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Jets in Nuclear Collisions

Why jets in nuclear collisions? How do we find jets in nuclear collisions? Is hard scattering different in nuclear collisions than in

e+e- or pp collisions? What happens in the nuclear medium?

Is jet transport & fragmentation changed? What do we still want to know?

Barbara JacakStony Brook UniversityJune 29, 2004

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Why collide nuclei at s=200 GeV/A?

high energy nuclear collisions should create quark gluon plasma

At high temperature and density: T~170 MeV and/or ~50 Debye screening by produced color-chargesexpect transition to “free” gas of quarks and gluons

Attractive potentialConfinement at large distance

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pressure builds up

how to probe the plasma?

PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM

Kpnd,

Hadrons reflect (thermal) properties when inelastic collisions stop (chemical freeze-out).

, e+e-, +Real and virtual photons emitted as thermal radiation.

Hard scattered or heavyq,g probes of plasma formed

System expands & cools

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Hard quarks & gluons jets

Hard scattering happens early

affected by initial state nucleus

Hard partons propagatefast quarks, gluons traverse

the interesting stuffradiate gluonsinteract with QGP partons

Fragmentation is last step - outside the medium

coneRFragmentation:

z hadron

parton

p

p

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Plasma physics of the quark gluon plasma?

Want to knowpressure, viscosity, energy gradients, equation of state,thermalization time & extent

determine from collective behavior

Other plasma parametersradiation rate, collision frequency, conductivity, opacity, Debye screening length?

what is interaction of q,g in the medum? need short wavelength strongly interacting

probe

high momentum q,g provide just this!

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What is the effect of the medium?

hadrons

q

q

hadronsleadingparticle

leading particle

schematic view of jet production

decreases their momentum fewer high momentum particles beam “jet quenching”

before they create jets, the scattered quarks radiate energy (~ GeV/fm) in the colored medium

Approach:calculate jet rate, test in pp, compare jets in A+A to p+p

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QCD and EM Radiation

EM

BUT radiated gluons also interact with gluons in the medium! Energy loss depends on gluon density along the path.

EM Radiation by scattering:Interference between initialand final state radiation

gluon quark

QCD

Radiation interferestoo

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Energy Loss in Dense QCD MatterEnergy Loss in Dense QCD Matter Ivan Vitev,Ivan Vitev, ISUISU

• Elastic energy loss

J.D.Bjorken, SLAC preprint (1982) unpublished

2 2 /2

46 1 ln jetelastic T

s

E TE T e

TL

• Inelastic (radiative) energy loss

QCD is very differentfrom QED in the

ability of the gluon to reinteract

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Energy loss expected

Since QCD is non-abelian, even 1 scattering in final state is sufficient to generate energy loss

Remember that radiated gluon couples to medium!

formation length of max E gluon: lF ~ 2E/2 ( = pT kick )

E ~ E x L/ x L 2/2E ~ 2 L 2 /2 standard radiationwith no interference

formation time of radiated gluon( gluon interaction probability)

So:

In normal, cold nuclei dE/dx ~ 0.5 GeV/fm

Prediction for RHIC: 10x E of cold nuclei

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A closer look at the calculation

• Radiative energy loss

(1) R s

3(1)

2

2g

g

2R s

2CE Log ... ,

4

Static medium

9 C 1E Log ... ,

4 A

(L)

dNdy (L

1+1D

)

L 2E

Bjo

L

2EL

L

rken

• Significantly larger than the elastic for static nuclear matter

• Can be related to the density of gluons/quarks in the system or T

• Takes into account geometry, the small number of scatterings, finite kinematics

M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594, (2001); Phys.Rev.Lett.85, (2000)

But medium is not static!Expands density drops

2 ,zV R LzL ct

0exp

2anding static

tE E

R

0

152

R

t

2

1desnity:

dN

dy R t

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How do we find jets in nuclear collisions?

In p+p can look for hadrons in the characteristic “cone” pattern

How to find the jet?

s=200 GeV energy is modest; jet not large

Central Au+Au collision

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3 Ways to “Skin a Cat Jet”

1) Single Particle Spectra:High pT dominantly from jets

d/dpT RAA, RdA

nuclear modification factor

2) 2-Particle Correlations:dN/d()

3) Jet Reconstruction:d/dET, Fragmentation function

trigger

“Trigger” = 0

Adler et al., PRL90:082302 (2003), STAR

near-side

away-sideNice work if you can get it!

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Jet physics in Au+Au

Trigger:hadron with pT > 2.5 GeV/cBiased, low energy, high z jets!

of associated partners

Count associated lower pT

particles for each trigger “conditional yield”Near side yield: number of jet associated particles from same jet in specified pT binAway side yield: jet fragments from opposing jet

triggernear side < 90°Partner from same jet

away side > 90° opposing jet

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Subtract the underlying event

CARTOON

flow

flow+jet dN

Ntrig d

includes ALL triggers(even those with no

associated particles inthe event)

jetUnderlying event isbig! Collective flow causes another correlation in them:

B(1+2v2(pTtrig)v2(pT

assoc)cos(2))

associated particles with non-flow angular

correlations -> jets!

Treat as 2 Gaussians

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combinatorial background large in Au+Au

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Benchmark calculation of probe rate on a simple system: p+p collisions

p-p PRL 91 (2003) 241803

Good agreementwith NLO pQCD

2

/( , )

a Nf x Q

2

/( , )ch a

D z Q

Parton distribution functions

Fragmentation functions

0

0 rates:dN/dpT

2dy1dy2 ~ dxa dxb dzc dzd

fa/N(xa,Q2) . fb/N(xb,Q2) . Dh1(zc,Q2) . Dh2(zd,Q2) .

dab /dQ2dy

To generalize for nuclei:fa/N(xa,Q2,r) fa/N(xa,Q2) .

Sa/A(xa,r) .

tA(r)

Nuclear modification to structure function (shadowing, saturation, etc.)

Nuclear thickness function

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Now check that it works in Au+Au

Not so easy – cannot use anything that should be affected by the medium!

Try QCD direct photons

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pQCD in Au+Au? direct photons

[w/ the real suppression]

( pQCD x Ncoll) / background Vogelsang/CTEQ6

[if there were no suppression]

( pQCD x Ncoll) / ( background x Ncoll)

Au+Au 200 GeV/A: 10% most central collisions

[]measured / []background = measured/background

Preliminary

Probe calculation works!

pT (GeV/c)

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Is the message in the medium?

Is there “jet quenching” as predicted from energy loss? count high pT particles (AA vs. pp) look at back-to-back jets

How much energy do fast partons lose?What does it tell us about the medium?

Where does the “lost” energy go?

What does the presence of q and q in the QGP do to jet fragmentation?

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Technique to search for jet quenching

Compare to baseline: nucleon-nucleon collisions at the same energy

To 0’th order: Au + Au collisions start with collisions of quarks & gluons in the individual N-N reactions(+ effects ofnuclear binding andcollective excitations)

Hard scattering (p transfer > few GeV) processes scale as the number of N-N binary collisions <Nbinary>

so for pT> 2 GeV/c expect: YieldA-A = YieldN-N . <Nbinary>

nucleons

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Nuclear Modification of Hadron Spectra?

ddpdT

ddpNdpR

TNN

AA

TAA

TAA /

/)(

2

2

<Nbinary>/inelp+p

nucleon-nucleon cross section

1. Compare Au+Au to nucleon-nucleon cross sections2. Compare Au+Au central/peripheral

Nuclear Modification Factor:

If no medium effect: RAA < 1 in regime of soft physics RAA = 1 at high-pT where hard scattering dominates Jet quenching: RAA < 1 at high-pT

AA

AA

AA

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pp

AuAubinaryAuAuAA Yield

NYieldR

/

Au-Au s = 200 GeV: high pT suppressed!

PRL91, 072301(2003)

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look for the jet on the other sideSTAR PRL 90, 082302 (2003)

Central Au + Au

Peripheral Au + Au

near side

away side

peripheral central

22 2 2( ) ( ) (1 cos(2 ))D Au Au D p p B v

Medium is opaque!

Trigger 4-6 GeV/c pT

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Suppression larger out-of-plane

Path Length Dependence

nGLVE L

di-hadron, 20-60% Central Background SubtractedSee J. Bielcikova et al., (nucl-ex/0311007) for background derivation

STAR Preliminary

s =200 GeVNN

Measured

ReflectedIn-plane

Out-of-plane

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Suppression: a final state effect?

Hadronic absorption of fragments: Gallmeister, et al. PRC67,044905(2003)Fragments formed inside hadronic medium

Hadron source is soft, after allRecombination of flowing partonsFries, Muller, Nonaka, Bass nucl-th/0301078Lin & Ko, PRL89,202302(2002), Hwa, et al.

Energy loss of partons in dense matterGyulassy, Wang, Vitev, Baier, Wiedemann…

PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM

Hadron gas

1AuAuR But absent in d+Au collisions! d+Au is the “control” experiment

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Suppression: an initial state effect?

Gluon Saturation (color glass condensate)

Wavefunction of low x gluons overlap; the self-coupling gluons fuse, saturating the density of

gluons in the initial state. (gets Nch right!)

Levin, Ryshkin, Mueller, Qiu, Kharzeev, McLerran, Venugopalan,

Balitsky, Kovchegov, Kovner, Iancu …

probe rest frame

r/ggg

dAu AuAuR R RdAu~ 0.5D.Kharzeev et al., hep-ph/0210033

1dAuR Broaden pT :•Multiple elastic scatterings

(Cronin effect) Wang, Kopeliovich, Levai, Accardi

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PHENIX Preliminary 0

PHOBOS Preliminary

STAR Preliminary

Experiments show NO suppression in d+Au!

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Centrality Dependence

Dramatically different and opposite centrality evolution of AuAu experiment from dAu control.

Jet Suppression is clearly a final state effect.

Au + Au Experiment d + Au Control

PHENIX preliminary

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Are back-to-back jets there in d+Au?

Pedestal&flow subtracted

hadronsleadingparticle suppressed

q

q

?

Yes!

So this is the rightpicture for Au+Au

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Property probed: density

Au-Au

d-AudAu

Agreement with data:Vitev, Gyulassy, Wang, others say dE/dx ~ 7.5 GeV/fm get dAu right too!

initial gluon density=

dNg/dy ~ 1100

~ 15 GeV/fm3

hydro initial state same 5-10 x critical

NB: Lowest energy radiation sensitive to infrared cutoff.

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Recap

Hard partons are excellent probes of QGP Can calculate their production rate with pQCD in Au+Au (surprisingly) Can do jet physics in heavy ion collision See jet quenching in single particles & back-to-back

correlationsInfer:dE/dx ~ 7.5 GeV/fmdNg/dy ~ 1100 ~ 15 GeV/fm3

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Turn to the fragmentation function

coneRFragmentation:

z hadron

parton

p

p

Standard picture

If true:

fragmentation independent of medium

Baryon/meson at high pT same in Au+Au and p+p

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Formation time of fragmentation hadrons

Uncertainty principle relates hadron formation time to hadron size, Rh and mass, mh

In laboratory frame: f ~ Rh (Eh /mh)consider 2.5 GeV pT hadrons

f ~ 9-18 fm/c for pions; Rh~0.5-1 fm

f ~ 2.7 fm/c for baryons (Rh~1 fm) Alternatively, consider color singlet dipoles from

combination of q & q from gluon splittingUsing gluon formation time, can estimatef ~ 2Eh (1-z)/(kT

2+mh2)

for z = 0.6-0.8 and kT ~ QCD (f baryons) ~ 1-2 fm/c R(Au nucleus) ~ 7 fm Baryon formation is NOT outside the medium!

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We observe a puzzle

h/0 ratio shows that p is enhanced only < 5 GeV/c

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Hydro. expansion at low pT + jet quenching at high pT.

Coalesce (recombine) boosted quarks hadrons enhances mid pT hadrons baryons especially

pQCD spectrum shifted by 2.2 GeV

Teff = 350 MeV

R. Fries, et al

Are extras from the (soft) underlying event?

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Phase space filled with partons:coalesce into hadrons

ReCo of hadrons: convolution of Wigner functions

Where does ReCo win?

),()2

,2

;2

,2

()2()2( 3

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,3

3

3qrq

PrRq

PrRW

rqddRd

Pd

dNMab

ba

M Wab(1;2) = wa(1)wb(2)

fragmenting parton:ph = z p, z<1

recombining partons:p1+p2=ph

Power law:

Exponential: TpTAew /~

DAeDwN TzPT /frag ~

TPTeAwwN /2reco ~

Tpw ~

TPN ~frag

2reco ~

TPN

Use lowest Fock state, i.e. valence quarks

R. Fries

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Coalescence Model results

Fries et al: Phys.Rev. C68 (2003) 044902Greco, Ko, Levai: PRC 68 (2003)034904

•particle ratios and spectra OK

•intermediate pT hadrons from

coalescence of flowing partons NOT from jets, so no jet-like associated particles

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But baryons show jet-like properties too…

Baryons at 2-4 GeV/c pT scale with Ncoll !

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So baryons seem jet-like!

baryons & antibaryons not suppressed!? parton E depends upon what fragmentation WILL be???

baryon excess due to fragmentation function modification?Step 1: determine if baryons are from jets

do we see hadronic partners from the same jet?Step 2: calculate effect of q,q in surrounding medium upon

(soft part of) fragmentation function

Rcp

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Step 1: use 2 particle correlations

Select particles with pT= 2.5-4.0GeV/c

Identify them as mesons or baryons viaTime-of-flight

Find second particle with pT = 1.7-2.5GeV/c

Plot distribution of the pair opening angles

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Jets in PHENIX

Large multiplicity of charged particles--solution: find jets in a statistical manner using angular correlations of particles

mixed events give combinatorial background 2 x 90 degree acceptance in phi and ||<0.35

--solution: correct for azimuthal acceptance,

but not for acceptance Elliptic flow correlations

--solutions: use published strength values and subtract (could integrate over 90° to integrate all even harmonics to zero)

PHENIX PRL 91 (2003) 182301

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Subtracting combinatorial background

CARTOON

flow

flow+jet dN

Ntrig d

includes ALL triggers(even those with no

associated particles inthe event)

jetAssociated particles from the underlying event. Collective flow causes another correlation in them:

B(1+2v2(pTtrig)v2(pT

assoc)cos(2))

associated particles with non-flow angular

correlations -> jets!

Treat as 2 Gaussians

1

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• jet partner equally likely for trigger baryons & mesons

• Same side: only slight decrease with centrality

•Away side: partner rate as in p+p confirms jet source of baryons!

• See disappearance of away-side jet for both baryons and mesons

Identify Trigger: Source of intermediate pT baryons?

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pions

only soft protons

partners expected from recombination

•Yield of partners per trigger expected from recombination of purely thermal (soft) constituent quarks

(dilutes jets)

Many baryons ARE from jets, but medium modifies those jets

Allow fast quark to combine with quarks from medium

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pT spectra of same jet associated particles

Spectra in lab, rather than jet, frame

Allows to compare with inclusive spectra

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Compare slope to inclusive hadron spectra

Generally higher

Perhaps thermalized in most central collisions?Calculations (step 2) desperately needed!

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Conclusion about fragmentation function

It’s modified in the medium!Au+Au jets richer in soft hadrons than p+p or d+AuAu+Au jets baryon yield increases with medium volume

Maybe some evidence that jet fragments are beginning to thermalize in the medium

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What do we still want to know?

Quantitative information on medium modification of jet fragmentation

Where does the energy radiated by fast partons go?Many soft gluons – no (per observed multiplicity)A few semi-hard gluons? … could be

How is the lost energy propagated in the medium?Infer energy, color transport properties of QGP basic plasma physics!Is the lost energy thermalized in the medium?

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values

B

(fm)

Npart R/R+F

R/R+F

p

Partner yield

Partner yield p

12 24 0.45 0.95 0.027 0.0047

0.0014 0.0007

7.5 156 0.65 0.97 0.0172 0.0030

0.0008 0.0004

0 390 0.8 0.98 0.0098 0.04017

0.0005 0.0003

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kT, jT at RHIC from p+p Data

J. Rak, Wed.

J. Rak, DNP03

s=200 GeV

di-hadron

Statistical Errors Only

near-side away-side

nearfar

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Moment Analysis of QCD Matter2 ( )

( )

T g

g

k x dx

E x x dx

I. Vitev, nucl-th/0308028

Induced Gluon Radiation ~collinear gluons in cone “Softened” fragmentation

in je

i j t

t

n e

: increases

z : decreases

chn

Gyulassy et al., nucl-th/0302077

coneRFragmentation:

z hadron

parton

p

p

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Collective effects? Pressure: a barometer called “elliptic flow”

Origin: spatial anisotropy of the system when created, followed by multiple scattering of particles in the evolving system spatial anisotropy momentum anisotropy

v2: 2nd harmonic Fourier coefficient in azimuthal distribution of particles with respect to the reaction plane

Almond shape overlap region in coordinate space 2cos2 v

x

y

p

patan

y2 x2 y2 x2

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Hydro. CalculationsHuovinen, P. Kolb,U. Heinz

v2 reproduced by hydrodynamics

STARPRL 86 (2001) 402

• see large pressure buildup • anisotropy happens fast • early equilibration !

central

Hydrodynamics assumes early equilibrationInitial energy density is inputEquation of state from lattice QCDSolve equations of motion

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But at forward rapidity reach smaller x

y = 3.2 in deuteron direction x 10-3 in Au nucleus

Strong shadowing, maybe even saturation?

d Au

Phenix Preliminary

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Pions in 3 detectors in PHENIX

Charged pions from TOF

Neutral pions from EMCAL

Charged pions from RICH+EMCAL

Cronin effect gone at pT ~ 8 GeV/c

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Centrality dependence of Cronin effect

Probe response of cold nuclear matter with increased number of collisions.

See larger Cronin effect for baryons than for mesons (as at Fermilab)

Qualitative agreement with model by Accardi and Gyulassy. Partonic Glauber-Eikonal approach: sequential multiple partonic collisions. nucl-th/0308029

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Does Cronin enhancement saturate?

A different approach:

Intrinsic momentum broadening in the excited projectile proton:

hpA: average number of collisions:

X.N.Wang, Phys.Rev.C 61 (2000): no upper limit.

Zhang, Fai, Papp, Barnafoldi & Levai, Phys.Rev.C 65 (2002): n=4 due to proton d dissociation.