Lecture 1Heavy Ion Collisions: geometry, timescales,

and collective behavior

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Barbara JacakStony Brook UniversityJanuary 10, 2012

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Outline(s)

TODAY Introduction and motivation to study the QCD plasma Stages and timescales in heavy ion collisions Geometry of the collisions Collective flow, hydrodynamics, and “the perfect liquid” Effects of fluctuations

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Lectures on heavy ion collisions and quark gluon plasma1. Geometry and collective behavior in heavy ion collisions2. Energy loss and opacity in the quark gluon plasma3. Properties of strongly coupled plasmas and what the

string theorists tell us 4. Electromagnetic probes, screening, and QGP outlook

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Goal: Create the hottest matter on earth

Heat to T > 1012 Klast seen: ~ 1 second after the Big Bang!

What is it? How does it work? What can we learn

about the transition?

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Inside a nucleon

Q2: momentum transfer in a collision

x: m

omen

tum

frac

tion

carr

ied

by p

arto

n

Gluon number is not fixedVirtual q-q pairs abundant

Scatter electrons off a p

slogQ2)n terms

sln(1/x))n terms

Theorists’ view Experimenter’s view

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Hot, dense QCD matter Gluons carry color interact among themselves

theory is non-abelian

Curious property at large distance:confinement of quarks in hadrons

+ +…

asymptotic freedom

At high temperature/density screening by produced colored particlesExpect phase transition to deconfined quark gluon plasmaLattice QCD Tc ~ 170 MeV

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From the practical point of view

What we see in the lab:All the particles which come out at the end of the collision

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RHIC at Brookhaven: heat matter up

Collide Au + Au ions for maximum volumes = 200 GeV/nucleon pair, p+p and d+A to compare

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The Tools

STARspecialty: large acceptancemeasurement of hadrons

PHENIXspecialty: rare probes, leptons,

and photons

At the LHC

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Pb+Pb at 2.76 TeV per NN

Also, ATLAS and CMS take data with Pb+Pb

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heavy ion collision & diagnostics

p,K,p,n,f,L,D,X,W,d,Hadrons qqq baryons & qq mesonsreflect (thermal) properties when inelastic collisions stop

not possible to measure as a function of time nature integrates over the entire collision history

thermal radiation

(g, g* e+e-, +-)

Hot QGP

e,pressure builds up

Hard scattered q,g(short wavelength) probes of plasmaformed

time

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Questions Can we create quark gluon plasma in the lab? thermodynamic properties (equilibrium)

T, P, rEquation Of State (relation btwn T, P, V, energy density)vsound, static screening length

transport properties (non-equilibrium)*particle number, energy, momentum, charge diffusion sound viscosity conductivity

In plasma: interactions among charges of multiple particles charge is spread, screened in characteristic (Debye) length,lD

also the case for strong, rather than EM force

*measuring these is new for nuclear/particle physics!

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study plasma with radiated & “probe” particles

as a function of transverse momentum90° is where the action is (max T, r)

pL between the two beams: midrapidity pT < 1.5 GeV/c

“thermal” particles radiated from bulk medium“internal” plasma probes

pT > 3 GeV/clarge Etot (high pT or M) set scale other than T(plasma)autogenerated “external” probedescribe by perturbative QCD

control probe: photonsEM, not strong interactionproduced in Au+Au by QCD Compton scattering

Geometry matters

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ameter = b

Use Glauber model of nucleons in the nucleus calculate # of participant nucleons Npart

# of binary NN collisions Ncoll

Glauber model: calculate probabilities

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bbB

bAzB

zA

Nucleus BNucleus A

volume element in B: dbBdzB

volume element in A: dbAdzA

Probability of finding a nucleon in volume element B =rB(bB,zB) dbBdzB (rB is nuclear density * nucleons in B)

OK, so what happens when two nuclei collide?

NB: b ≠ 0!

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Does the matter exhibit collectivity? Look for collective flow via velocity boosts

Is the expansion hydrodynamical?Model expansion of the system with fluid dynamics

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Collective motion & elliptic flow (v2)

dN/df ~ 1 + 2 v2(pT) cos (2f) + …

hydrodynamics works!

Almond shape overlap region in coordinate space

x

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momentum space

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Surprise: matter flows like a liquid

• huge pressure buildup • large anisotropy

it all happens fast • efficient equilibration mechanism??

only works with low viscosity/entropy“perfect” liquid (D. Teaney, PRC68, 2003)

Kolb, et al

Hydrodynamics reproduces elliptic flow of q-q and 3q states Mass dependence requires soft EOS, NOT gas of hadrons

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Eccentricity:

Mechanism for fast thermalization?

Must be thermalized in < 1 fm/c!Otherwise v2 smaller than in the data

Can this be achieved with gg, qg, and qq binary scatterings?NO!Making this picture yield sufficient v2, requires

boosting the pQCD parton-parton cross sections by a factor of ~50!

Mechanism not knownI’ll discuss some ideas in lecture 3

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Elliptic flow scales with number of quarks

transverse KE

implication: valence quarks, not hadrons, are relevant pressure builds early, dressed quarks are born of flowing field

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small viscosity/entropy was a surprise

Viscosity: inability to transport momentum & sustain a wave

low viscosity absorbs particles & transports disturbances

Viscosity/entropy near 1/4p limit from quantum mechanics!

liquid at RHIC is “perfect”

Example: milk. Liquids with higher viscosities will not splash as high when poured at the same velocity.

Good momentum transport: neighboring fluid elements “talk” to each other

QGP is strongly coupledShould affect opacity : e.g. q,g collide with “clumps” of gluons, not individuals

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pT dependence of v2

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√s dependence

QuarknumberScalingworks at√s = 62

@ 17 GeV?

Pb+Pb at LHC similar flow as at RHIC

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STAR at RHIC

Preliminary, STAR, PHENIX and E895 data

103 104

ALICE

v2 saturates @ 39 GeV

pT = 1.7 GeV

pT = 0.7 GeV

@ LHC Tinit ~30% higherh/s(t) sampled differently

ALICE

Perfect liquid? Quantify viscosity of QGP!

Use hydro with lattice EOS Set initial energy density to reproduce observed

particle multiplicity Use various values of h/s

Quantum mechanical lower bound is 1/4pdetermined with help from AdS/CFT

Constrain with data(Account for hadronic state viscous effects with

a hadron cascade afterburner)

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3-d viscous hydro and RHIC data

h

h

h

h

Answer depends on1) Details of hydro code2) Viscous correction3) Initial conditions4) Freezeout particle mix

(being addressed)5) Dynamics at freezeout… h/s ≤ 0.08 - 0.16

Glauber CGC

Smaller eccentricity

Larger eccentricity

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Momentum dependence of viscous correction

hh

h

Fluctuations matter! Nucleons move around inside the

nucleus-> locations of NN scattering fluctuate-> apparent symmetry effects yielding

only even harmonics not realistic

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arXiv:1109.6289

h/s=0.08

Reproduce with hydro IF include fluctuating initial

conditions Provides a tool to better

pin down the viscosity/entropy ratio

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Higher moments more sensitive to viscosity

vnh/s=0.16)/vn(ideal)vnh/s=0.08)/vn(ideal)

arXiv:1109.6289 Longitudinal expansion at v ~ c “freezes in” small shape

perturbationse.g. triangular fluctuations (v3)

Viscosity opposes dissipation!

Fluctuations, flow and the quest for h/s

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Glauber Glauber initial state h/s = 1/4p

MC-KLN CGC initial state h/s = 2/4p

v2 described by both Glauber and CGC

but different values of h/s

2 models withDifferent fluctuations,

Eccentricity, r distribution

200 GeV Au+Au

Theory calculation:Alver et al.PRC82,034913  

Lappi, Venugopalan, PRC74, 054905Drescher, Nara, PRC76, 041903

Stefan Bathe for PHENIX, QM2011

arXiv:1105.3928

arXiv:1105.3928

Theory calculation:Alver et al.PRC82,034913  

v3 described only by Glauber breaks degeneracy

pT and √s dependence

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v2

v3

arXiv:1105.3928

Glauber CGC

Smaller eccentricity

Larger eccentricity

At the LHC

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v2v3

ALICE

Thermal photons also flow!

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inclusive photon v2

Au+Au@200 GeVminimum bias Statistical subtraction

inclusive photon v2

- decay photon v2 = direct photon v2

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.2.

2 --

g

g

RvvR

vBGinc

dir

inclusive photon v2

Au+Au@200 GeVminimum bias

p0 v2

p0 v2 similar to inclusive photon v2

Au+Au@200 GeVminimum bias

Direct photon v2

Large flow magnitude is very surprising!

arXiv:1105.4126

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backup slides

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Calculating transport in QGP

weak coupling limit ∞ strong coupling limitperturbative QCD not easy! Try a pure field…kinetic theory, cascades gravity supersym 4-d interaction of particles (AdS/CFT)

23,32,n2…

Expect if c-cbar pairs numerous or correlated

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PRL.98: 172301,2007

Open charm flows but J/y does not

So, cc coalescence in final state @ RHIC is not largeHigher at LHC?

susceptibilities & net-baryon fluctuations

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Relation between the baryon susceptibilities, cB, and cumulants of the net-baryon fluctuations

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minimum h at phase boundary?

Csernai, Kapusta & McLerran PRL97, 152303 (2006)

quark gluon plasma

B. Liu and J. Goree, cond-mat/0502009

minimum observed in other strongly coupled systems –kinetic part of h decreases with G while potential part increases

strongly coupled dusty plasma

Barbara Jacak - Lattice 2011 44

Direct photon flow ingredients

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ginc. v2 with external conversion method

200GeV Au+Au 20-40% PHENIX Preliminary

ginc. v2

(2BBC)

Key cross checks:ginc are really g’s: check using g-> e+e-Rg for virtual vs. real g

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heavy quark suppression & flow?PRL.98: 172301,2007arXiV: 1005.1627

Collisional energy loss?

v2 decrease with pT?

role of b quarks?

Critical point search: low energy Au+Au @ RHIC

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S. Gupta, QM2011

Tools:Fluctuations, partonic collective flows

S. Gupta, QM2011

Can we locate the QCD critical point?

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+ deconfinement onset

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Fluctuations as Critical Point Signature

Event-by-event net-baryon fluctuation ratios from STAR are so far consistent with the Hadron Resonance Gas

Hadron freezeout not (yet) near critical pointCalculations of higher moments from LQCD deviate from HRG

calculations and may provide conclusive evidence for critical point if observed in data

Karsch, et al. PLB 2010.10046

Beam Energy Scan in PHENIX

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Is there a critical point separating 1st order phase transition & smooth cross-over? Quark-number scaling of V2

• saturation of flow vs collision energy• find h/s minimum at critical point from flow

Critical point searches via:• fluctuations in <pT> & multiplicity• K/π, π/p, pbar/p chemical equilibrium• RAA vs s, ….

Dense gluonic matter (d+Au, forward y): large effects observed

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Shadowing/absorption stronger than linear w/nuclear thickness

Di-hadron suppression at low x pocket formula (for 22):

sepepx TTfrag

Au

--

2121

hh

pppairpp

dApair

dA

colldA N

J

//1

trend as, e.g. in CGC …

arXiv:1105.5112arXiv:1010.1246

pppairpp

dApair

dA

colldA N

J

//1

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Beam Energy Scan at RHIC

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√sNN (GeV) Status Experiment

5.0 TBD STAR

7.7 analyzed STARPHENIX (limited statistics)

11.5 analyzed STAR

19.6 Collected in 2011 STAR, PHENIX

27 Collected in 2011 STAR, PHENIX

39 analyzed STAR, PHENIX

62 analyzed STAR, PHENIX

130 collected in Run-1, analyzed limited statistics

STAR, PHENIX