Probing High-Temperature QCD Matter

at the Relativistic Heavy-Ion Collider (RHIC)

Saskia Mioduszewski

18 September 2008

Group Members

Postdocs:Rory F. ClarkeAhmed Hamed

Graduate Students:Matthew CervantesMartin Codrington (Chemistry)

Supported by D.O.E. and Sloan Foundation

Goal of RHIC: To Study Fundamental Puzzles of Hadrons

• Confinement– Quarks do not exist as free particles

• Generation of mass– Free quark mass ~ 5-7 MeV – Quarks become “fat” in hadrons,

constituent mass ~ 300-400 MeV

• Complex structure of hadrons– Sea anti-/quarks– Gluons– Origin of Spin of the nucleon

These phenomena must have occurred with formation of hadrons

nuclear matter p, n

~ 10 s after Big Bang

Hadron Synthesisstrong force binds quarks and gluons in massive objects: protons, neutrons mass ~ 1 GeV/c2

~ 100 s after Big Bang

Nuclear Synthesisstrong force binds protons and neutrons in nuclei

Expectation from Numerical Simulations of Finite-Temperature QCD

Stefan-Boltzmann limit

Expectation: create a “weakly coupled gas of quarks and gluons” by reaching Tc in high-energy heavy-ion collisions

New State of Matter created at CERN

At a special seminar on 10 February, spokespersons from the experiments on CERN's Heavy Ion programme presented compelling evidence for the existence of a new state of matter in which quarks, instead of being bound up into more complex particles such as protons and neutrons, are liberated to roam freely.

(Year 2000)

Pb+Pb collisions at √sNN = 17 GeV at the SPS

“Travel” Back in Time

Quest of heavy-ion collisions: heat and compress nuclear matter

– create Quark Gluon Plasma (QGP) as transient state in heavy ion collisions (e.g. Au+Au collisions)

– verify existence of QGP– study properties of QGP– study QCD confinement and how hadrons get their masses

neutron stars

Quark Matter

Hadron Resonance Gas

Nuclear Matter

Color Superconductor

SIS

AGS

SPS

RHIC& LHC

early universe

B

T

TC~170 MeV

940 MeV 1200-1700 MeVbaryon chemical potential

tem

per

atu

re

RHIC & SPS

Relativistic Heavy Ion Collider

• RHIC was proposed in 1983

• RHIC began providing collisions in 2000

• √sNN = 200 GeV = 10 x Collision-Energy at SPS

New probe available

High-pT particles from “hard” scattering

RHIC Specifications• 3.83 km circumference• Two independent rings

– 120 bunches/ring– 106 ns crossing time

• Capable of colliding ~any nuclear species on ~any other species

• Energy: 22-500 GeV for p-p 5-200 GeV for Au-Au

(per N-N collision)• Luminosity

– Au-Au: 5 x 1027 cm-2 s-1

– p-p : 1.5x1032 cm-2 s-1 (polarized)

The RHIC Experiments

STAR

PHENIX

STAR

Characterizing the collisions

• Different centralities, i.e. size of overlap region

• Asymmetry of reaction zones

• How does the matter behave?

• Can we probe the matter that exists only for a short time?

15 fm b 0 fm0 Npart 394

Spectators

Participants

For a given b, “billiard ball” model predicts Npart (No. participants)and Nbinary (No. binary collisions)

Not all A+A collisions are the same -- “Centrality”

0 Nbinary ~1000

Kinematics for colliders

2tanln Pseudo-rapidity:

Transverse momentum (pT) and pseudorapidity ()provide a convenient description

Mid-rapidity: η = 0, perpendicular to the incident beamsη = 4: Scattering at θ = 2.1o in the CM (or lab) frame

Radial Flow– Collective Expansion of system due to

pressure

– Heavier particles shifted to higher pT

– Observable: <T> from slopes as a function of mass and/or centrality

– Spectra can be described by hydrodynamic models for pT< 2-3 GeV/c and mid-peripheral to central events

Single Particle Spectra (low pT)

• Decreasing slope for increasing particle mass and centrality

peripheral

central

< T

>

Elliptic Flow in Non-central Collisions

Early state manifestation of collective behavior: • Asymmetry generated early in collision, quenched by expansion observed asymmetry emphasizes early time

Fourier Expansion: dN/d ~ 1 + 2 v2(pT) cos (2) + ...

x

y

p

patan2cos2 vSecond Fourier coefficient v2:

Coordinate space: initial asymmetry

Momentum space: final asymmetry

multiple collisions (pressure)

py

px

Data compared to Hydro

Reaction Plane (Angle 2)

Hydrodynamics with 0 viscosity

Thermalization in < 1 fm/c

pT [GeV/c]

v2

How does the expected “Quark Gluon Plasma” compare with the “Perfect Fluid” that we have found at RHIC?

Can we quantify the properties of this new form of matter?

Same behavior as observed in gases of

strongly coupled Li atoms

The matter we have created at RHIC behaves like a strongly coupled fluid, not like “weakly coupled gas of quarks and gluons”

K. M. O’Hara et al, Science 298, 2179

/S

[1/

4]

AdS/CFT for calculating properties of strongly-coupled gauge theories

RHIC “fluid” mightbe at ~2-3 on this scale (at T~1012 K)

How small can viscosity be?

Conjectured lower bound on viscosity/entropy = 1/4

P.K. Kovtun, D.T. Son, and A.O. Starinets, Phys. Rev. Lett. 94:111601, 2005.

Probing the MediumThe QCD analogue of x-ray tomography

• Need an external calibrated source

• Calculate absorption cross sections

Interpret the results

“Hard” processes to probe the matter • Large momentum transfer – or close distance• Can resolve partons: valence quarks, sea quarks

and gluons – scattered parton fragments into a “jet”• Coupling is weak - pQCD applicable

dtd

Aaf /A

a

Abf /B

b

dDh2

d

2h

cDh1

c

1h

quark or

gluon

JetFragmentation Function

cone of hadrons “jet”

p p

hard-scattered

parton in p+p

hadron distributionsoftened, jets broadened?

hard-scatteredparton during Au+Au

increased gluon-radiationwithin plasma?

Jets in heavy ion collisions

Hard scattering

Thermally-shaped Soft Production

Hard Scattering

• Good agreement with NLO perturbative QCD calculations

• High pT particle yields serve as a calibrated probe of the nuclear medium in nucleus+nucleus (A+A) and deuteron+nucleus (d+A) collisions

Production cross section of 0

p+p collisions = “baseline”

Systematizing Our Expectations• Describe in terms of

scaled ratio RAA

= 1 for “baseline expectations”

• Will present most of Au+Au and d+Au data in terms of this ratio

“no effect”

ppAuAubinary

AuAuAA YieldN

YieldR

centralN

binary = 975 94

Scaling of calibrated probe works in peripheral Au+Au, but strong suppression in central Au+Au

peripheralN

binary = 12.3 4.0

Discovery of Strong Suppression

Nuclear Modification Factor

RHIC 200 GeV central -

Suppressionperipheral –

Nbinary scaling

ppperipheralbinary

peripheral

YieldN

Yield

Comparison of peripheral to central

binary scaling

ppcentralbinary

central

YieldN

Yield

Theoretical Understanding?

Understood in an approach that calculates energy loss of hard-scattered parton through gluon radiation in a dense partonic medium (15 GeV/fm3 ~100 x normal nuclear matter)

Au+Au suppression (I. Vitev and M. Gyulassy, hep-ph/0208108)d+Au enhancement (I. Vitev, nucl-th/0302002 )

Our high pT probeshave been calibratedand are now being used to explore propertiesof the medium

Au-Au

d-Au

* Note deuteron-gold control experiment with no suppression

What have we learned?

• Nuclear matter created at RHIC is very opaque and dense (estimates of 100 x normal nuclear matter density)

• Strong collective behavior

• Coupling must be strong for v2 to be so large

Now we want to characterize this new matter more quantitatively (viscosity, transport coefficients, color charge density)

Jet Reconstruction in Au+Au Collisionsee q q

(OPAL@LEP)pp jet+jet

(STAR@RHIC)

Au+Au ??? (STAR@RHIC)

0-

dN/d

Jet Studies via Correlations

pT,trig – pT of the trigger particle

pT,assoc bin – range of pT selected to associate with the trigger particle

pT,trig > 4 GeV/c

pT,assoc = 2-4 GeV/c

Azimuthal distributions in Au+Au

Near-side: peripheral and central Au+Au similar to p+p

Strong suppression of back-to-back correlations in central Au+Au collisions

Au+Au peripheral Au+Au central

pedestal and flow subtracted

Phys Rev Lett 90, 082302

Escaping Jet -“Near Side”

Lost Jet -“Away Side”

“Reappearance of away-side jet”With increasing trigger pT, away-side jet correlation reappears

4 < pT,trig< 6 GeV/c, 2< pT,assoc< pT,trig Increasing pT,trig

Increasin

g pT

,assoc

Medium Modification to Fragmentation Function

Are we probing the medium? Or is it simply too opaque?

Punch-through Jet ?Or just tangential emission ?

Centrality8 < pT,trig< 15 GeV/c, pT,assoc > 6 GeV/c

Hard Scattering + jet

increased gluon-radiationwithin plasma?

• If is produced in hard scattering, instead of q or g, expect it to escape without interaction calibrated probe

• Then could study jet on opposite side as a function of the energy of photon

Is there any particle not affected by the opaque medium?

Effect of Dense Medium on Direct Photons

Hadrons are suppressed, photons are not – photons serve as the “control” experiment

PHENIX, Phys. Rev. Lett. 96, 202301 (2006)

ppγ

centralbinary

centralγ

γAA YieldN

YieldR

0

Fragmentation Function

Fragmentation Function - Study the particle distribution in a jet

initial

Modified Jet

• Calculate yields as a function of pT,assoc/pT,trig from correlation function

• Compare distribution in vacuum to medium to look for medium modification

Integrate yields

-rich triggers00 triggers triggers

Direct Measure of Medium Modification to Fragmentation Function

initialDirect

0

Ass

ocia

ted

yie

lds

per

trig

ger

Modified Jet

A. Hamed, Hard Probes 2008

STAR Preliminary

Ratio of Central Au+Au to Peripheral (~ Medium/Vacuum) Jet Yields

Within the current uncertainty in the scaling the medium effect on jets associated to a direct trigger is similar to jets associated to 0 trigger.

Summary

• RHIC has been successfully operating since 2000• The expectation of QGP as a weakly coupled gas of

quarks and gluons has been challenged by data• Medium created is strongly interacting (liquid-like)

and very opaque• Currently experiments are trying to make

measurements that can characterize the medium properties more quantitatively

• +jet measurement holds promise to be one of such probes

• Higher luminosity needed for definitive +jet measurement

• Future at RHIC is exciting

Extra Slides

0

Extraction of direct away-side yields

R=Y-rich+h/Y0+h

near near

Y+h = (Y-rich+h - RY0+h )/(1-R)away away

Assume no near-side yield for direct

 then the away-side yields per trigger obey

A. Hamed STAR Experiment ICHEP08 Philadelphia, PA July 29th -August 5th.A. Hamed STAR Experiment ICHEP08 Philadelphia, PA July 29th -August 5th.

Results: Method of extract direct associated yield

This procedure removes correlations due to contamination (asymmetric decay photons+fragmentation photons) with assumption that correlation is similar to

0 – triggered correlation at the same pT.

O(αs2α(1/αs+g))

This atomic system may also be near the bound.

T. Schafer, arXiv:0707.1540v1 (2007).

What do we learn from RAA?

Effect of collision medium on hadron pT spectra:

• Parton scattering with large momentum transfer Hard-scattered partons (jets) present in early stages of

collisions

• Hot and dense medium Hard-scattered partons sensitive to hot/dense medium

Theory predicts radiative energy loss of parton in QGP

• Emission of hadrons High pT hadrons (jet fragments)

Dense medium (QGP) would cause depletion in spectrum of leading hadron at high pT - “jet quenching”

High-pT Predictions X-N. Wang, Phys. Rev. C58 (1998) 2321

It has been predicted that jet production will be affected by medium effects due to the production of hot dense matter in high energy relativistic heavy ion collisions

Scaling from p+p to A+A

• For hard-scattering processes, expect point-like scaling. For inclusive cross sections :

• For semi-inclusive yields, expect :

2

pp

AA A sources like-point ofnumber the of ratio the σ

σ

class centralityA A for theN

collisionsbinary Nucleon -Nucleon ofnumber Yield

Yield

binary

pp

AA

0-

dN/d

Elliptic flow

Jet Studies via Correlations

pTtrig – pT of the trigger particle

pTassoc bin – range of pT selected to

associate with the trigger particle

pTtrig > 4 GeV/c

pTassoc = 2-4 GeV/c

An example of Nbinary ~ A*B scaling

• Small cross section processes scale as though scattering occurs incoherently off nucleons in nucleus

• scale as A1.0 in +A

• scale as Nbinary ~A*B in A+B

7.2 GeV muons on various targets. M. May et al., Phys. Rev. Lett. 35,

407, (1975)

“Binary-Scaling” and RAA

• Define Nuclear Modification Factor RAA

Effect of nuclear medium on yields

pp

centralbinarycentral

Yield

NYield /

peripheralbinaryperipheral

centralbinarycentral

NYield

NYield

//

pp

peripheralbinaryperipheral

Yield

NYield /

• The probability for a “hard” collision for any two nucleons is small

• The total probability in A+A collision is multiplied by the number of times we try, i.e. – the cross-section scales with the number of binary collisions - Nbinary

Yield of 0 measured by PHENIX

p+p collisions Au+Au collisions

Evolution of Jet Structure

At higher trigger pT (6 < pT,trig < 10 GeV/c), away-side yield varies with pT,assoc

For lower pT,assoc (1.3 < pT,assoc <1.8 GeV/c), away-side correlation has non-gaussian shape becomes doubly-peaked for lower pT,trig

pedestal and flow subtracted

4 < pT,trig< 6 GeV/c, 2 < pT,assoc< pT,trig