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Dihadron Tomography of High Energy AA Collisions in NLO pQCD

Hanzhong Zhang

Department of Physics, Shandong UniversityInstitute of Particle Physics, Central China Normal University

Jinan, Jan. 9, 2008

Collaborators: Enke Wang Joseph F. Owens Xin-Nian Wang

1) Phys. Rev. Lett. 98(2007)212301 2) J. Phys. G. 34(2007)S8013) To be submitted.

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Outline

I. Introduction

II. Modified fragmentation function model

III. Numerical analysis on single hadron and dihadron production

IV. Conclusions

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I. Introduction

1. What is “Dihadron tomography” ?

1) Medical x-ray tomography:

see inside a “bone” by x-ray.

2) Jet tomography:

see inside “QGP” by a parton jet,

not only by single jet, but also by dijet.

3) Hadron/Dihadron tomography:

we can’t “catch” a parton jet/dijet,

but can “catch” a hadron/dihadron.

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2. How to know a tomography of QGP ?---- Jet Quenching !

Jet quenching:

Induced by multiple scattering in QGP medium, a parton

jet will radiate gluon and lose its energy.

hadrons

q

q

hadrons

leadingparticle

leading particle

N-N collision

hadrons

q

q

hadrons

Leading particle suppressed

leading particle suppressed

A-A collision

5

),,()(|)|,,(),,(

2

1|)(|)(

2

1

2/

2/

2/

22

)(

ccchbAbaAa

baBAcba

eabcd

hAA

EQzDcdabbrQxfrQxf

sxxbrtrtdzdxrdxbdddK

d

d

Jet quenching in 2→2 processes

LO analysis of jet quenching in AA :

2→2 processes (tree level)

A factor K=1.5-2 was put by hand to account for higher order corrections

3. Why NLO study?

pQCD

Parton

Model

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Jet quenching in 2→3 processes2→3 processes (tree level)

NLO (Next to Leading Order ) corrections:

One-loop corrections

Jeff. Owens , PRD65(2002)034011; B.W. Harris and J. Owens, PRD65(2002)094032.

qg EE 4

9

K is absent

NLO:More stronger quenching;More clearer QGP picture.

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4. Why dihadron tomography study?

• Single hadron suppression factor is found to be

fragile to probe the dense matter. K. J. Eskola , et al, NPA747 (2005) 511-529

• One of the motives of this work:

How about dihadron? fragile or robust?

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Jet Quenching effect in AA is incorporated via a model of modified fragmentation functions:

II. Modified fragmentation functions model

),(

)],(/),()[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 where

Two contributions from jets in vacuum and medium!

Jet energy loss

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),(

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

2'0/

/

2'0/

'2'0

/

'/2

/

cchL

gghc

gcch

c

cLccch

zDe

zDz

zLzD

z

zeEzD

),,,(0

000

nrb

dLg

L

the averaged scattering number,

It determines the thickness of the outer corona where a parton jet survives in the overlapped region.

|)],(|)([2

),,(2

00 rbtrtA

Rrb AA

Ag

the gluon density distribution,

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gg

L

d

Lnrbd

dL

dEE

),,(

0

000

0

1

)/5.7/()6.1/( 02.1

001

EEdL

dE

d

In 1-demension expanding medium, the total energy loss is written as a path integration:

The energy loss per unit lenth with detailed balance:(Enke Wang and Xin-Nian Wang, PRL87(2001)142301)

An energy loss parameter proportional to the initial gluon density 00

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010

0

2ˆ

dCs dL

dE

Nq

In BDMPS calculation for the radiative parton energy loss,

is equivalent to 0q̂0

2 ˆ 4

LqN

E CS Baier, Dokshitzer, Mueller,

Peigne, Schiff, NPB484(1997)265

where is a jet transport or energy loss parameter,q̂

reflects the ability of the medium to “quench” jets.

By Wang2 and BDMPS formulas, estimate the average jet transport parameter by

J. C. Solana and X. -N. Wang,hep-ph/0705.1352

0

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III. Numerical analysis on single hadron and dihadron production

1. Single hadron tomography

2. Dihadron tomography

3. Estimate jet transport parameter

4. Comparison between different shadowing

5. LHC predictions

0q̂

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1. Single hadron tomography

single inclusive or production

0 2/)( hh

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The invariant p_T spectra of single hadron

With ,p_T spectra in AA is not also sensitive to the choice of

Set ,since p_T spectra in pp is not at all sensitive to the choice of

Th p2.1

h

Th p2.1

0

fmGevGeVAuAu /68.1)200(0

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Nuclear modification factordydpdN

dydpdpR

TNN

binary

TAA

TAA 2

2

/

/)(

NLOAAR

is 10% larger than

LOAAR

is not sensitive to the initial gluon density

)( TAA pR 00

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Centrality dependence

dydpddpbT

dydpdbddpNR

TNN

TAA

TAA

T

partAA 22

222

/)(

/)(

AAR is not sensitive to ,and

partN

gpartN ~

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Similar to the study by K. J. Eskola , H. Honkanen, C. A. Salgado, U. A. Wiedemann, NPA747 (2005) 511-529

is a fragile probe of dense matter.AAR

1.68

loses its effectiveness as a good probe of dense matter

Why the single hadron tomographyis fragile to probe the dense matter?

The bigger is,the flatter is.

AAR

0

18

y

xSingle hadron

Color strength = single hadron yield from partons in the square

parton jet

emission surface

completely suppressed

Single hadron is dominated by vertical surface emission

fmGev /68.10

coronathickness

AAR

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Is there a robust probe of the dense matter produced in AA collisions?

Let’s see dihadron production!

Trigger one hadron of a dihadron, check the other hadron --- the associated hadron

2. Dihadron tomography

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Fit dAu data by pp result to fix scales,

Mhh 2.1

Invariant mass

221

2 )( ppM

trigT

assocTT

T

hhAA

trigAA

TAA ppzdz

dN

NzD /,

1)( No jet quenching in d+Au,

)()( TppTdAu zDzD

The dihadron spectra in Au+Au collisions

68.10

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)(/)()( TppTAATAA zDzDzI

The dihadron suppression factor in Au+Au collisions

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If no jet quen-ching,

.

)(

const

ND partyieldAA

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Comparison between single hadron and dihadron tomography in Au+Au collisions

dihad

ron

single

had

ron

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3.0AAI

1.68

Dihadron is a robust probe of dense matter.

The curve is steeper than when AARAAI 0.20.10

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2 comparison between single hadron and dihadron suppression factor

AAR

N

j TjEx

TjThAATj

ExAA

pN

pRpR

12

20

02

)()1(

)],()([)(

for

95.045.0

158

T

trigT

z

GeVp

GeVpT 204 for single

for dihadron

fmGeV /1.25.10

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Why does the dihadron behave more robust than single hadron to probe the dense matter?

Single hadron is dominated by vertical surface emission

dihadron ?

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partonic di-jet

N

Stangential

y

xtriggered hadron

associated hadron

Color strength = dihadron yield from partons in the square

Dihadron is from tangential surface emission + punch-through jets

fmGev /68.10

punch-through jets25% left

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3. Estimate jet transport parameter

0q̂

fmGeVq /2.26.1ˆ 20 2

00 2.26.1ˆ GeVq fm10

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4. Comparison between different shadowing

p+Au@RHIC 200GeV

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Au+Au@RHIC 200GeV

Single hadron and dihadron are all not sensitive to different shadowing at RHIC

dihad

ron

single

had

ron

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Trigger:20GeVat LHC

LHC

5. LHC predictions

0 is estimated as 4.5-5. 5 GeV/fm at LHC

Single hadron fragileDihadron robust

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There are much more punch-through jets in higher energy AAcollisions, increases while decreases with collision energy.

AARAAI

RHIC LHC

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Different shadowing in p+Pb@LHC 5500GeV

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Different shadowing in Pb+Pb@LHC 5500GeV

Single hadron not sensitive to different shadowing.

Dihadron sensitive to different shadowing because of much more punch-through jets.

dihad

ron

single

had

ron

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2) Punch-through jets contributing to hadron spectra at LHC

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Why is only Dihadron Iaa at LHC sensitive to different shadowing parameterizations, HIJ, EKS, nDS, nPDF?

1) Punch-through jets are created from central system region;

2) Initial partons participating in strong interaction in central region should be associated with stronger shadowing effects than those initial partons in the outer layer of the system;

3) So punch-through jets manifest a strong shadowing effect. There are much more punch-through jet contributing to dihadron spectra at LHC than at RHIC. So does dihadron than single hadron.

H. Zhang, J.F. Owens, E. Wang and

X.-N. Wang , hep-ph/0000008

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Because of the stronger quenching effects, the single hadron is dominated by vertical surface emission;the dihadron is from tangential surface emission + punch-through jets.

The dihadron is more sensitive to the initial gluon densitythan the single hadron . When becomes insensitive in higher energy A+A collision, is a sensitive probe of dense matter.

AAI

2

AARAAI

AAR

-fit to both single and dihadron spectra can be achieved with a narrow range of the energy loss parameter

at RHIC energy, it provide convincing evidence for the jet quenching description.

1)

2)

3)

IV. Conclusions

fmGeV /1.25.10

4) Dihadron Iaa at LHC is found to be able to distinguish different shadowing parameterizations.

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Thank for your attention!

谢谢！

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Hard sphere model

|)(|)()( 2 brtrrtdbT BAAB

222

/12

3)( Rr

R

ArtA

R bT

b bT

ABNNin

ABNNin

ebd

ebdcentrality 2

0

)(2

0

)(2

]1[

]1[

r

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nuclear modification factor

dydpdN

dydpdpR

TNN

binary

TAA

TAA 2

2

/

/)(

|)(|)(),(max

min

22maxmin brtrrtbddbbN

b

b AAbinary

)(

2222

/13

)(br

partpart RrrdR

AbNN

dydp

bbd

bbdydp

dN

T

hAA

AAinT

hAA

2maxmin

maxmin2

),(

),(

1

the formula of spectra in AATp

dydpddpbT

dydpdbddpNR

TNN

TAA

TAA

T

partAA

22

222

/)(

/)(

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(Shi-Yuan Li and Xin-Nian Wang , PLB527(2002)85)

(Enke Wang and Xin-Nian Wang, PRL87(2001)142301)

(B. B. Back et al. [PHOBOS collaboration], PRC70(2004)021902)

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Nuclear shadowing

effects only

in small pT region

So in large pT,

medium effects

only come from

Jet Quenching !!!

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p-p data at 200GeV are used to fix scales,

The invariant p_T spectra of single hadron

Th p2.1

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Invariant mass: 221

2 )( ppM

How to fix scales: M

trigTtrighAAtrigTtrig

assotrigTassoTtrighhAATtrigassotrigTtrig

T

hhAA

trigAA

TAA

TtrigTassoT

dydpddydp

ddydydpdpdpddydydp

dz

dN

NzD

ppz

/

/

1)(

,/

If no medium effects, )()()( TppTdAuTAuAu zDzDzD

(X. –N. Wang , PLB 595(2004)165

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The dihadron azimuthal distributions

trigTtrighAAtrigTtrig

assotrigTassoTtrighhAAassotrigTassoTtrig

hhAA

trigAA dydpddydp

ddydydpdpddydydpdp

d

dN

N /

/1

ddydydpdppp

bbd

bbddydydpdppp

dN

TTTT

hhAA

AAinTTTT

hhAA

212121

maxmin

maxmin212121 2

),(

),(

1

2

212

221

maxmin

maxmin212

221

),(

),(

1

dydydpdp

bbd

bbdydydpdp

dN

TT

hhAA

AAinTT

hhAA

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The ratio between the yield/trigger in AA and in pp:

trigpp

hhpp

trigAA

hhAA

trigpp

hhpp

trigAA

hhAA

yieldpp

partyieldAA

partAA

bb

NN

bNbN

D

NDNI

/

)(/)(

/

)(/)()()(

If no jet quen-ching,

1AAI

PRL95(2005)152301

0.3

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50

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53

54

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