly coupled nearly perfect liquid reaching almost the minimum value of shear viscosity to entropy density ratio (η/s)
The quark-gluon liquid
48Elliptic flow vs pT (LHC vs RHIC)
Observe v2(pT)LHC ≈ v2(pT)RHIC above 1 GeV to about 5% despite factor 14 increase in energy, but consistent with hydro predictions! (Int.v2 30% larger due to radial flow)
ALICE
10-20%20-30%30-40%
Lines/bands are STAR 200 GeV dataElliptic flow coefficient, v2{4}
PRL 105 (2010) 252302
49Identified particle v2 versus pT (LHC)
Observed mass ordering in v2 due to radial flow can be described by hydrodynamical models
arXiv:1202.3233
50Summary
Bulk observables lead to results which are consistent with the interpretation that we create thermalized matter with liquid properties.
MultiplicityThermal photonsHBTParticle yieldsParticle spectra
Transverse flow
Hard probes(jets, heavy flavor)
Observables
If you have questions about today's lecture please send them to “cloizides at lbl dot gov”
Tomorrow
51Extra
52Centrality dependence of dN/dη
Factorization in energy and centrality: Shape is strikingly similar to RHIC
Glauber IC
CGC IC
Two-component models need to incorporate strong nuclear modification. Saturation models naturally imply
arXiv:1202.3233
53Nuclear geometry and collision centrality
ZDCV0
Correlate particle yields from ~causally disconnected parts of phase space
→Correlation arises from common dependence on collision impact parameter
Nuclei are macroscopic objects: Characterize collisions via impact parameter
54Nuclear geometry and collision centrality
Nuclei are macroscopic objects: Characterize collisions via impact parameter
For
war
d ne
utro
ns
Charged hadrons ~3
● Order events by centrality metric
● Typically, classify them as “ordered” fraction of total cross section
– eg. 0-5% most central collisions● Not trivial to obtain total cross
section as it requires good control of background and trigger efficiency for very peripheral collisions
● Connect to Glauber theory via particle production model to obtain
– Number of (inelastically scattered) participating nucleons
– Number of binary nucleon collisionsPRC 88 (2013) 044909
55Glauber Monte-Carlo model
x
yParticipants
Impact parameter (b)
● Calculate vs impact parameter
● #Participants (<Npart>)
– Nucleons struck at least once
● #NN-collisions (<Ncoll>)
– Total number of collisions● Size of interaction area (<S>)
● Semi-classical model of nucleus+nucleus collision based on incoherent nucleon+nucleon scatters
● Nucleons distributed according to measured proton charge distribution in nucleus, e.g. Pb nucleus
– Radius (6.62 ± 6fm)– Skin depth (0.546 ± 0.02 fm)
● Assume repulsion by enforcing inter-nucleon distance (e.g. 0.4 ± 0.4 fm)
● Collision process by assuming● Straight-line nucleon trajectories ● Interaction radius given by inelastic
proton-proton cross section (σNN)● Equal probabilities for all (including)
subsequent scatterings
Ann.Rev.Nucl.Part.Sci. 57 (2007) 205
56Initial temperature at LHC
● Measure R = (inc (mc
● Uncertainties (exactly or partially) cancel in the ratio
● Normalization● Photon reconstruction
efficiency
Excess
● Inverse slope: T=304±51 MeV● Larger than at RHIC
● Tinit expected to be > T
● But currently models have difficulties reproducing the yield
Preliminary
Excess
57Canonical suppression
Redlich and Tounsi, hep-ph/0111159
√sNN=130 GeV
17.3 GeV
12.3 GeV
8.3 GeV
For Npart≥60, Grand Canoncial ok to better than 10%
58Shear viscosity in fluids
Shear viscosity characterizes the efficiency of momentum transport
quasi-particle interaction cross section
Comparing relativistic fluids: η/s• s = entropy density• scaling parameter η/s emergy from hydro equations• generalization for non-rel. Fluids: η/s (w=enthalpy)
Liao and Koch, PRC81 (2010) 014902
Large σ → small η/s→ strongly-coupled matter→ “perfect liquid”
59Shear viscosity in QCD
pQCD w/ running coupling
Chiral limit,resonance gas
1/4 Lattice QCD
Temperature (MeV)
Analytic: Csernai, Kapusta and McClerran PRL 97, 152303 (2006)Lattice: H. Meyer, PR D76, 101701R (2007)
ηs
=1
4
Minimal boundfrom AdS/CFT
60Description of initial state?
200 GeV
130 GeV
62.4 GeV
19.6 GeV
Number of participants
PHOBOS
PRL 102 142301 (2009)
Mid-rapidity density
Two-component model dNd
= dN
d pp 1− x N coll x N part /2 dNd
∝N part s
Color glass condensate
PRC 70 021902 (2004) PRL 94 022002 (2005)
Glauber IC CGC IC
Two classes of models describe the multiplicity (believed to be sensitive to initial state) equally well
61Ambiguity translates into conclusions
Hirano et al., PLB 636 299 (2006)
Eccentricity
Ambiguity in description of initial state allows for various models: Size of viscous corrections and/or soft equation of state?
Higher eccentricity leads to higher flow
62The hot QGP is a nearly perfect fluid ...
Combination of many calculations, including state-of-art results from Israel-Stewart theory for a conformal fluid (2+1D), hint to a low shear viscosity to entropy ratio:
1
4<
ηs
<3
4Largest part of uncertaintiesstill from the ambiguity in the description of initial state.
200 GeV Au+Au data
CGC initial conditions MC Glauber initial conditions
Song et al, PRL 109 (2012) 139904