1Jim Thomas - LBL

Energy Loss and Flow in Heavy Ion Collisions at RHICNiels Bohr was almost right about the liquid drop model

Jim ThomasLawrence Berkeley National Laboratory

Berkeley, CA

University of Notre Dame

February 20th, 2008

2Jim Thomas - LBL

The Phase Diagram for Nuclear Matter

The goal is to explore nuclear matter under extreme conditions – T > mc2 , > 10 * 0 and net 0

• One of the goals of RHIC is to understand the QCD in the context of the many body problem

• Another goal is to discover and characterize the Quark Gluon Plasma

• RHIC is a place where fundamental theory and experiment can meet after many years of being apart

3Jim Thomas - LBL

Who is RHIC and What Does He Do?

RHIC

• Two independent rings

• 3.83 km in circumference

• Accelerates everything, from p to Au

s L p-p 500 1032

Au-Au 200 1027

(GeV and cm-2 s-1)

• Polarized protons

• Two Large and two small detectors were built

h

BRAHMS

PHOBOS

PHENIX

STARSTAR

And for a little while longer, it is the highest energy heavy ion collider in the world

Long Island

Long Island

4Jim Thomas - LBL

The Large Detectors – PHENIX and STAR

STAR PHENIX

5Jim Thomas - LBL

STAR is a Suite of Detectors

Barrel EM Calorimeter

FTPCs

Time Projection Chamber

Silicon TrackerSVT & SSD

Endcap Calorimeter

Magnet

Coils

TPC Endcap & MWPC

Central Trigger Barrel & TOF

Beam Beam Counters

4.2 meters

Not Shown: pVPDs, ZDCs, and FPDs

A TPC lies at the heart of STAR

PMD

6Jim Thomas - LBL

Au on Au Event at CM Energy ~ 130 GeV*A

Real-time track reconstruction

Pictures from Level 3 online display. ( < 70 mSec )

Data taken June 25, 2000.

The first 12 events were captured on tape!

7Jim Thomas - LBL

Au on Au Event at CM Energy ~ 130 GeV*A

Two-track separation 2.5 cm

Momentum Resolution < 2%

Space point resolution ~ 500 m

Rapidity coverage –1.8 < < 1.8

A Central Event

Typically 1000 to 2000 tracks per event into the TPC

8Jim Thomas - LBL

Particle ID using Topology & Combinatorics

Secondary vertex: Ks + p +

+ + K e++e-

Ks + + - K + + K -

p + - + + -

from K+ K- pairs

K+ K- pairs

m inv

m inv

same event dist.mixed event dist.

background subtracted

dn/dm

dn/dm

“kinks”

K +

9Jim Thomas - LBL

Identified Mesons and Baryons: Au+Au @ 200 GeV

and p yields .vs. pTPhys. Rev. Lett. 97 (2006) 152301

10Jim Thomas - LBL

0

0 . 2

0 . 4

0 . 6

0 . 8

1

1 . 2

1 . 4

1 . 6

-6 -4 -2 0 2 4 6y

dy

dn

Nomenclature: Rapidity vs xf

• xf = pz / pmax

– A natural variable to describe physics at forward scattering angles

• Rapidity is different. It is a measure of velocity but it stretches the region around v = c to avoid the relativistic scrunch

– Rapidity is relativistically invariant and cross-sections are invariant

)/(tanh 1 Epyor z

Rapidity and pT are the natural kinematic variable for HI collisions( y is approximately the lab angle … where y = 0 at 90 degrees )

When the mass of the particle is unknown, then y

1tanh yy

z

z

pE

pEy ln

2

1

β

11Jim Thomas - LBL

Strange Baryons and Mesons: Au+Au @ 200 GeV

, , and yields .vs. pTPhys. Rev. Lett. 98 (2007) 060301

12Jim Thomas - LBL

Transverse Radial Expansion: Isotropic Flow

The transverse radial expansion of the source (flow) adds kinetic energy to the particle distribution. So the classical expression for ETot

suggests a linear relationship

-

K -

p

Au+Au at 200 GeV

Typical STAR Data

2KFOObs massTT

Slopes decrease with mass. <pT> and the effective temperature increase with mass.

T ≈ 575 MeV

T ≈ 310 MeV

T ≈ 215 MeV

13Jim Thomas - LBL

Chemical and Kinetic Freeze-out

• Chemical freeze-out (first)– End of inelastic interactions

– Number of each particle species is frozen

• Useful data– Particle ratios

• Kinetic freeze-out (later)– End of elastic interactions

– Particle momenta are frozen

• Useful data– Transverse momentum distributions

– and Effective temperatures

space

tim

e

inelasticinteractions

Chemicalfreeze-out

elasticinteractions

Kineticfreeze-out

blue beam yellow beam

14Jim Thomas - LBL

Chemical Freeze-out – from a thermal model

• The model assumes a thermally and chemically equilibrated fireball at hadro-chemical freeze-out which is described by a temperature T and (baryon) chemical potential : dn ~ e-(E-)/T d3p

• Works great, but there is not a word of QCD in the analysis. Done entirely in a color neutral Hadronic basis!

Thermal model fits

Compare to QCD on the (old) Lattice:

Tc = 154 ± 8 MeV (Nf=3)

Tc = 173 ± 8 MeV (Nf=2)(ref. Karsch, various)

MeV 629(RHIC)μ

MeV 7177(RHIC)T

B

ch

MeV 270(SPS)μ

MeV 170160(SPS)T

B

ch

input: measured particle ratios output: temperature T and baryo-chemical potential B

15Jim Thomas - LBL

• Final-state analysis suggests RHIC reaches the phase boundary

• Hadron spectra cannot probe higher temperatures

• Hadron resonance ideal gas (M. Kaneta and N. Xu,

nucl-ex/0104021 & QM02)

– TCH = 175 ± 10 MeV

– B = 40 ± 10 MeV

• <E>/N ~ 1 GeV(J. Cleymans and K. Redlich, PRL 81, p. 5284, 1998 )

Lattice results

Neutron STAR

Putting RHIC on the Phase Diagram

We know where we are on the phase diagram but eventually

we want to know what other features are on the diagram

16Jim Thomas - LBL

RHIC Physics is Relativistic Nuclear Physics

17Jim Thomas - LBL

Unlike Particle Physics, the initial state is important

• Only a few of the nucleons participate in the collision as determined by the impact parameter

• There is multiple scattering in the initial state before the hard collisions take place

– Cronin effect

• The initial state is Lorentz contracted

• Cross-sections become coherent. – The uncertainty principle allows wee

partons to interact with the front and back of the nucleus

– The interaction rate for wee partons saturates ( ρσ = 1 )

• The intial state is even time dilated– A color glass condensate

• proton • neutron • delta • pion string

18Jim Thomas - LBL

Dependent Distributions – Flow

• The overlap region in peripheral collisions is not symmetric in coordinate space

• Almond shaped overlap region

– Larger pressure gradient in the x-z plane drives flow in that direction

– Easier for high pT particles to emerge in the direction of x-z plane

• Spatial anisotropy Momentum anisotropy

• Perform a Fourier decomposition of the momentum-space particle distribution in the plane

– For example, v2 is the 2nd harmonic Fourier coefficient of the distribution of particles with respect to the reaction plane

))2cos(2)cos(21(2

121

2

3

3

vvdydpp

Nd

pd

dNE

TT

directed elliptic isotropic

19Jim Thomas - LBL

Interpreting Flow – order by order

n=1: Directed Flow has a period of 2 (only one maximum)

– v1 measures whether the flow goes to the left or right – whether the momentum goes with or against a billiard ball like bounce off the collision zone

n=2: Elliptic flow has a period of (two maximums)

– v2 represents the elliptical shape of the momentum distribution

))4cos(2)2cos(2)cos(21(2

1421

2

3

3

vvvdydpp

Nd

pd

dNE

TT

directed elliptic isotropic higher order terms

20Jim Thomas - LBL

V1: Pions go opposite to Neutrons

• hi

62 GeV Data

At low energy, the pions go in the opposite direction to the ‘classical’ bounce of the spectator baryons

200 GeV Data

At the top RHIC energy, the pions don’t flow(v1 at =0 )but at ALICE, v1 may have a backward wiggle.Reveals the EOS

21Jim Thomas - LBL

Interpreting Flow – order by order

n=1: Directed Flow has a period of 2 (only one maximum)

– v1 measures whether the flow goes to the left or right – whether the momentum goes with or against a billiard ball like bounce off the collision zone

n=2: Elliptic flow has a period of (two maximums)

– v2 represents the elliptical shape of the momentum distribution

))2cos(2)cos(21(2

121

2

3

3

vvdydpp

Nd

pd

dNE

TT

directed elliptic isotropic

22Jim Thomas - LBL

V2 vs. pT and Particle Mass

• The mass dependence is reproduced by hydrodynamic models

– Hydro assumes local thermal equilibrium

– At early times

– Followed by hydrodynamic expansion

D. Teaney et al., QM2001 Proc.P. Huovinen et al., nucl-th/0104020

PRL 86, 402 (2001) & nucl-ex/0107003

Anisotropic transverse flow is large at RHIC

• v2 is large– 6% in peripheral

collisions (for pions average over all pT )

• Flow is developed very rapidly

– Data suggests very early times ~ fm/c

• Hydro calculations are in good agreement with the data

– Hydro assumes local thermal equilibrium

– Followed by hydrodynamic expansion

– The mass dependence is reproduced by the models

23Jim Thomas - LBL

Elliptic Flow: in an ultra-cold Fermi-Gas

Li-atoms released from an optical trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions

– Elliptic flow is a general feature of strongly interacting systems!

A Simulation of Elliptic Flow

24Jim Thomas - LBL

v2 at high pT shows meson / baryon differences

Asym. pQCD Jet Quenching

Bulk PQCD Hydro

qn Coalescence

25Jim Thomas - LBL

-meson Flow: Partonic Flow

-mesons are special: - they show strong collective flow and - they are formed by coalescence of thermalized s-quarks ‘They are made via coalescence of seemingly thermalized quarks in central Au+Au collisions, the observations imply hot and dense matter with partonic collectivity has been formed at RHIC’

Phys. Rev. Lett. 99 (2007) 112301 and Phys. Lett. B612 (2005) 81

26Jim Thomas - LBL

The Recombination Model ( Fries et al. PRL 90 (2003) 202303 )

The flow pattern in v2(pT) for hadrons

is predicted to be simple if flow is developed at the quark level

pT → pT /n

v2 → v2 / n ,

n = (2, 3) for (meson, baryon)

27Jim Thomas - LBL

Elliptic flow scales with the number of quarks

Implication: quarks, not hadrons, are the relevant degrees of freedom at early times in the collision history

28Jim Thomas - LBL

Hints of Elliptic Flow with Charm

• D e +X

Single electron spectra from PHENIX show hints of elliptic flow

Is it charm or beauty?

• The RHIC upgrades will cut out large photonic backgrounds:

e+e-

and reduce other large stat. and systematic uncertainties

Better if we can do direct topological identification of Charm

Shingo Sakai, QM 2006 PRL 98, 172301 (2007)

29Jim Thomas - LBL

Constituent Quark Scaling?

• Hadrons are created by the recombination of quarks and this appears be the dominant mechanism for hadron formation at intermediate pT

• Baryons and Mesons are produced with equal abundance at intermediate pT

• The collective flow pattern of the hadrons appears to reflect the collective flow of the constituent quarks.

Partonic Collectivity

30Jim Thomas - LBL

Lets look at some collision systems in detail …

Final stateInitial state

Au + Au

d + Au

p + p

31Jim Thomas - LBL

Partonic energy loss via leading hadrons

Energy loss softening of fragmentation suppression of leading hadron yield

ddpdT

ddpNdpR

TNN

AA

TAA

TAA /

/)(

2

2

Binary collision scaling p+p reference

32Jim Thomas - LBL

Au+Au and p+p: inclusive charged hadrons

p+p reference spectrum measured at RHIC

PRL 89, 202301

33Jim Thomas - LBL

PHENIX data on the suppression of 0s

Factor ~5 suppression for central Au+Au collisions

lower energy Pb+Pb

lower energy

34Jim Thomas - LBL

The Suppression occurs in Au-Au but not d-Au

d+Au

Au+Au

No quenching

Quenching!

35Jim Thomas - LBL

Heavy Flavor Energy Loss … RAA for Charm

• Heavy Flavor energy loss is an unsolved problem

– Gluon density ~ 1000 expected from light quark data

– Better agreement with the addition of inelastic E loss

– Good agreement only if they ignore Beauty …

• Beauty dominates single electron spectra above 5 GeV

• RHIC upgrades will separate the Charm and Beauty contributions

Theory from Wicks et al. nucl-th/0512076v2

Where is the contribution from Beauty?

36Jim Thomas - LBL

Partonic energy loss

Energy loss suppression of leading hadron yieldThe jet can’t get out!

ddpdT

ddpNdpR

TNN

AA

TAA

TAA /

/)(

2

2

Binary collision scaling p+p reference

d+Au

Au+Au

No quenching

Quenching!

37Jim Thomas - LBL

Jet Physics … it is easier to find one in e+e-

Jet event in eecollision STAR Au+Au collision

38Jim Thomas - LBL

Angular Distribution: Peripheral Au+Au data vs. pp+flow

C2(Au Au)C2(p p) A *(1 2v22 cos(2))

Ansatz: A high pT triggered Au+Au event is a superposition of a high pT triggered p+p event plus anisotropic transverse flow

v2 from reaction plane analysis

“A” is fit in non-jet region (0.75<||<2.24)

39Jim Thomas - LBL

Angular Distribution: Central Au+Au data vs. pp+flow

C2(Au Au)C2(p p) A *(1 2v22 cos(2))

40Jim Thomas - LBL

Lessons learned – Dark Matter … its opaque

• The backward going jet is missing in central Au-Au collisions when compared to p-p data + flow

• The backward going jet is not suppressed in d-Au collisions

• These data suggest opaque nuclear matter and surface emission of jets

Surface emission

Suppression of back-to-back correlations in central Au+Au collisions

41Jim Thomas - LBL

Where does the Eloss go?

PHENIX p+p Au+Au

Lost energy of away-side jet is redistributed to rather large angles!

Trigger jetAway-side jet

42Jim Thomas - LBL

Mach Cone: Theory vs Experiment

• Hint of a Mach Cone?

STAR preliminary

0-12% 200 GeV Au+Au

away

near

Medium

mach cone

Mediumaway

neardeflected jets

43Jim Thomas - LBL

Nuclear Fluid Dynamics ... with friction

• The energy momentum tensor for a viscous fluid

• Conservation laws: and where

• The elements of the shear tensor, , describe the viscosity of the fluid and can be thought of as velocity dependent ‘friction’

• Simplest case: scaling hydrodynamics– assume local thermal equilibrium

– assume longitudinal boost-invariance

– cylindrically symmetric transverse expansion

– no pressure between rapidity slices

– conserved charge in each slice

• Initially expansion is along the Z axis, so viscosity resists it– Conservation of T means that energy and momentum appear in the

transverse plane … viscosity drives radial flow

• Viscosity is velocity dependent friction so it dampens v2 – Viscosity (/z ) must be near zero for elliptic flow to be observed

pguupT )(

0 T 0

j uj ii

44Jim Thomas - LBL

AdS/CFT correspondence (from H. Liu)

N = 4 Super-Yang-Mills theory with SU(N)

Maldacena (1997) Gubser, Klebanov, Polyakov, Witten

A string theory in 5-dimensional anti-de Sitter spacetime

NN = 4 Super-Yang-Mills (SYM):

anti-de Sitter (AdS) spacetime: homogeneous spacetime with a negative cosmological constant.

maximally supersymmetric gauge theory

scale invariant

A special relative of QCD

The value turns out to be universal for all strongly coupled

QGPs with a gravity description. It is a universal lower bound.

1

4s

45Jim Thomas - LBL

PHENIX PRL 98, 172301 (2007)

• RAA of heavy-flavor electrons in 0%–10% central collisions compared with 0 data and model calculations

• V2 of heavy-flavor electrons in minimum bias collisions compared with 0 data and the same models.

• Conclusion is that heavy flavor flow corresponds to /s at the conjectured QM lower bound

0 0

46Jim Thomas - LBL

Caption: The viscosity to entropy ratio versus a reduced temperature.

Lacey et al. PRL 98:092301(07) hep-lat/0406009; hep-ph/0604138 Csernai et al, PRL97, 152303(06)

The universal tendency of flow to be dissipated due to the fluid’s internal friction results from a quantity known as the shear viscosity. All fluids have non-zero viscosity. The larger the viscosity, the more rapidly small disturbances are damped away.

Quantum limit: /sAdS/CFT ~ 1/4

pQCD limit: ~ 1

At RHIC: ideal (/s = 0) hydrodynamic model calculations fit to data

Perfect Fluid at RHIC?!

H2O N2

He

hadronicpartonic

Viscosity and the Perfect Fluid

47Jim Thomas - LBL

Old Chinese Proverb

Beware of theorists waiting for data– Confusion

48Jim Thomas - LBL

PRL 99, 172301 (2007) … new insights

• Romatschke2 perform relativistic viscous hydrodynamics calculations

• Data on the integrated elliptic flow coefficient v2 are consistent with a ratio of viscosity over entropy density up to /s 0.16

• But data on minimum bias v2 seem to favor a much smaller viscosity over entropy ratio, below the bound from the anti–de Sitter conformal field theory conjecture

49Jim Thomas - LBL

Did a meteor impact on the Yucatan kill the Dinosaurs?

50Jim Thomas - LBL

Conclusions About Nuclear Matter at RHIC

• Its hot– Chemical freeze out at 175 MeV

– Thermal freeze out at 100 MeV

• Its fast– Transverse expansion with an average velocity greater than 0.55 c

– Large amounts of anisotropic flow (v2) suggest hydrodynamic expansion and high pressure at early times in the collision history

• Its opaque– Saturation of v2 at high pT

– Suppression of high pT particle yields relative to p-p

– Suppression of the away side jet

• There are hints that it is thermally equilibrated– Excellent fits to particle ratio data with equilibrium thermal models

– Excellent fits to flow data with hydrodynamic models that assume equilibrated systems

– Hints of heavy flavor flow

• And it has nearly zero viscosity and perhaps a Mach cone– Perhaps it is at or below the quantum bound from the AdS/CFT conjecture

Niels Bohr was almost right … he just didn’t know about q and g

51Jim Thomas - LBL

Kinetic Freezeout from Transverse Flow

<ßr> (RHIC) = 0.55 ± 0.1 cTKFO (RHIC) = 100 ± 10 MeV

Explosive Transverse Expansion at RHIC High Pressure

Tth

[GeV

]< r

> [

c]

STA

RPH

EN

IX

Thermal freeze-out determinations are done with the blast-wave model to find <pT>

STAR Preliminary

52Jim Thomas - LBL

3<pt,trigger<4 GeV

pt,assoc.>2 GeV

Au+Au 0-10%

preliminary

53Jim Thomas - LBL

The Development of a Weibal Instability

54Jim Thomas - LBL

55Jim Thomas - LBL

56Jim Thomas - LBL

Charm Cross Sections at RHIC

1) Large systematic uncertainties in the measurements2) Theory under predict by a factor ~ 2 and STAR ~ 2 x PHENIX3) Directly reconstructed charm hadrons Upgrades

57Jim Thomas - LBL Nu Xu

A pQCD Study

- At RHIC energy, baryons are mostly from gluons and pions are mostly from quark jets.

- Observation at high pT : RCP( ) ~ RCP (p) RCP (K) ~ RCP ()

- pQCD color factor effects:E(g)/E(q) ~ 9/4

A clear challenge to pQCD predictions!

Future tests with charm hadrons(quarks) and -meson(gluon).

STAR: nucl-ex/0703040. Phys. Lett. B, in print

58Jim Thomas - LBL Nu Xu

Inclusive cross-section (jets, 0,±,p±)

Mid-y jets, 0,± and p± productions are well reproduced by NLO pQCD calculations over many orders of magnitude 1) powerful tool for analyzing spin physics. 2) reliable reference for study high-energy nuclear collisions.

STAR: PRL 97, 252001(06); PL B637, 161(06)

p p o

59Jim Thomas - LBL

Hadron Spectra from RHIC p+p and Au+Au collisions at 200 GeV

sss

ss

uud

ud

Multi-strange hadron spectra are exponential in their shapes. STAR white papers - Nucl. Phys. A757, 102(2005).

mT pT2 m 2

mo

re c

entr

al c

oll

isio

ns

0-5%

60Jim Thomas - LBL

Current State of Affairs

• A theory is something nobody believes, except the person who made it.

• An experiment is something everybody believes, except the person who made it.

– attributed to Albert Einstein

61Jim Thomas - LBL

Recombination TestedThe complicated observed flow pattern in v2(pT)

d2n/dpTd ~ 1 + 2 v2(pT) cos (2 )is predicted to be simple at the quark level under

pT → pT / n , v2 → v2 / n , n = 2,3 for meson,baryon

if the flow pattern is established at the quark level

Compilation courtesy of H. Huang

62Jim Thomas - LBL

At low pt: mass ordering

hydrodynamics

At larger pt: Baryons – mesons

quark coalescence

We need v2 of and 0

Quark Coalescence

S.A. Voloshin, Nucl. Phys. A715, 379 (2003).

Z. Lin et al., Phys. Rev. Lett., 89, 202302 (2002).

R. Fries et al., nucl-th/0306027.

D. Molnar and S.A. Voloshin, PRL 91, 092301(2003).

63Jim Thomas - LBL

Multi-Strange Baryons v2

Multi-strange baryons flow !

Partonic Collectivity !Partonic Collectivity !

64Jim Thomas - LBL

Summary of Performance Achieved to date

• Features of the STAR TPC– 4 meters in diameter, 210 cm drift

– No field wires in the anode planes

– Pad readout, Low gain on anodes

– Low drift field

– Very compact FEE electronics

– Analog Delay with SCA then onboard ADC

– Data delivered via optic fiber

– Uniform E and B fields

– ‘ExB’ and most Electrostatic distortions correctable to 50 – 100 m level

• Position resolution– 500 m in the real world with calibration

errors

– Space point resolution ~ 100 m for select laser events, 250 - 350 m for select tracks

– Function of dip angle and crossing angle

• Good particle separation using dE/dx– 6.5% dE/dx resolution @ 100 cm – -proton separation : > 1 GeV/c

• 2-Track resolution– 2.5 cm for HBT pairs – 1.5 cm for laser tracks– limited by 3 pad response function

and desire for fast algorithms

• Momentum resolution– 2% minimum at 0.25 Tesla (half field)– for pT > 1.5 GeV in 0.25 T field

• dk/k = 0.016 pT + 0.012 (central)• dk/k = 0.011 pT + 0.013 (peripheral)• 2.9% 3.3% peripheral/central

@ 1.5 GeV

STAR performance is excellent and meets essentially all design

specifications!

65Jim Thomas - LBL

TPC Gas Volume & Electrostatic Field Cage

• Gas: P10 ( Ar-CH4 90%-10% ) @ 1 atm

• Voltage : - 28 kV at the central membrane 135 V/cm over 210 cm drift path

420 CM

Self supporting Inner Field Cage: Al on Kapton using Nomex honeycomb; 0.5% rad length

66Jim Thomas - LBL

Identified Particle Spectra at 200 GeV

+, -, K+, K- spectra versus centrality

PRL 92 (2004) 171801 and Phys. Lett. B595 (2004) 143

Bose-Einstein fits

mTmAe

/mt exponential fits

K-)1/( / effTmeA

+

67Jim Thomas - LBL

Anti-Proton Spectra at 200 & 130 GeV / N

Au + Au p + X

130 GeV data

p

200 GeV data

22 2/ pAegaussian fits

p andp spectra versus centrality

PRL 92 (2004) 171801 and PRL 87 (2001) 262302

p

68Jim Thomas - LBL

• In the early universe

p / p ratio = 0.999999

• At RHIC, pair-production

increases with s

• Mid-rapidity region is not yet

baryon-free!

• Pair production is larger than

baryon transport

• 80% of protons from pair

production

• 20% from initial baryon

number transported over 5

units of rapidity

Anti-Baryon/Baryon Ratios versus sNN

In HI collisions at RHIC, more baryons are pair produced than are brought in by the

initial state

4Tr

pair

Y

Y

8.0

Transpair

pair

p

pbar

YY

Y

Y

Y

69Jim Thomas - LBL

Anti-Particle to Particle Ratios

Excellent agreement between experiments at y = 0, s = 130

STAR results on thep/p ratio p/p = 0.11 ± 0.01 @ 20 GeV p/p = 0.71 ± 0.05 @ 130 GeV p/p = 0.80 ± 0.05 @ 200 GeV

p/p ratios

K+/K- ratios

70Jim Thomas - LBL

71Jim Thomas - LBL

Equation of State Parameters at RHIC

In central Au+Au collisions: - partonic freeze-out:

*Tp = 165 ± 10 MeV weak centrality dependence

p ≥ 0.2 (c)

- hadronic freeze-out:

*Tfo = 100 ± 5 (MeV) strong centrality dependence

fo = 0.6 ± 0.05 (c)

Systematic study are needed to understand the centrality dependence of the EOS parameters * Thermalization assumed

72Jim Thomas - LBL

Cold nuclear matter:0 ~ 0.16 GeV/fm3

30x0

nucl-ex/0311017

PRL 87 (01) 52301

R2

dydz 0

Boost invariant hydrodynamics: Bjorken Estimate of Initial Energy Density

d

dNp

Rdy

dE

Rch

TT

2

31122

~ 0.2 - 1 fm/ctime to thermalize the

system

~ 6.5 fm

Bjorken Estimate of Initial Energy Density

3/5.4 fmGeV3/7.0 fmGeVC

73Jim Thomas - LBL

At RHIC, , , , and J/ show collective motion in 200 GeV Au + Au central collisions! PHENIX (, K, p, J/): PRC69, 034909(04), QM05; STAR (, , ): QM05.

f A exp mT /Tslope

SPS results:No collective motion for multi-strange and charm hadrons!

RHIC results:Collective motion for multi-strange and charm hadrons!

p ≥ 0.2c

Slope Parameters

74Jim Thomas - LBL

This gap is a manifestation of the approximate SU(2)R x SU(2)L chiral symmetry of QCD with pions as the Nambu-Goldstone bosons

QCD is a Rich Theory with Many Features

Hadron “level” Diagram

Hadron 'level' diagram

0

500

1000

1500

0 10 20 30 40

Degeneracy

Mass (MeV)

Kfo

{W. Zajc

MFFDiL a

aˆ~

4

1We have a theory of the strong

interaction

Low(er) energy nuclear physics uses OPEP or descriptions in terms of a pion gas. These worked because QCD is a theory with a mass gap.

75Jim Thomas - LBL

Something Funny Happens at T > mc2

An exponentially increasing density of hadronic states suggests– A “limiting temperature” TH

– A phase transition(?) in hadronic matter

This was noticed before quarks were identified as the constituents of matter– ( Hagedorn, Nuovo Cimento Supp., 3 (147) 1965 )

Fit this form with TH = 163 MeVDensity of States .vs. Energy

HTmaemdm

dnm /~)(

dmem

dmem

TTm

a

Tm

H

)11

(

/

~

)(

Which requires T < TH

Thermal equilibrium suggests

76Jim Thomas - LBL

Three Particle Correlations Conical Emission

P/ = cs2 Mach cone. Data: Unambiguous evidence for conical emission in

central Au+Au collisions. Trigger at higher pT, more statistics are needed.

pTtrig=3-4 GeV/c

pTassoc=1-2 GeV/c

0-12% Au+Au

=(12)/2

Δ 2

Δ1 Δ1

0-12% Au+Au jet v2=0

J. Ulery, HP2006, C. Pruneau, QM2006

d+Au

Δ1

Δ 2

Δ 2

=(12)/2

77Jim Thomas - LBL

correlations vs the reaction plane

pTtrigger=4-6 GeV/c, 2<pT

associated<pTtrigger, ||<1

y

x

in-plane

Out-of-plane

Effect of path length on suppression is experimentally accessible

-/4

/43/4

-3/4

Back-to-back suppression out-of-plane stronger than in-plane

78Jim Thomas - LBL

Lattice QCD predictions

TC ~ 170 MeV, was a very stable prediction over time & technologies … until recently when it went up to 190 MeV

(F. Karsch, hep-lat/0106019 and M. Cheng et al., hep-lat/0710.0354)

Stephan Boltzman limits for a free Quark Gluon gas

En

erg

y D

ensi

ty

Temperature

TC ~ 170 15 MeV

C ~ 0.7 GeV/fm3

0 ~ 0.16 GeV/fm3

Karsch QM2004

79Jim Thomas - LBL

A Macroscopic many body system: It Flows

Spatial anisotropy Momentum anisotropy

– For example, v2 is the 2nd harmonic Fourier coefficient of the distribution of particles with respect to the reaction plane

))2cos(2)cos(21(2

121

2

3

3

vvdydpp

Nd

pd

dNE

TT

directed elliptic isotropic

80Jim Thomas - LBL

Suppresion of inclusive hadron yield

• central Au+Au collisions: factor ~4-5 suppression • pT >5 GeV/c: suppression ~ independent of pT

nucl-ex/0305015

Au+Au relative to p+p Au+Au central/peripheral

RAA RCP

81Jim Thomas - LBL

Identifying jets on a statistical basis in Au-Au

STAR DataAu+Au @ 200 GeV/c

0-5% most central4 < pT(trig) < 6 GeV/c

2 < pT(assoc.) < pT(trig)

• Identify jets on a statistical basis in Au-Au

• Given a trigger particle with pT > pT (trigger), associate particles with pT > pT (associated)

),(11

),(2 NEfficiencyN

CTRIGGER

• You can see the jets in p-p data at RHIC

82Jim Thomas - LBL

v2 vs. Centrality

• v2 is large– 6% in peripheral

collisions

– Smaller for central collisions

• Hydro calculations are in reasonable agreement with the data

– In contrast to lower collision energies where hydro over-predicts anisotropic flow

• Anisotropic flow is developed by rescattering

– Data suggests early time history

– Quenched at later times

Anisotropic transverse flow is large at RHIC

PRL 86, (2001) 402

more central

Hydro predictions