CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 1 / 26 Collective Expansion in Relativistic Heavy Ion Collisions -- Search for.

CCAST, Beijing, China, 2004CCAST, Beijing, China, 2004

Nu Xu 1 / 26

//Talk/2004/07USTC04/NXU_USTC_8July04//Collective Expansion inCollective Expansion in Relativistic Heavy Ion Collisions Relativistic Heavy Ion Collisions

-- Search for the partonic EOS at RHIC-- Search for the partonic EOS at RHIC

Nu Xu

Lawrence Berkeley National Laboratory

Many Thanks to OrganizersProf. Weiqing Chao

Jinghua Fu, Yugang Ma, Enke Wang

J. Castillo, X. Dong, H. Huang, H.G. Ritter, K. Schweda, P. Sorensen, A. Tai, Z. Xu


Nu Xu 2 / 26

//Talk/2004/07USTC04/NXU_USTC_8July04//

OutlineOutline

Introduction

Bulk properties - ∂PQCD

- hadron spectra- elliptic flow v2

Summary and Outlook


Nu Xu 3 / 26


PPhase diagram of strongly hase diagram of strongly interacting matterinteracting matter

CERN-SPS, RHIC, LHC: high temperature, low baryon density

AGS, GSI (SIS200): moderate temperature, high baryon density


Nu Xu 4 / 26


High-energy Nuclear CollisionsHigh-energy Nuclear Collisions

Initial Condition - initial scatterings - baryon transfer - ET production - parton dof

System Evolves - parton interaction - parton/hadron expansion

Bulk Freeze-out - hadron dof - interactions stop

jets

J/D

K, K*

p

d, HBT

elliptic flow velliptic flow v22

radial radial flowflowTT

Q2

time

partonic scatterings?early thermalization?

TTCC

TTchch

TTfofo


Nu Xu 5 / 26


Identify and study the properties of matter with partonic degrees of freedom.

Penetrating probes Bulk probes - direct photons, leptons - spectra, v1, v2 …

- “jets” and heavy flavor - partonic collectivity - fluctuations

jets - observed high pT hadrons (at RHIC, pT(min) > 3 GeV/c) collectivity - collective motion of observed hadrons, not necessarily reached

thermalization among them.

Physics Goals at RHIC

HydrodynamicFlow

CollectivityLocal

Thermalization=


Nu Xu 6 / 26


Equation of State

€

∂μTμν = 0

∂μ jμ = 0 j μ (x) = n(x)uμ (x)

T μν = ε(x) + p(x)[ ]uμuν − gμν ∗p(x)

Equation of state:

- EOS I : relativistic ideal gas: p = /3- EOS H: resonance gas: p ~ /6- EOS Q: Maxwell construction:

Tcrit= 165 MeV, B1/4 = 0.23 GeV

lat=1.15 GeV/fm3

P. Kolb et al., Phys. Rev. C62, 054909 (2000).

With given degrees of freedom, the EOS - the system response to the changes of the thermal condition - is fixed by its p and T or .

Energy density GeV/fm3


Nu Xu 7 / 26


Collision Geometry

x

z

Non-central Collisions

Number of participants: number of incoming nucleons in the overlap regionNumber of binary collisions: number of inelastic nucleon-nucleon collisions

Charged particle multiplicity collision centralityReaction plane: x-z plane

Au + Au sNN = 200 GeV

beam


Nu Xu 8 / 26


Charged Hadron Density19.6 GeV 130 GeV 200 GeV

Charged hadron pseudo-rapidity

1) High number of Nch indicates initial high density;2) Mid-y, Nch Npart nuclear collisions are not incoherent;3) Saturation model works

Initial high parton density at RHICPRL 85, 3100 (00); 91, 052303 (03); 88, 22302(02); 91,

052303 (03)

PHOBOS Collaboration


Nu Xu 9 / 26


Suppression and Correlation

In central Au+Au collisions: hadrons are suppressed and back-to-back ‘jets’ are disappeared. Different from p+p and d+Au collisions.

Energy density at RHIC: > 5 GeV/fm3 ~ 300

Parton energy loss: Bjorken 1982(“Jet quenching”) Gyulassy & Wang 1992…


Nu Xu 10 / 26


Energy Loss and Equilibrium

Leading hadrons

Medium

In Au +Au collision at RHIC: - Suppression at the intermediate pT region - energy loss

- The energy loss leads to progressive equilibrium in Au+Au collisions STAR: nucl-ex/0404010


Nu Xu 11 / 26


Energy Loss

(1) Measured spectra show evidence of suppression up to pT ~ 6 GeV/c; (2) Jet-like behavior observed in correlations: - hard scatterings in AA collisions

- disappearance of back-to-back correlations

“Partonic” Energy loss process leads to progressive equilibrium in the medium

Next step: fix the partonic Equation of State, bulk properties


Nu Xu 12 / 26


Pressure, Flow, …

dd = dU + pdV = dU + pdV – entropy; p – pressure; U – energy; V – volume

= kBT, thermal energy per dof

In high-energy nuclear collisions, interaction among constituents and density distribution will lead to: pressure gradient pressure gradient collective flow collective flow

number of degrees of freedom (dof) Equation of State (EOS) No thermalization is needed – pressure gradient only depends on the density gradient and interactions. Space-time-momentum correlations!


Nu Xu 13 / 26


Transverse Flow Observables

As a function of particle mass:• Directed flow (v1) – early• Elliptic flow (v2) – early• Radial flow – integrated over whole evolution

Note on collectivity:1) Effect of collectivity is accumulative – final effect is the sum of all processes. 2) Thermalization is not needed to develop collectivity - pressure gradient depends on density gradient and interactions.

€

dNptdptdyd

= 12

dNptdptdy

1+ 2vi (cos i )i=1

∑⎡

⎣⎢

⎤

⎦⎥

pt = px2 +py

2 , mt = pt2 +m2


Nu Xu 14 / 26


Hadron Spectra from RHICmid-rapidity, p+p and Au+Au collisions at 200 GeVmid-rapidity, p+p and Au+Au collisions at 200 GeV

ce nt ral ity5%

10-20%

20-40%

40-60%

60-80%

€

mT = pT2 + m2

Results from BRAHMS, PHENIX, and STAR experiments

(sss)(ssd)(usd)

(ss)


Nu Xu 15 / 26


Compare with Model Results

Model results fit to , K, p spectra well, but over predicted <pT> for multi-strange hadrons - Do they freeze-out earlier?

Phys. Rev. C69 034909 (04); Phys. Rev. Lett. 92, 112301(04); 92, 182301(04); P. Kolb et al., Phys. Rev. C67 044903(03)


Nu Xu 16 / 26


Thermal model fitThermal model fit

Source is assumed to be:– Local thermal equilibrated– Boosted radially

random

boostedE.Schnedermann, J.Sollfrank, and U.Heinz, Phys. Rev. C48, 2462(1993)

€

Ed3N

dp3∝ e−(uμ pμ )/T fo p

σ

∫ dσ μ ⇒

dN

mTdmT

∝ rdrmTK1

mT coshρ

Tfo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟0

R

∫ I0

pT sinhρ

Tfo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

ρ = tanh−1β r β r = β S

r

R

⎛

⎝ ⎜

⎞

⎠ ⎟α

α = 0.5,1,2


Nu Xu 17 / 26


Thermal fits: Tfo vs. < >

1) 1) , , KK, and , and pp change change smoothly from peripheral smoothly from peripheral to central collisions.to central collisions.

2) At the most central2) At the most central collisions, <collisions, <TT> reaches> reaches

0.6c.0.6c.

3) Multi-strange particles 3) Multi-strange particles ,, are found at higher Tare found at higher Tfofo

(T~T(T~Tchch) and lower <) and lower <TT>>

Sensitive to early Sensitive to early partonic stage!partonic stage!

How about vHow about v22??

STAR: NPA715, 458c(03); PRL 92, 112301(04); 92, 182301(04).

200GeV Au + Au collisions200GeV Au + Au collisions

Chemical Freeze-out: inelastic interactions stopKinetic Freeze-out: elastic interactions stop


Nu Xu 18 / 26


y

x

py

px

coordinate-space-anisotropy momentum-space-anisotropy

Anisotropy Parameter vAnisotropy Parameter v22

€

=⟨y2 − x 2⟩

⟨y 2 + x 2⟩v2 = cos2ϕ , ϕ = tan−1(

py

px

)

Initial/final conditions, EoS, degrees of freedom


Nu Xu 19 / 26


v2 at Low pT

- At low pT, hydrodynamic model fits well for minimum bias events indicating early thermalization in Au+Au collisions at RHIC!- More theoretical work needed to understand details: v2 centrality dependence; consistency between v2 and spectra…

P. H

uo

vi ne

n, p

r ivate

com

mu

nica

t i on

s, 20

04


Nu Xu 20 / 26


v2 at All pT

v2, the spectra of multi-strange hadrons, and thescaling of the number ofconstituent quarks

Partonic collectivity has been attained at RHIC! Deconfinement, model dependently, has been attained at RHIC!

Next question is thethermalization of lightflavors at RHIC:- v2 of charm hadrons- J/ distributions !!

PHENIX: PRL91, 182301(03) STAR: PRL92, 052302(04)Models: Greco et al, PRC68, 034904(03)


Nu Xu 21 / 26


Nuclear Modification Factor

)/(

)/()(

2

2

dydpNNd

dydpNNdpR

Tperipheralbinary

peripheral

Tcentralbinary

central

TCP = 1) Baryon vs. meson effect!

2) Hadronization via coalescence

3) Parton thermalization (model)- (K0, ): PRL92, 052303(04); NPA715, 466c(03); - Greco et al, PRC68,034904(03);PRL90, 202102(03) - R. Fries et al, PRC68, 044902(03); ), Hwa, nucl-th/0406072


Nu Xu 22 / 26


Bulk Freeze-out Systematics

The additional increase in T is likely due to partonic pressureat RHIC.

1) v2 self-quenching, hydrodynamic model works at low pT

2) Multi-strange hadron freeze-out earlier, Tfo~ Tch

3) Multi-strang hadron show strong v2


Nu Xu 23 / 26


Partonic Collectivity at RHIC

1) Copiously produced hadrons freeze-out: Tfo = 100 MeV, T = 0.6 (c) > T(SPS)

2)* Multi-strange hadrons freeze-out: Tfo = 160-170 MeV (~ Tch), T = 0.4 (c)

3)** Multi-strange v2: Multi-strange hadrons and flow!

4)*** Constituent Quark scaling: Seems to work for v2 and RAA (RCP)

Partonic (u,d,s) collectivity at RHIC!


Nu Xu 24 / 26


Summary & OutlookSummary & Outlook

(1) Charged multiplicity - high initial density

(2) Parton energy loss - QCD at work

(3) Collectivity - pressure gradient ∂PQCD

Deconfinement and Partonic collectivity

Open issues - partonic (u,d,s) thermalization - heavy flavor v2 and spectra - di-lepton and thermal photon spectra


Nu Xu 25 / 26


CERN-SPS, RHIC, LHC: high temperature, low baryon density

AGS, GSI (SIS200): moderate temperature, high baryon density

PPhase diagram of strongly hase diagram of strongly interacting matterinteracting matter

GSIGSI

RHICRHICLHCLHC


Nu Xu 26 / 26


Future readings:Future readings:

- http://qm2004.lbl.gov/

- Quark Matter conference proceedings 2002 Nucl.Phys. A715, 1c(2003).

- Quark Matter conference proceedings 2001 Nucl.Phys. A698, 1c(2002).

- “Introduction to High Energy Heavy Ion Collisions’’ - By C.Y. Wong (Oak Ridge),. 1995. Singapore, Singapore: World Scientific (1994) 516 p.

- “Introduction to Relativistic Heavy Ion Collisions’’ - By L.P. Csernai (Bergen U.),. 1994.

Chichester, UK: Wiley (1994) 310 p.

- Recent discussions on the QGP discovery http://www.bnl.gov/riken/May14-152004workshop.htm

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 1 / 26 Collective Expansion in Relativistic Heavy Ion Collisions -- Search for.

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