explore the qcd phase diagram - partonic equation of state at rhic

Nu Xu 1/36International School of Nuclear Physics, 30 th Course, Erice-Sicily, 16 - 24 September 2008

Explore the QCD Phase Diagram

- Partonic Equation of State at RHIC

Nu XuLawrence Berkeley National Laboratory

Many Thanks to the Organizers


Outline

1) Introduction- Hydrodynamic approach- Collectivity vs. local thermalization

2) Recent experimental data- Transverse momentum distributions- Partonic collectivity at RHIC

3) Outlook - Heavy quark measurements

thermalization - RHIC energy scan

QCD tri-critical point


- Identify and study the properties of the matter (EOS) with partonic degrees of freedom.

- Explore the QCD phase diagram.

Physics Goals at RHIC

HydrodynamicFlow Collectivity Local

Thermalization=


Pressure, Flow, …

tds = dU + pdV s– entropy; p – pressure; U – internal energy; V – volume

t = kBT, thermal energy per dof

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

pressure gradient 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!


Timescales of Expansion Dynamics

microscopic view macroscopic viewvs

scattering rate nab ~ expansion rate m um

dilution rate t s

A macroscopic treatment requires that the scattering rate is larger than macroscopic rates

€

d3 pa

(2π )3∫ d 3 pb

(2π )3 fa (pa ) fb (pb )σ ab (s)r v a −

r v b

um

T

t


RHIC BRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

Relativistic Heavy Ion Collider (RHIC)Brookhaven National Laboratory (BNL), Upton, NY

Animation M. Lisa

- RHIC: The highest energy heavy-ion collider in the world!

sNN = 200 - 5 GeV

Au + Au, Cu + Cu, d + Au

- RHIC: The highest energy polarized proton collider!

s = 200, 500 GeV


STAR Detector

MRPC ToF barrelReady for run 10

RPSD

PMD

FPD

FMS

EMC barrel

EMC End Cap

DAQ1000Ready for run 9

Complete

Ongoing

R&D

TPC

FTPC

Full azimuthal particle identification!e, π, ρ, K, K*, p, φ, Λ, Δ, Ξ, Ω, D, ΛC, J/ψ …

Nu Xu 8/36International School of Nuclear Physics, 30 th Course, Erice-Sicily, 16 - 24 September 2008 8

Au + Au Collisions at RHIC

STAR

Central Event

(real-time Level 3)


Particle Identification (i)

STAR

pions

kaons protons

deuterons

electrons

STAR MRPC TOF: nucl-ex/03090121) Timing resolution: ~ 85 ps2) PID: and K ~ 1.9 GeV/c p and /K ~ 3 GeV/c3) Efforts on R&D by ALICE at CERN

STAR TPC:1) dE/dx PID up to p ~ 1 GeV/c

|y| < 0.5; pT ~ 1 GeV/c2) Azimuthal acceptance: ~ 23) Tracking efficiency: ~ 90%, homogenous

Other methods: conversion, EMCal, SVT, Si-m vertex detector, …

http://www.star.bnl.gov/protected/spectra/ruanlj/TOFrpaper/tofr_beta_p_prplot.gif


Multi-strange particles are reconstructed via the decay mode :

X L + p +

Combination of momenta of the daughter particles

invariant mass spectra

Reconstruction V0


Particle Identification (ii)

Reconstruct particles in full azimuthal acceptance of STAR!


-mesons from Au+Au Collisions

ssbar fusion -meson formation! STAR: Phys. Lett. B612, 81(2005)

STAR: PRL. 98 (2007) 062301

The observed strangeness enhancement is NOT due to the Canonical suppression! STAR: Preliminary


Transverse Flow Observables

1) Radial flow – integrated over whole history of the evolution 2) Directed flow (v1) – relatively early3) Elliptic flow (v2) – relatively early

- Mass dependent: characteristic of hydrodynamic behavior.

€

dr σ

dΩ= d3σ

dpxdpydpz

= dNp tdp tdydϕ

= 12π

dNp tdp tdy

1+ 2v icos(i ϕ )i=1∑

⎡

⎣ ⎢

⎤

⎦ ⎥

p t = p x2 + p y

2 , m t = p t2 + m2

v i = cos(iϕ )event

ϕ = tan−1 py

px

⎛ ⎝ ⎜

⎞ ⎠ ⎟


Hadron Spectra from RHICp+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

f ∝ exp(−mT /Tslope )

mor

e ce

ntra

l col

lisio

ns

0-5%


Statistical Model

• Assume thermally (constant Tch) and chemically (constant ni) equilibrated system at chemical freeze-out

• System composed of non-interacting hadrons and resonances

• Given Tch and m 's (+ system size), ni's can be calculated in a grand canonical ensemble

• Obey conservation laws: Baryon Number, Strangeness, Isospin• Short-lived particles and resonances need to be taken into account

22

0/))((

2

2 ,12 iiTpEi mpE

edppgn

ii

+=±

= ∫∞

−m


Yields Ratio Results

- In central collisions, thermal model fit well with S = 1. The system is thermalized at RHIC.- Short-lived resonances show deviations. There is life after chemical freeze-out. RHIC white papers - 2005, Nucl. Phys. A757, STAR: p102; PHENIX: p184.

Thermalmodel fits

data

Tch = 163 ± 4 MeV

mB = 24 ± 4 MeV


The QCD Phase Diagram

Tch ~ TC (LGT)at RHIC

*Thermalization is assumed!

Recent review:A. Andronic, et al, NP A772, B. 167(06)


Thermal Model Fits (Blast-Wave)Source is assumed to be:

– Locally thermal equilibrated– Boosted in radial direction

random

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

€

E d3Ndp3 ∝ e−(uμ pμ )/T fo p

σ∫ dσ μ ⇒

dNmT dmT

∝ rdrmTK1mT coshρ

Tfo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟0

R∫ I0pT sinh ρ

Tfo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

ρ = tanh−1 βT βT = β SrR ⎛ ⎝ ⎜

⎞ ⎠ ⎟α

α = 0.5, 1, 2

Extract thermal temperature Tfo and velocity parameter T


Blast Wave Fits: Tfo vs. T

1) , K, and p change smoothly from peripheral to central collisions.

2) At the most central collisions, T reaches 0.6c.

3) Multi-strange particles , are found at higher Tfo

and lower T

light hadrons move with higher velocity compared to strange hadrons

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

200GeV Au + Au collisions


Compare with Model Results

- Hydro model works well for , K, p, but over-predicts flow for multi-strange hadrons - partonic flow only?!- Initial ‘collective kick’ introduced (P. Kolb and R. Rapp, PRC67)


Slope Parameter Systematics

€

mT = pT2 +m 2

f ∝ exp(−mT /Tslope )

Partonic flow!


y

x

py

px

coordinate-space-anisotropy momentum-space-anisotropy

Anisotropy Parameter v2

€

ε =⟨y 2 − x 2⟩⟨y 2 + x 2⟩

v2 = cos2ϕ , ϕ = tan−1(py

px

)

Initial/final conditions, EoS, degrees of freedom


v2 at Low pT Region

- Minimum bias data! - At low pT, model result fits mass hierarchy well - Collective motion at RHIC- More work needed to fix the details in the model calculations.

P. Hu ovin en, priv ate comm

u nic atio ns, 200 4


Collectivity, Deconfinement at RHIC - v2 of light hadrons and multi-strange hadrons - scaling by the number of quarks

At RHIC: Nq scaling novel hadronization processê Parton flow De-confinement

PHENIX: PRL91, 182301(03) STAR: PRL92, 052302(04), 95, 122301(05) nucl-ex/0405022, QM05

S. Voloshin, NPA715, 379(03)Models: Greco et al, PRC68, 034904(03)Chen, Ko, nucl-th/0602025Nonaka et al. PLB583, 73(04)X. Dong, et al., Phys. Lett. B597, 328(04).….

i ii


-meson Flow: Partonic Flow

“-mesons are produced via coalescence of seemingly thermalized quarks in central Au+Au collisions. This observation implies hot and dense matter with partonic collectivity has been formed at RHIC”

STAR: Phys. Rev. Lett. 99 (2007) 112301// * STAR, Duke, TAMU

** OZI rule


Centrality Dependence STAR: Phys. Rev. C77, 54901(2008)

200 GeV Au+Au

Larger v2/εpart indicates stronger flow in more central collisions. NO εpart scaling. The observed nq-scaling does not necessarily mean thermalization.

S. Voloshin, A. Poskanzer, PL B474, 27(00).D. Teaney, et. al., nucl-th/0110037


EoS Parameters at RHIC

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

*Tpfo = 165 ± 10 MeV weak centrality dependence

vpfo ≥ 0.2 (c)

- hadronic freeze-out:*Tfo = 100 ± 5 (MeV) strong centrality dependence

vfo = 0.6 ± 0.05 (c) Systematic study, understand the centrality dependence of the EoS parameters

* Thermalization assumed


sQGP and the QCD Phase Diagram

200 GeV Au+Au collisions at RHIC, strongly interacting matter formed:

Jet energy loss: RAA

Strong collectivity: v0, v1, v2

Hadronization via coalescence: nq-scaling

Questions:Has the thermalization reached, or how large is the η at RHIC?

When (at which energy) does this transition happen?

What does the QCD phase diagram look like?


Quark Masses

1) Higgs mass: electro-weak symmetry breaking. (current quark mass)

2) QCD mass: Chiral symmetry breaking. (constituent quark mass)

é New mass scale compared to

the excitation of the system.

é Important tool for studying properties of the hot/dense medium at RHIC.

é Test pQCD predictions at RHIC.Total quark mass (MeV)


STAR Detector

MRPC ToF barrelReady for run 10

RPSD

PMD

FPD

FMS

EMC barrel

EMC End Cap

DAQ1000Ready for run 9 FGT

Complete

Ongoing

MTD

R&DHFT

TPC


HFT

TPC

FGT

STAR DetectorsEMC+EEMC+FMS

(-1 ≤ ≤ 4)TOF

DAQ1000

Full azimuthal particle identification!


Direct Radiation

Expanding partonic matter at RHIC and LHC!Di-leptons allow us to measure the direct radiation from the matter with partonic degrees of freedom, no hadronization!

- Low mass region: , , e-e+

minv e-e+

medium effect Chiral symmetry

- High mass region: J/ e-e+

minv e-e+

Direct radiation

PRL (07)


The QCD Critical Point- LGT prediction on the transitiontemperature TC is robust.

- LGT calculation, universality, andmodels hinted the existence ofthe critical point on the QCD phasediagram* at finite baryon chemicalpotential. - Experimental evidence for eitherthe critical point or 1st order transition is important for ourknowledge of the QCD phase diagram*.

* Thermalization has been assumed

M. Stephanov, K. Rajagopal, and E. Shuryak, PRL 81, 4816(98)

K. Rajagopal, PR D61, 105017 (00)

http://www.er.doe.gov/np/nsac/docs/Nuclear-Science.Low-Res.pdf





Observable I: Quark Scaling

- m ~ mp ~ 1 GeV- ss not K+K- - sh << sp,

In the hadronic case, no numberof quark scaling and the value of v2 of will be small.


Observable II: χq, χS

F. Karsch, 2008.

Event by event:

1. net-proton Kurtosis Kp(E)2. two proton correlation functions C2(E)3. ratio of the d/p4. ratio of K/p

€

Kp =Np

4 − 3 Np2 2

Np2


sQGP and the QCD Phase Diagram

200 GeV Au+Au collisions at RHIC, strongly interacting matter formed:

Jet energy loss: RAA

Strong collectivity: v0, v1, v2

Hadronization via coalescence: nq-scaling

Questions:Has the thermalization reached, or how large is the η at RHIC?

When (at which energy) does this transition happen?

What does the QCD phase diagram look like?

explore the qcd phase diagram - partonic equation of state at rhic

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