enke wang (institute of particle physics, huazhong normal university) i.jet quenching...

Enke Wang (Institute of Particle Physics, Huazhong Normal University)

I. Jet Quenching

II. Modification of Hadron Fragmentation Function

III. Jet Tomography of Strong Interaction Matter

IV. An explanation of heavy quark energy loss puzzle

V. Summary and Discussion

Jet Quenching and Its effects in Strong Interaction Matter

I. Jet QuenchingRutherford experiment atom discovery of nucleus

SLAC DIS experiment e proton discovery of quarks

A-A collisions: Naturally provides jet and the QGP

Jet (hard probe) created by parton scattering before QGP is formed

– high transverse momentum

– calculable in pQCD

penetrating beam (jet) absorption or scattering pattern

QGP

Hard Probes of Quark Matter:

27 YEARS AGO

Brief History of Theoretical Research about Jet Quenching

1982: J. D. Bjoken: Fermilab-pub-82/59-THY Energy loss in elastic scattering

1992/1995: X.-N. Wang, M. Gyulassy: PRL68(92) 148, PRD45 (92)844, NPB420(94)583, PRD51(95)3436 Energy loss is dominated by gluon radiation

1995/1997: BDMPS (R. Baier, Yu. L. Dokshitzer, A. Mueller, S. Peigue, D.Schiff) :PLB345(95) 277, NPB478(96)577,NPB483(97)291,NPB484(97)265 Gluon multiple scattering and gluon radiation

2000: GLV(M. Gyulassy, P. Levai, I. Vitev): PRL85(00)5535, NPB594(01)371

U. Wiedemann: NPB588(2000)303 Opacity expansion

2001/2002: E. Wang, X.-N. Wang: PRL87(01)142301, PRL89(02)162301 Detailed Balance; Jet Tomography

Basic Idea for Jet Quenching

hadrons

q

q

hadrons

leadingparticle

leading particle

hadrons

q

q

hadrons

Leading particle suppressed

leading particle suppressed

p-p collision A-A collision

At RHIC: • Hard/Semihard processes is important• High- Pt parton (jet)• Jet quenching• Jet production dominates particle yields

at high Pt

Suppression of high Pt hadron spectra

Jet quenching and Observation

hadrons

q

q

hadrons

Leading particle suppressed

leading particle suppressed

A-A collision

Jet Quenching:

EEE '

E

Modification of Fragmentation Function:

),( 20 QzD hhq

hh zzz ')1(

),(),(),(~ 2202 QzDQzDQzD hhhqhhq

hqABT

AA

Dtd

dPDFsT

dydp

d ~

ˆ2

Particle Production:

hp

S~

'pp

)'

',(

p

pz

p

pz h

hh

h

Jet Quenching in QCD-based Model

G-W (M. Gyulassy, X. –N. Wang) Model:

Static Color-Screened Yukawa Potential

First Order in opacity Correction

First Order in opacity Correction

Medium-induced radiation intensity distribution:

Induced radiative energy loss:

Induced gluon number distribution:

)cos(1)2)(( 111122

22

)1(

zBCqvqdLC

kdxd

dNx

g

sR

Non-Abelian LPM Effect

2)1( LE LE )1(

QCD:

QED:

Higher order in Opacity

Reaction Operator Approach: (GLV)

Induced gluon number distribution:Non-Abelian LPM Effect

Radiated Energy Loss vs. Opacity

First order in opacity correction is dominant!

Jet Quenching with Detailed Balance

x0 p

Gluon radiation: E loss radEGluon absorption E absorption absE

Net energy loss of jet:

absrad EEE －)1(

Detailed Balance

Temperature and Density QGP SystemE. Wang, X.-N. Wang, Phys. Rev. Lett. 87 (2001) 142301

Final-state Radiation

k

x0 p

k

x0 p

Energy loss induced by thermal medium:

0

)0()0(

)0(

T

abs d

dp

d

dpdE

22

2 )2('62

4ln

3

E

FsET

E

TC=

Net contribution: Energy gain

Stimulated emission increase E loss Thermal absorption decrease E loss

Energy Loss in First Order of Opacity

Energy loss induced by rescattering in thermal medium: )1()1()1(

absradEEE

Take limit:

1EL E LT 2

Zero Temperature Part:

0

)0(

)1(

T

rad d

dpdE

048.0

2ln

4 2

2

L

EC

g

Fs

L2

GLV ResultTemperature-dependent Part:

0

)1()1(

)1(

T

abs d

dp

d

dpdE

2

22 )2('61ln

3

E

g

Fs

T

L

E

LTC

Energy gain

Numerical Result for Energy Loss

3.0S

)1()1()0(

radabsabsEEEE

• Intemediate large E, absorption is important

•Energy dependence becomes strong

•Very high energy E, net energy gain can be neglected

Parameterization of Jet Quenching with Detailed Balance Effect

)/5.7/()6.1/( 02.1

001

EEdL

dE

d

Average parton energy loss in medium at formation time:

Energy loss parameter proportional to the initial gluon density 2

00

1

ARd

dN

Modified Fragmentation Function (FF)

),(

)],(/),()[1(),,(

2'0/

/

2'0/

'2'0

/

'/2

/

cchL

gghc

gcch

c

cLccch

zDe

zDz

zLzD

z

zeEzD

(X. -N. Wang , PRC70(2004)031901)

,//),/( ''cTgcTcTc EpLzEppz

Light Quark Energy Loss

PHENIX,

Nucl. Phys. A757 (2005) 184

Theoretical results from the light quark energy loss is consistent with the experimental data

II. Modification of Hadron Fragmentation Function

e-

, )) (( ,( )qh

q h hHdW

d f x p q Dxd

zz

x

pypedy

xf yixpBq )()0(

2

1

2)(

/( ) 0 (0) , , ( ) 02 2 2

h hip y zhq h h q h h q

S

z dyD z e Tr p S p S y

Frag. Func.

22 )(2)(2

1),,( xpqxpqpTreqpxH q

e-A DIS

Modified Fragmentation Function

2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q

Cold nuclear matter or hot QGP medium lead to the modification of fragmentation function

Twist-four calculationX.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591

e-

Modified Frag. Function in Cold Nuclear Matter

2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q 2 12

24

0

( , ) ( , )2

h

Q

S hq h h L q h

z

zd dzD z Q z x D

z z

2 ( , ) 21( , ) (virtual)

(1 ) ( )

Aqg L A S

L Aq c

T x x Czz x

z f x N

Modified splitting functions

_2 1(

1 2 1 2

2)

1

( , ) (0) ( ) ( ) ( )2 2

( ) ( )1 1

B

L Lix p y ix

ix p yA

y

g

y

q L

pe

dyT x x dy dy e A F y F y y A

y y ye

Two-parton correlation:

LPM

Modified Frag. Function in Cold Nuclear Matter

hadrons

ph

parton

E

),,()(0 EzDzD ahah

)(0 zDah

are measured, and its QCD evolutiontested in e+e-, ep and pp collisions

Suppression of leading particles

Fragmentation function without medium effect:

Fragmentation function with medium effect:

),1

(1

1),( 0

z

zD

zEzD ahah

Heavy Quark Energy Loss in Nuclear MediumB. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301; NPA757 (2005) 493

Mass effects:

1) Formation time of gluon radiation time become shorter

222 )1(

)1(2

Mzl

qzz

T

f

LPM effect is significantly reduced for heavy quark

2) Induced gluon spectra from heavy quark is suppressed by

“dead cone” effect

4

2

2

04

222

2

/]1[][

Mzl

lf

T

T

qQ

zq

l

q

M

T

0

Dead cone Suppresses gluon radiation amplitude at 0

Heavy Quark Energy Loss in Nuclear Medium

)]},,(),,()[1(),,(2

1{

~)~~(~

)1(

1~

),(

22

2

22

1

/~22

3

4

2~

~

1

0

2

2

2

2

22

MlzcMlzceMlzc

x

xxxd

zz

zdz

xQN

xCCQxz

TT

xx

T

L

ML

x

xL

Ac

BsA

B

Q

g

AL

M

LPM Effect

,~~

2

2

Qx

Mx

x

x

A

B

A

L

AN

A Rmx

1

1) Larg or small :

Bx

2Q

A

A

B

c

SAQ

gR

Qx

x

N

CCz

2

2~~

2) Larg or small :2Q

2

22

2~~

A

A

B

c

SAQ

gR

Qx

x

N

CCz

Bx

Heavy Quark Energy Loss in Nuclear Medium

The dependence of the ratio between charm quark and light quark energy loss in a large nucleus

2Q

The dependence of the ratio between charm quark and light quark energy loss in a large nucleus

Bx

III. Jet Tomography of Strong Interaction Matter

E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301

2 21 1 22 2

22 2 2 2

0 0 0 0

1 (1 )( ,

()

, )

( )2

Q Qs A sT

g L T

Aqg

T cT T T

L

Aq

Cd zz dz z z x d dz

Nk

T x x

f x

Jet Tomography in Cold Nuclear Matter:Quark energy loss = energy carried by radiated gluon

2 2 13ln

2A

s N Ac B

CE C m R

N x

Energy loss

3/2AE

Comparison with HERMES Data

HERMES Data: Eur. Phys. J. C20 (2001) 479

22 0060.0)(~

GeVQC 33.0)( 2 Qs22 3GeVQ , ,

Expanding Hot Quark Gluon Medium

_2 1(

1 2 1 2

2)

1

( , ) (0) ( ) ( ) ( )2 2

( ) ( )1 1

B

L Lix p y ix

ix p yA

y

g

y

q L

pe

dyT x x dy dy e A F y F y y A

y y ye

2( , )~ ( ) 1 cos

( )

Aqg L

gAq f

T x x ydy y

f x

0

32

( )2

lnR

s dE

E

R. Baier et al

Initial Parton Density and Energy Loss

jet1

jet2

0

32

2( ) ln

R

s

EE d

00( ) ( )R r

01 0

2d

A

E ER

Initial energy loss in a static medium with density 0

:0E

0 0.1 fm 015

2AR

1

0.5 GeV/fmd

dE

dx

6.140

dx

dEGeV/fm

Initial parton density (Energy loss ) is 15~30 times that in cold Au nuclei !

Comparison with STAR data

STAR, Phys. Rev. Lett. 91 (2003) 172302

Tomography of Jet quenching in QGP Medium in NLO

1) Single jet Single hadron spectra

2) Dijet Hadron-triggered away-side hadron spectra

3) Gamma-jet Photon-triggered away-side hadron spectra

Single jet Dijet Gamma-jet

fmy 0

y

x

Single hadron

parton jet

emission surface

completely suppressed

Surface Emission of Single Hadron Production

fmGeV /68.10

coronathickness

H. Zhang, J. F. Owens, E. Wang and X.-N. Wang , Phys. Rev. Lett. 98 (2007) 212301

partonic di-jet

tangential

fmx 0

y

x

triggered hadron

associated hadron

Color strength = dihadron yield from partons in the square

fmGeV /68.10

punch-through jets25% left

Surface Emission + Punch-through jet in Dihadron Production

punch-jets

Surface emission bias

fmGeVFixed /0.50

dihadron

single hadron

At LHC

Prediction at LHC

Gamma-jet by NLO pQCD parton model

LO (tree level): NLO corrections: (e.g. 23)

FFsdPDFsTd ABAA

T

JetT pp

Tp

TJetT

TJetT

pp

pp

,

1JetTp

2JetTp

),( 21 JetT

JetT

JetT ppofOnep

hadrons with transverse momentum may be larger than that of the photon

T

JetT pp

Tp

JetTp

Fix triger: Tp

T

hT

T p

pz

Gamma-Hadron Suppressions Factor

1) NLO radiative corrections lead to hadrons with z_T>1, surface emission,

2) z_T<0.6, volume emission, more sensitive to \eps_0

3) 0.6<z_T<1.4, competition of two mechanisms of hadron emssions.

4) Similarity in value between I_AA for dihadron and Gam-hadron.

)(/)()( TppTAATAA zDzDzI

H.Z. Zhang, J.F. Owens, E. Wang and X.-N. Wang , PRL 103 (2009) 032302

Tomography of surface and volume emissions

1) The spatial transverse distribution of the initial Gama-jet production vertexes that contribute to the Gama-hadron pairs with given values of z_T.

2) The color strength : Gama-hadron yield

3) Projections of the contour plots onto y-axes .

9.0Tz

3.0Tz

At large z_T, jet emissions in the outer corona, no energy loss.At small z_T, jets emisions near the center of the medium, energy loss.

QGP system is not static, it is a expanding system

Reactionplane

Y

XFlow

Flo

w

QED:

Static Charge: Coulomb electric field

Moving Charge: electric and magnetic field

QCD:

Static Target: static color-electric field

Moving Target: color-electric and color-magnetic field

IV. An explanation of heavy quark energy loss puzzle

Puzzle for Heavy Quark Energy Loss

k

E

M

dP

k

dkkdCdP Fs

,

)/1()(

0

2220

022

022

22

B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301 Y. Dokshitzer & D. Kharzeev PLB 519(2001)199

Heavy quark has less dE/dx due to suppression of small angle gluon radiation

“Dead Cone” effect

J. Adams et. al, PRL 91(2003)072304M. Djordjevic, et. al.

PRL 94(2005)112301

STARSTAR

No Significant Difference BetweenHeavy Quark Jet and Light Quark Jet

Non-photonic electrons from heavy quark decays

Charged hadrons fromLight quark fragmentation

Interaction Potential with Flow

system fixed at target parton:

Static potential

'

system for observer:

Lorentz boost from system

'

vqvqvv

qq

qvqq

nnnn

nnn

02

00

)(1

'

)('

vVvAvv

AA

AvVV

nnnn

nnn

')'(1

'

)''(

2

21

1

v

)()()'()'(2' 0 nTRTqvqVnn aannn

0' nA

22'

4)'(

n

sn q

qv

New Model Potential with Flow

)()()(~)(2),(

)()()(~)(2),(

0

0

nTRTveqvqvqxqA

nTRTeqvqvqxqV

nn

nn

nn

nn

aaxqi

nnnnnn

aaxqi

nnnnnn

222 )(

4)(~

nn

sn qvq

qv

The features of the new potential:

1) Collective flow produces a color-magnetic field

2) non-zero energy transfor:

Four-vector potential : )),(),,(( nnnnnnflow xqAxqVA

vxqA nnn

),(

nn qvq0

Dead Cone Reduce Significantly with Flow

Dead Cone:

Reason: Collective flow changes the poles of the propagator

Energy Loss vs. Flow Velocity

Average Flow Velocity and Effective Average Energy Loss

3D ideal Hydrodynamic simulation for 0-10% central events of Au-Au collisions at RHIC energy:

Average Flow Velocity:

Effective Average Energy Loss:

Numerical Results of Effective Average Energy Loss

3D ideal Hydrodynamic simulation for 0-10% central events of Au-Au collisions at RHIC energy

V. Summary and Discussion

1) Jet can be used as a hard probe to explore the QGP.

2) Jet quenching lead to modification of hadron fragmentation function, which result in the suppression of high transverse momentum spectra observed in experiment.

3) Different tomography picture of the QGP for single jet, dijet and gamma-jet: surface vs. volume emission.

4) New potential for the interaction of a hard jet with the parton target has been derived. Collective flow reduce significantly the dead cone from mass effect for heavy quark jet. Heavy quark energy loss increase obviously in the presence of collective flow. An explanation of heavy quark loss puzzle is given in the framework of jet quenching theory.

Discussion

1) Dihadron azimuthal correlations in head-on collisions in AMPT :

Talk this afternoon by Qingjun Liu

2) Multiple parton scattering and modified fragmentation function in medium : Talk this afternoon by Weitian Deng

3) Gamma-jet tomography of high-energy nuclear collisions in NLO pQCD :

Talk this afternoon by Hangzhong Zhang

Thank YouThank You