From Heavy-Ion Collisions to Quark Matter

1

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 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


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.



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)



● 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

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From Heavy-Ion Collisions to Quark Matter