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Results from RHIC Measurements of High Density Matter Thomas S. Ullrich Brookhaven Nation Laboratory and Yale University January 7, 2003 Introduction Soft Physics Hard Physics (QCD) Phase Diagram of Nuclear Matter e.g. two massless flavors (Rajagopal and Wilczek, hep-ph/-0011333)

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results from rhic measurements of high density matter

Results from RHIC Measurements of High Density Matter

Thomas S. Ullrich

Brookhaven Nation Laboratory and Yale University

January 7, 2003

  • Introduction
  • Soft Physics
  • Hard Physics
qcd phase diagram of nuclear matter
(QCD) Phase Diagram of Nuclear Matter

e.g. two massless flavors (Rajagopal and Wilczek, hep-ph/-0011333)

  • T >> LQCD: weak coupling  deconfined phase (Quark Gluon Plasma)
  • T << LQCD: strong coupling  confinement
  •  phase transition at T~ LQCD?

Thomas Ullrich, BNL

lattice qcd at finite temperature

q

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Critical energy density:

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Lattice QCD at Finite Temperature
  • Coincident transitions: deconfinement and chiral symmetry restoration
  • Recently extended to mB> 0, order still unclear (2nd, crossover ?)

Ideal gas (Stefan-Boltzmann limit)

F. Karsch, hep-ph/0103314

TC ~ 175 MeV  eC ~ 1 GeV/fm3

Thomas Ullrich, BNL

the phase transition in the laboratory
The Phase Transition in the Laboratory

soft physics

regime

e.m. probes (l+l-, g)

hard (high-pT) probes

Chemical freezeout (Tch  Tc) : inelastic scattering stops

Kinetic freeze-out (Tfo Tch): elastic scattering stops

Thomas Ullrich, BNL

rhic @ brookhaven national laboratory
2 concentric rings of 1740 superconducting

magnets

3.8 km circumference

counter-rotating beams of ions from p to Au

RHIC @ Brookhaven National Laboratory

BRAHMS

PHOBOS

Relativistic

Heavy

Ion

Collider

PHENIX

STAR

h

Long Island

  • 2000 run:
    • Au+Au @ sNN=130 GeV
  • 2001 run:
    • Au+Au @ sNN=200 GeV (80 mb-1)
    • polarized p+p @ s=200 GeV (P ~15%, ~1 pb-1)

Thomas Ullrich, BNL

geometry of heavy ion collisions

z

y

x

Reaction plane

Geometry of Heavy Ion Collisions

Non-central

collision

“peripheral” collision (b ~ bmax)

“central” collision (b ~ 0)

Number of participants (Npart):number of incoming nucleons (participants) in the overlap region

Number of binary collisions (Nbin): number of equivalent inelastic nucleon-nucleon collisions

Nbin Npart

Thomas Ullrich, BNL

slide7

STAR

Peripheral Event

From real-time Level 3 display.

color code  energy loss

Thomas Ullrich, BNL

slide8

STAR

Mid-CentralEvent

From real-time Level 3 display.

Thomas Ullrich, BNL

slide9

STAR

Central Event

From real-time Level 3 display.

Thomas Ullrich, BNL

charged particle multiplicity
Charged Particle Multiplicity

19.6 GeV

130 GeV

200 GeV

Central at 130 GeV:

4200 charged particles !

PHOBOS Preliminary

Central

dNch/dh

Peripheral

Total multiplicity per participant pair scales with Npart

h

Thomas Ullrich, BNL

energy density at rhic
Energy Density at RHIC

What is the energy density achieved?

How does it compare to the expected phase transition value ?

PHENIX

EMCAL

For the most central events:

Bjorken formula for thermalized energy density

130 GeV

time to thermalize the system

(t0 ~ 1 fm/c)

~6.5 fm

eBjorken~ 4.6 GeV/fm3

pR2

~30 times normal nuclear density~1.5 to 2 times higher than at SPS (s = 17 GeV)

~ 5 times above ecritical from lattice QCD

Thomas Ullrich, BNL

hydrodynamics modeling high density scenarios
Hydrodynamics: Modeling High-Density Scenarios
  • Assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles)
  • Equations given by continuity, conservation laws, and Equation of State (EOS)
  • EOS relates quantities like pressure, temperature, chemical potential, volume
    • direct access to underlying physics
  • Works qualitatively at lower energybut always overpredicts collectiveeffects - infinite scattering limitnot valid there
    • RHIC is first time hydro works!

lattice QCD input

Thomas Ullrich, BNL

rhic spectra an explosive source

purely thermal

source

light

1/mT dN/dmT

heavy

mT

explosive

source

light

T,b

T

1/mT dN/dmT

heavy

mT

RHIC Spectra - an Explosive Source
  • various experiments agree well
  • different spectral shapes for particles of differing mass strong collective radial flow
  • very good agreement with hydrodynamicprediction

data: STAR, PHENIX, QM01

model: P. Kolb, U. Heinz

Thomas Ullrich, BNL

single particle spectra and radial flow
Single Particle Spectra and Radial Flow

Au+Au @ 130 GeV, central and peripheral (STAR, PHENIX):

Hydrodynamics

even works for

peripheral

collisions up to

b ~ 10 fm!

(Heinz & Kolb

hep-ph/0204061)

Problem with

pions at low pT

 mp> 0

required

p

p

p

p

p

p

p

p

K+

t = 0.6 fm/c, emax (b=0) = 24.6 GeV/fm3, <e>(t =1 fm/c) = 5.4 GeV/fm3

Tmax(b=0) = 340 MeV, Tch = 165 MeV, Tfo = 130 MeV

Thomas Ullrich, BNL

t fo and b r vs s
Tfo and <br> vs. s
  • <r >
    • increases continously
  • Tfo
    • saturates around AGS energy
  • Strong collective radial expansion at RHIC
  • high pressure
  • high rescattering rate
  • Thermalization likely

Slightly model dependent

here:

blastwave model

(Kaneta/Xu)

Thomas Ullrich, BNL

azimuthal anisotropy of particle emission elliptic flow
Azimuthal Anisotropy of Particle Emission: Elliptic Flow

SPS, RHIC

AGS

Almond shape overlap region in coordinate space

Anisotropy in momentum space

Interactions

v2: 2nd harmonic Fourier coefficient in dN/d with respect to the reaction plane

Thomas Ullrich, BNL

time evolution when does elliptic flow develop
Time Evolution: When Does Elliptic Flow Develop?

Au+Au at b=7 fm

P. Kolb, J. Sollfrank, and U. Heinz

t2

t3

t1

t4

Equal energy density lines

Zhang, Gyulassy, Ko, PL B455 (1999) 45

Elliptic flow observable sensitive to early evolution of system

Mechanism is self-quenching

Large v2 is an indication of early thermalization

v2

Thomas Ullrich, BNL

charged particle v 2 vs centrality

V2

Hydrodynamic model

SPS

AGS

PRL 86 (2001) 402

Nch/Nmax

Charged Particle v2 vs. Centrality

midrapidity : |h| < 1.0

STAR PRL87 (2001)182301

Peripheral  Central

Hydrodynamical models can describe data at low pT (~2 GeV/c)

 compatible with early equilibration

Contrast to lower collision energies where hydro overpredicts elliptical flow

Thomas Ullrich, BNL

models to evaluate t ch and b statistical thermal models
Models to Evaluate Tch and B: Statistical Thermal Models
  • Statistical Thermal Model
  • F. Becattini; P. Braun-Munzinger, J. Stachel, D. Magestro
  • J.Rafelski PLB(1991)333; J.Sollfrank et al. PRC59(1999)1637
  • Assume:
    • Ideal hadron resonance gas
    • thermally and chemically equilibrated fireball at hadro-chemical freeze-out
  • Recipe:
    • grand canonical ensemble to describe partition function  density of particles of species i
    • fixed by constraints: Volume V, , strangeness chemical potentialS,isospin
    • input: measured particle ratios
    • output: temperature T and baryo-chemical potential B

Particle density of each particle:

Qi : 1 for u and d, -1 for u and d

si : 1 for s, -1 for s

gi:spin-isospin freedom

mi : particle mass

Tch : Chemical freeze-out temperature

mq : light-quark chemical potential

ms : strangeness chemical potential

gs : strangeness saturation factor

Compare particle ratios to experimental data

Thomas Ullrich, BNL

statistical models from ags to rhic
Statistical Models: from AGS to RHIC

Slight variations in the models, but roughly:

Different implementation of

statistical model

Fact: all work well at AGS, SPS

and RHIC

early universe

250

RHIC

quark-gluon plasma

200

Does the success of the model

tell us we are dealing indeed with locally chemically equilibrated systems? this+flow  If you ask me YES!

Lattice QCD

Chemical Temperature Tch [MeV]

SPS

150

AGS

deconfinement

chiral restauration

100

SIS

hadron gas

50

neutron stars

atomic nuclei

0

0

200

400

600

800

1000

1200

Baryonic Potential B [MeV]

Thomas Ullrich, BNL

summary on soft p t 2 gev c physics
Summary on “Soft” (pT < 2 GeV/c) Physics
    • Particle production is large
      • Total Nch ~ 5000 (Au+Au s = 200 GeV)  ~ 20 in p+p
      • Nch/Nparticipant-pair ~ 4 (central region)  ~2.5 in p+p
    • Vanishing baryon/antibaryon ratio (0.7-0.8)
      • close to net baryon-free but not quite (net proton dN/dy~10)
    • Energy density is high  4-5 GeV/fm3 (model dependent)
      • lattice phase transition ~1 GeV/fm3, cold matter ~ 0.16 GeV/fm3
    • System exhibits collective behavior (radial + elliptic flow)
      •  strong internal pressure that builds up very early
    • The system appears to freezes-out very fast
      • explosive expansion (HBT, correlation studies)
    • Particles ratios suggest chemical equilibrium
      • Tch170 MeV, mb<50 MeV  near lattice phase boundary
    • Large system at freeze-out  2  size of nuclei
  • Overall picture: system appears to be in equilibrium
  • but explodes and hadronizes rapidly

Thomas Ullrich, BNL

high p t particles @ rhic jet tomography

leading particle

q

q

leading particle

High-pT Particles @ RHIC – Jet Tomography

Products of parton fragmentation (jet “leading particle”).

Early production in parton-parton

scatterings with large Q2.

Direct probes of partonic phases

of the reaction

Sensitive to hot/dense medium:

parton energy loss (“jet quenching”).

Info on medium effects accessible through comparison toscaled "vacuum" (pp) yields (“binary scaling”):

Production yieldscalculablevia pQCD:

Thomas Ullrich, BNL

jets in heavy ion collisions
Jets in Heavy Ion Collisions

e+e- q q (OPAL@LEP)

pp jet+jet (STAR@RHIC)

Au+Au ??? (STAR@RHIC)

Hopeless task? No, but a bit tricky…

Thomas Ullrich, BNL

partonic energy loss theory
Partonic Energy Loss: Theory
  • Elastic scattering (Bjorken 1982):
  • Gluon radiation is factor ~10 larger:
    • Thick plasma (Baier et al.):
  • Thin plasma (Gyulassy et al.):
  • Linear dependence on gluon density glue:
    • DE measures gluon density
    • DE is continuous function of energy density
    •  not a direct signature of deconfinement

Thomas Ullrich, BNL

energy loss in cold matter
Energy Loss in Cold Matter

Wang and Wang, hep-ph/0202105

Modification of fragmentation functions in e-Nucleus scattering:

dE/dx ~ 0.5 GeV/fm for 10 GeV quark

Existing data is extensively studied but p+A measurements at RHIC

are desperately needed  Run III (2003) d+Au

Thomas Ullrich, BNL

measuring hadron suppression

N-N cross section

<Nbinary>/sinelp+p

Measuring Hadron Suppression

1. Compare Au+Au to nucleon-nucleon cross sections

2. Compare Au+Au central/peripheral

Nuclear

Modification

Factor:

If no “effects”:

R < 1 in regime of soft physics

R = 1 at high-pT where hard

scattering dominates

Suppression:

R < 1 at high-pT

Thomas Ullrich, BNL

leading hadrons in fixed target experiments

AA

Leading Hadrons in Fixed Target Experiments

Central Pb+Pb collisions at SPS

p+A collisions:

SPS: any parton energy loss effects buried by initial state multiple scattering, transverse radial flow,…

Multiple scattering in initial state(“Cronin effect”)

Thomas Ullrich, BNL

hadron suppression au au at 130 gev
Hadron Suppression: Au+Au at 130 GeV

Phenix: PRL 88 022301 (2002)

p0 and charged hadrons, central collisions

STAR: nucl-ex/0206011

Charged hadrons, centrality dependence

Clear evidence for high pT hadron suppression in central nuclear collisions

Thomas Ullrich, BNL

hadron suppression au au at 200 gev

Preliminary sNN = 200 GeV

Hadron Suppression: Au+Au at 200 GeV

Phenix p0: peripheral and central over measured p+p

STAR charged hadrons: central/peripheral

PHENIX preliminary

200 GeV preliminary data: suppression of factor 4-5 persists to pT=12 GeV/c

Thomas Ullrich, BNL

hadron suppression central au au data vs theory
Hadron Suppression: Central Au+Au (Data vs. Theory)
      • Parton energy loss :

dE/dx ≈ 0.25 GeV/fm (expanding)

dE/dx|eff ≈7 GeV/fm (static source)

~ 15 times that in cold Au nuclei

      • Opacities:

<n> = L/≈ 3 – 4

      • Gluon densities:
  • dNg/dy ~ 900

What does it tell us about the medium ?

S.Mioduszewski

PHENIX Preliminary

nucl-ex/0210021

All models expect a moderate increase of RAA at higher pT

Thomas Ullrich, BNL

elliptic flow at high p t theory

jet

jet

Elliptic “Flow” at High-pT: Theory

Jet propagation through anisotropic matter (non-central collisions)

Snellings; Gyulassy, Vitev and Wang (nucl-th/00012092)

STAR @ 130 GeV

  • Finite v2: high pT hadron correlated with reaction plane from “soft” part of event (pT<2 GeV/c)
  • Finite asymmetry at high pT sensitive to energy density

STAR @ 200 GeV

Thomas Ullrich, BNL

2 particle correlations at high p t direct evidence for jets

Dh < 0.5

Dh > 0.5

2-Particle Correlations at High-pT: Direct Evidence for Jets
  • Jet core: Df × Dh ~ 0.5 × 0.5  study near-side correlations (Df~0) of high pT hadronpairs
  • Complication: elliptic flow high pT hadrons correlated with the reaction plane (~v22)
  • Solution: compare azimuthal correlation functions for
    • Dh<0.5 (short range)  particles in jet cone + background
    • Dh>0.5 (long range)  background only
  • Azimuthal correlation function:
    • Trigger particle pT trig> 4 GeV/c
    • Associate tracks 2 < pT < pTtrig
  • Caveat: Away-side jet contribution
  • subtracted by construction,
  • needs different method…

Near-side correlation shows jet-like signal in central Au+Au

Thomas Ullrich, BNL

2 particle correlations at high p t back to back jets

p+p measured in RHIC detectors

0<||<1.4

unlike sign

like sign

p+p

2 Particle Correlations at High-pT: Back-to-Back Jets?
  • away-side (back-to-back) jet can be “anywhere” (Dh~2.5)
  • Ansatz: correlation function: high pT-triggered Au+Au event =
    • high pT-triggered p+p event
    • +
    • elliptic flow
    • +
    • background

A: from fit to “non-jet”

region Df~p/2

v2 from reaction plane analysis

Thomas Ullrich, BNL

suppression of back to back pairs
Suppression of Back-to-Back Pairs

Peripheral Au + Au

  • Near-side well-described
  • Away-side suppression in central
  • collisions

STAR Preliminary

STAR Preliminary

near side

Central Au + Au

away side

Away side jets are suppressed!

Thomas Ullrich, BNL

slide37

High pT phenomena: suppression of inclusive rates, finite elliptic flow, suppression of back-to-back pairs

 compatible with extreme absorption and surface emission

Thomas Ullrich, BNL

summary

?

Summary
  • Soft physics:
    • Low baryon density
    • System appears to be in equilibrium (hydrodynamic behaviour)
    • Explosive expansion, rapid hadronization
  • Hard physics:
    • Jet fragmentation observed, agreement with pQCD
    • Strong suppression of inclusive yields
    • Azimuthal anisotropy at high pT
    • Suppression of back-to-back hadron pairs
    • large parton energy loss and surface emission?
  • Coming Attractions:
    • d+Au: disentangle initial state effects in jet production
    • (shadowing, Cronin enhancement)  resolution of jet quenching picture
    • J/ and open charm: direct signature of deconfinement?
    • (Charm via single electrons: PHENIX, PRL 88, 192303 (2002))
    • Polarized protons: DG (gluon contribution to proton spin)
    • Surprises …

Thomas Ullrich, BNL