PD Dr. Klaus Reygers Institut für Kernphysik Universität Münster

Hard Scattering and Jets in Heavy-Ion Collisions

Naturwissenschaftlich-Mathematisches Kollegder Studienstiftung des deutschen Volkes

Kaiserslautern 30.9. – 5.10.2007

PD Dr. Klaus ReygersInstitut für Kernphysik Universität Münster

2 Hard Scattering and Jets in Heavy-Ion Collisions

Content

1 Introduction1.1 Quark-Gluon Plasma

1.2 Kinematic Variables

2 Lepton-Nucleon, e+e-, and Nucleon-Nucleon Collisions2.1 Deep-Inelastic Scattering and the Quark-Parton Model

2.2 Jets in e+e--Collisions

2.3 Jets and High-pT Particle Production in Nucleon-Nucleon Collisions

2.4 Direct Photons

3 Nucleus-Nucleus Collisions3.1 Parton Energy Loss

3.2 Point-like Scaling

3.3 Particle Yields and Direct Photons at High-pT

3.4 Further Tests of Parton Energy Loss

3.5 Two-Particle Correlations

3.6 Jets in Pb+Pb Collisions at the LHC

3 Hard Scattering and Jets in Heavy-Ion Collisions – 3.1 Parton Energy Loss

3.1 Parton Energy Loss


Jet Tomography in A+A Collisions

Hard parton-parton scatterings take place in initial phase, prior to the formation of a QGP

Scattered quarks und gluons sensitive to medium properties: „jet tomography“


Parton energy loss in a finite, static medium consisting of colorcharge carriers

22

2

2ln ...

4s E

E C LL

a ml m

æ öç ÷D =- +ç ÷ç ÷ç ÷è ø

Energy loss for gluon jets larger than for quark jets:

3 for gluon jets

4 / 3 for quark jetsC

ìïï=íïïî

Energy loss due to gluon radiation dominant:

rad colld / d d / dE x E x

2

:

:

:

L

m

l

Parton Energy Loss

Typical momentum transfer frommedium to parton Mean free path of the radiated gluons in the medium

Path length of the parton in the medium

2~E LD

Total energy loss in the medium:

Detailed numerical calculation shows:

/ const.

for 20 GeV

E E

E

D »

<

(effect of quantummech. interference)


Parton Energy Loss: Why E L2 ?

Probability for radiating a gluon: Lµ

Number of scatterings with momentum transfer kT until it decoheres: Lµ

Total energy loss: 2E LD µ


Relation between Transport Coefficient andEnergy Density of the Medium

increases smoothly with energy density

Nuclear matter

ideal qgp

hot, massless pion gas

cold pion gas

q̂

2nuclear matter

ˆ 0.5 1 GeV / fmq < -

QGP (and hot hadron gas):

qgp nuclear matterˆ ˆq q

2ˆ /q Medium characterized by

(Momentum transfer per mean free path)


Parton Energy Loss in Expanding Medium

3 Gluon2

d9 1 2ln ...

4 ds

N EE C L

A y L

pa

m

æ öç ÷D =- +ç ÷ç ÷ç ÷è ø

Taking into account the expansion of the fire ball (Bjorken Model):

Initial gluon density

Transverse area(A ~ R1/3 für b = 0)

Energy loss linear in L

Energy loss becomes linear in L for 1D Bjorken expansion


Medium-Modified Fragmentation Functions (I)

energyloss

qE (1 ) qEe-

parton

hadron h, energy

hE

2/ ( , )h qD z Q( )P e

Prob. Distr. for parton energy loss (“Quenching weight”)

Consider fixed parton energy loss 2/

1( , )

1h q

dn dn dzD z Q

dx dz dx e= × = ×

-

,(1 )

(1 )

h h

q q

E Ez x

E E

x

e

e

= =-

=-

Average over energy loss probability

1

med 2 2/ /

0

1( , ) ( ) ( , )

1 1h q h q

xD x Q d P D Qe e

e e=

- -òHadrons resultingfrom gluon bremsstrahlungneglected


Medium-Modified Fragmentation Functions (II)

Fragmentation functionu → for a medium with L = 7 fm and various gluon densities


Quenching Weights (I)

quenching weight

probability to have no induced gluon radiation

continuous quenching weight

0ˆas function of in the limit :p q E® ¥

Note that P(E) is a generalized probability which can take negative values as long as this equation holds

taken from PhD thesis of C. Loizides


Quenching Weights (II): Continuous Weight

taken from PhD thesis of C. Loizides

These quenching weights hold for parton energies E →


Parton Energy Loss in the Limit E →

More realistic models need to take finite parton energies into account


Energy loss in the GLV Formalism for Cu+Cu, Au+Au, and Pb+Pb

energy loss # radiated gluonsCalculated fractional energy loss and number of radiated gluons shown for three centralities in each figure:

Au+Au at sNN = 200 GeV:

Cu+Cu at sNN = 200 GeV:

Pb+Pb at sNN = 5500 GeV:

dNg/dy = 2000, 3000, 4000

I. Vitev, Phys.Lett.B639:38-45,2006


Simple Estimate of the Relative Energy Loss

pT independence of RAA implies constant fractional energy loss

Loss Loss: , i.e., (1 )TT T

T

pS p S p

p

2

Loss

1/( 2)Loss

1

1

n

AA

nAA

R S

S R

0 spectra at RHIC energy (sNN = 200 GeV) described with n 8

Sloss from 0 RAA

PHENIX, nucl-ex/0611007

1T

d

dn

T

Np

p

0 spectrum without energy loss:

Constant fractional energy loss:

This leads to:

16 Hard Scattering and Jets in Heavy-Ion Collisions – 3.2 Point-like Scaling

3.2 Point-like Scaling


Calculate increase of the effective luminosity of nucleons (and partons, respectively) based on known nuclear geometry

Result:Particle yields scale with the average number Ncoll of inelastic

nucleon-nucleon collisions in the absence of nuclear effects

hart hartAB

d d

d d

A B p p

T T

NT

p p

s+ +

= ×

unel.AB coll NN/T N s=

Only changecompared to p+p

Expectation for Particle Yields from Hard Scattering Processes in A+A collisions


Digression: Luminosity of a Collider

Rate of event for a given physics process:

N L s= ×

Luminosity [(scm2)-1]

Cross section [cm2]

Event rate [s-1]

If two bunches of particles collide with frequency f then :

1 2 1 2

beam 4 x y

n n n nL f f

A ps s= =

Transverse area of the beam

ni: number of particles in bunch i

Example:Au+Au at RHIC: L = 2 x 1026 cm-2 s-1


Effective Nucleon Luminosity: The Nuclear overlap function

A A( ) : ( , )dT s s z zr=ò

Nuclear thickness:

Normalization:

2A ( )dT s s A=ò

“nucleon luminosity” in area s 2

AB A Bd ( ) ( ) ( )dT s T s T s b s= × -

2AB A B( ) ( ) ( )dT b T s T s b s= × -ò

p+pcoll AB inel( ) ( )N b T b s= ×

unit: 1/area

2d s at :

“Total nucleon luminosity” for collisions at impact parameter b (nuclear overlap function):

Thus, number of interactions for process with cross section

int AB int( ) ( )N b T b s= × In particular:


Impact Parameter Distribution of a A+A collisions

Au+Au at sNN = 200 GeV

500 000 Glauber MC collisions

slope: 2

Analytic approximation:A+B NNinel inel( ) 1 exp( ( ) )ABp b T b

Glauber MC:

A+Binel

d2 ( )

db p b

b

A+Binel

0

dd

db

b

Au+Au@200GeVinel 6.9 bs »Total cross section:

probability for an inelastic A+B collision at impact parameter b


Averaging TAB(b) over an Impact Parameter Distribution

Observable: Hard process per inelastic A+A collisions, i.e.

A+Bhard hardA+B

inel

( )( )

( )ABT b

N bp b

Typical example: pT dependent pion yield per inelastic event:

A+Binel inel

( )1( )

( )

p pAB

A BT T

T bdN db

N dp p b dp

Averaging over an impact parameter range f (say b1 b b2):

2

1

2

1

inel A+Binel

2 ( )1

2 ( )

b

AB p pb

ABbA B fT T Tf

b

b T b dbdN d d

TN dp dp dp

b p b db

A+Binel ( )p b

weighting factor:

2

1

2d 2 db

f b

b b b Note that


Nuclear Modification Factor (I)

Definition of nuclear modification factor:

Consider special case b1 = 0, b2 = :

0A+B

inel A+B inelinel

0

2 ( )1

2 ( )

AB A B p p

A BT T T T Tf

b T b dbdN d AB d d d

ABN dp dp dp dp dp

b p b db

(holds for hard scattering in the absence of nuclear effects)

inel

2

1

/( )

/( ) /

1

A BA BT fT

AB T p pAB Tfp p

AB T

f

dNN dpd dp

R pT d dp

d b T b d dp

In practice:

inelcoll NN/AB f f

T N where is determined with a GlauberMonte Carlo code

coll fN

(in the absence of nuclear effects)


Ncoll from Glauber Monte-Carlo calculation

In the absence of nuclear effects:RAB = 1 at high pT (pT > 2 GeV/c)

2T

T 2coll T

d / d d( )

d / d dA B

AB

p p

N p yR p

N N p y+

+

=´

“no medium effects”

RAB

= 1R

AB

RAB

< 1

pT (GeV)

Nuclear Modification Factor (II)


Glauber Monte-Carlo Approach

Nucleons of both nuclei randomly distributed in space according to Woods-Saxon distribution

Impact parameter b drawn from distribution d/db = 2b

Collision between two nucleons take place if their distance d in the transverse plane satisfies

NNinel /d

Npart and Ncoll through simulation of many A+B collisions (typically ~ 106)

Au+Au bei sNN = 200 GeV

NNinel 42 mb at 200 GeVNNs


Examples of Glauber-MC Events (I)


Side view: Transverse plane:


Examples of Glauber-MC Events (II)

Au+Au at sNN = 200 GeV

Side view: Transverse plane:


Npart und Ncoll vs. Impact Parameter

Npart(b)

Ncoll(b)

4/ 3coll partN NµApproximate relation between Npart and Ncoll:

28 Hard Scattering and Jets in Heavy-Ion Collisions – 3.3 Particle Yields at Direct Photons at High-pT

3.3 Particle Yields at Direct Photons at High-pT


Cronin-Effect in p+A Collisions

Proton-Nucleus Collisions:

p+A Collisions:

Nuclear modification factor

RpA

> 1, at intermediate pT, before

RpA

= 1 is reached in the limit

of very high pT

Common explanation of the Cronin effect: Multiple soft scattering in p+A leads to additional transverse momentum kT


0 spectra in p+p- and Au+Au Collisionen

peripheral:N

coll = 12.3 4.0

centralN

coll = 955 94

Strong suppression of the 0 spectrum in central Au+Au collisions relative to Ncoll-scaled p+p spectrum


production in Au+Au at sNN = 200 GeV

factor 4-5 suppression

Ncoll = 5 ± 1Ncoll = 12 ± 4Ncoll = 29 ± 8Ncoll = 61 ± 10Ncoll = 120 ± 14Ncoll = 220 ± 23Ncoll = 374 ± 40Ncoll = 603 ± 59Ncoll = 955 ± 94

2

T 2coll

d / d d( )

d / d d

T A BAB

T p p

N p yR p

N N p y+

+

=´

No suppression in peripheral Au+Au collisions

Factor 4-5 suppression in central Au+Au collisions


Particle Composition in A+A

For a parton that hadronizes in the vacuum after traversing the medium (A+A collision), particle ratios should be similar to those in d+Au or e++e-

This is indeed approximately true for pT > 6 GeV/c

2 < pT < 6 GeV/c: quark coalescence ?


What’s going on at Intermediate pT (~2 < pT < ~6 GeV/c) ?

Coalescence of quarks from the QGP is a conceivablemodel for hadronization at intermediate pT


Alternative Explanation: Effects of Cold Nuclear Matter ?

Hadron suppression e.g. due to strong modification of parton distributions in heavy nuclei (initial state effects)?

Example: Color Glass Condensate Model

Fewer gluons in wavefunction of incoming Au nuclei

Result: Fewer hard parton-parton scatteringsand therefore fewer particles at high pT

Hadron suppression in Au+Au can be described!

Control Measurements

Hadron production in d+Au

High-pT direct photons in Au+Au

Kharzeev, Levin, McLerran,Phys.Lett. B 561, 93 (2003)


Cold Nuclear Matter Effects studied at RHIC with d+Au

nucl-ex/0610036

d+Au 0

200 GeVNNs =

RdA 1: Cold nuclear matter effectsare small at sNN = 200 GeV


Centrality Dependence of RAA in d+Au and Au+Au

Au + Au Experiment d + Au Control Experiment

Preliminary DataFinal Data


Direct Photons at high pT

Production of direct photons and hadrons at high pT sensitive to the same parton luminosity

Direct photons escape the medium unscathed

s

s

s

Example:


Photon Sources in A+A Collisions

Direct photons from hard scattering dominate at high pT

Experimental challenge: Background from hadron decays, e.g.,

Method:direkt = Gesamt – Zerfall T

1np

hard:

/ E Tethermal:

Decay photons


Direct Photons in Au+Au

QCD + Ncoll scaling describes direct photon spectra in Au+Au


Phys.Rev.Lett.94:232301,2005


Nuclear Modification factor for direct Photons

A+B

coll T p+p

d / d

d / dT

AB

N pR

N N p=

´

Factor 5 suppression

energy lossfor q and g

No energyloss for ‘s

Hadrons are suppressed whereas direct photons are not:Evidence for parton energy loss (as expected in the QGP)


Centrality Dependence of 0 and Direct Photon Production in Au+Au at sNN = 200 GeV


More Recent Data with Higher Statistics

Possible Explanations for direct photon suppression at pT 18 GeV/c:

Proton/neutron difference

Modification of parton distribution (EMC effect?)

Quenching of fragmentation photons


Reminder: Direct and Fragmentation Component

dir

ect

frag

m.

NLO pQCD calculation by W. Vogelsang (p+p at s=200 GeV)


Jet Quenching: Data vs. Theory

without parton energy loss

Wang

Wang

Levai

Levai

Vitev

Au+Au at sNN

= 200 GeVq

q

q

q

q

q

q

q

Data imply

high initial gluon density

high energy density

Energy loss for a 10 GeV quark:

Gluonend / d 1000 200N y » ±

3c10 GeV/fme e>

1,5 2 GeVED = -

with parton energy loss


3.4 Further Tests of Parton Energy Loss


How to Learn More about Jet Quenching ?

Suppression of high pT hadron yields

Dependence on colliding system

Dependence on center-of-mass energy

Dependence on path length L in the medium

Difference between energy loss for light (up, down) and heavy quarks (charm)

Study modification of di-hadron correlations in Au+Au with respect to p+p


0 RAA in Au+Au and Cu+Cu at sNN = 200 GeV

Approximately same RAA in Au+Au and Cu+Cu for similar Npart values in accordance with jet quenching models


sNN Dependence of RAA (I):Au+Au at 62 GeV and 200 GeV

Similar RAA for pT > 6 GeV in Au+Au at 62 and 200 GeV


sNN Dependence of RAA (II):RAA in Cu+Cu at 22.4, 62.4 and 200 GeV

Cronin enhancement appears to win over parton energy loss in central Cu+Cu collisions at 22 GeV


sNN Dependence of RAA (III): RAA in Pb+Pb Collisions at the CERN SPS

Suppression in very central Pb+Pb collisions (Npart > 300)


Path Length Dependence of RAA (I)

In Plane

Out of Plane

fD

Dependence of RAA on angle with respect to reactionplane allows to study pathlength dependence of energyloss

reaction plane

3 < pT < 5 GeV/c

PHENIX, nucl-ex/0611007


Path Length Dependence of RAA (II)

In Plane

Out of Plane fD

Averaged over jet productions points in (x,y) plane

Approximate scaling in Lxy expected in parton energy loss

models

Experimental evidence weak

Path length dependence of jetquenching remains an open question


Jet Quenching and Angular Anisotropy (I)

Bulk (Hydrodynamic) Matter

Pressure gradient converts position space anisotropy to momentum space anisotropy

Jet Propagation

Energy loss results anisotropy based on location of hard scattering in collision volume

y

x

y

x

Common wisdom: low pT high pT

v2 at high pT should result from jet quenching

Anisotropy in particle production related to collision geometry

2 cos 2v f= atan y

x

p

pf =( )( )

3 2

31

11 2 cos

2 n rnt t

d N d NE v nd p p dp dy

jp

¥

=

æ öç ÷= + - Yç ÷ç ÷ç ÷è øå

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

reaction plane

A. Drees


Jet Quenching and Angular Anisotropy (II)

Charged hadron v2:v2 {2-particle}

v2 {AuAu – pp}

v2 {4-particle}

v2 remains large at high pT – too large to be explained by geometry of jet quenching?

Origin of v2 at high pT unclear

STAR, Phys.Rev.Lett.93:252301, 2004


Measurement of Charm Production via Electrons

Observable:Excess electrons after subtraction of trivial sources ( conversion, 0 Dalitz decay [0→e+e-], …)

Electrons from decay of charm and bottom quarks dominant source of excess electrons

0( ) ( ) eD cu K su e n- +® + +

D meson reconstruction via K channel requires good secondary vertex reconstruction:

/

0

D : 312 m

D : 123 m

c

c

lab

pL v c c

mc

1 3GeV/c:

dominated by c decay

4GeV/c:

dominated by c and

b decays

T

T

p

p

< <

>


Excess Electrons in p+p at s = 200 GeV

Perturbative QCD calculation (FONLL = Fix-order-next-to-leading-log) in agreement with measurement within systematic uncertainties


Excess Electrons in Au+Au at sNN = 200 GeV (I)

Total charm yield (i.e. pT > 0.3 GeV/c) scales with TAB as expected for charm production in hard processes

High pT > 4 GeV/c charm yields appear to be suppressed in central Au+Au collisionsFONLL calculation scaled by TAB


Excess Electrons in Au+Au at sNN = 200 GeV (II)

Models based on radiative parton energy loss predict

Thus, electrons from charm and bottom quarks should be less suppressed than pions

Experimental observation:Electrons from charm (and bottom) decays as strongly suppressed as pions

Simultaneous measurement of electron flow further constrains energy loss modelsPHENIX, Phys.Rev.Lett.98:172301,2007

gluon quark , 0 quark , 0m mE E E= ¹D > D > D


Excess Electrons in Au+Au at sNN = 200 GeV (III)

PHENIX

Parton energy loss calculation

Radiative energy loss not sufficient to describe excess electron RAA

Inclusion of elastic scattering improves the situation only slightly

Radiative energy loss

Radiative energy loss +elastic scattering

60 Hard Scattering and Jets in Heavy-Ion Collisions - 3.5 Two-Particle Correlations

3.5 Two-Particle Azimuthal Correlations


Two-Particle Correlations

Angular correlations around 0 as in p+p

Suppression of angular correlations around 180

Expectation in jet quenching scenario:


10.2 Jet-Quenching Two-Particle Correlations in p+p

Trigger particle: pT > 4 GeV/c

Associated particle: pT > 2 GeV/c

p+p 2 Jets

Triggerteilchen

Triggerteilchen


Two-Particle Correlations in A+A

pp jet+jet STAR

Trigger particle with high pT > pT cut 1

to all other particles with pT > pT cut-2

Au+Au ???

0 /2 0

yiel

d/t

rig

ger

p+p

yiel

d/t

rig

ger

0 /2 0

Au+Au

random backgroundelliptic flow

0 /2

0

yiel

d/t

rig

ger

Au-Au

statistical background subtraction

suppression?

Jet correlations in Au-Au viastatistical background subtraction


Two-Particle Correlations in Au+Au at sNN = 200 GeV

No jet correlation around 180 in central Au+Au

Consistent with jet quenching picture

Au+Au peripheral Au+Au central

background and ellip. flow subtracted

PRL 90, 082302 (2003) Trigger particle: pT > 4 GeV/cAssociated particle: pT > 2 GeV/c


Dependence of the Away-side Peak on Angle w.r.t. The Reaction Plane

Stronger suppression at = 180° if jet axis is perpendicularto reaction plane, in line with jet quenching scenario.

STARSTAR PRL 93, 25230120-60% central

In-plane

Out-of-plane


Two-Particle Correlations: Towards higher pT

Trigger particle: pT > 8 GeV/c

Associated particle: pT > 6 GeV/c

trigger particle

For higher jet energies the correlation at = 180° in central Au+Au is not fully suppressed anymore


What happens to the jet energy ?

Jet suppression at high pT accompanied by multiplicity enhancement at lower pT

High pT

Low pT


pT Distributions of Associated Particles

Associated charged hadron pT distribution(4 < pT,trigger < 6 GeV/c)

pT distribution on away side in central Au+Au similar to inclusive distribution:hint of thermalization of hadrons on away side


A so-far Unexplained Phenomenon: The Ridge

Components

Near-side jet peak

Near-side ridge

Away-side (and v2)

3 < pt,trigger < 4 GeV

pt,assoc. > 2 GeV

Au+Au 0-10%

preliminary

hadron-hadron

“ridge” = broad correlation in on the near side


Near Side Yields per Trigger Particle

After subtraction of the “ridge”: jet-yield per trigger independent of centrality

Jet + rid

ge

Ridge subtraced


What’s going on on the Away Side? (I)

Trigger > 2.5 GeVpartner > 1 GeV


What’s going on on the Away Side? (II)

D D

PHENIX preliminary

Possible explanations of the splitting of the away-side peak include Mach cones flow induced jet deflection and many more ….

Mach cone?


Three-Particle Correlations (Principle)

Example: PHENIX


Three-Particle Correlations: PHENIX Result Consistent with Mach Cone Scenario

75 Hard Scattering and Jets in Heavy-Ion Collisions - 3.6 Jets in Pb+Pb Collisions at the LHC

3.6 Jets in Pb+Pb Collisions at the LHC


Single Particle Cross Section at the LHC

p+p


Annual Jet Yield in ALICE Acceptance

1 ALICE year = 1 month of runningluminosity L = 51026 cm-2 s-1

Pythia simulation (Pb+Pb, no jet quenching)

Rate of jets with ET > 100 GeV is greater than 1 Hz


Jets in Pb+Pb at the LHC

Jets with ET > ~ 50 GeV in Pb+Pb at s = 5500 GeV at the LHC can be identified above the background on an event-by-event basis

ALICE simulation

Cone size for jet reconstruction

bac

kgro

un

d

Influence of background from the underlying event minimized withcone size R ~ 0.3 – 0.4


A Prediction for RAA in Pb+Pb at the LHC

PD Dr. Klaus Reygers Institut für Kernphysik Universität Münster

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