A NLO Analysis on Fragility of Dihadron Tomography in High Energy AA Collisions I.Introduction...

A NLO Analysis on Fragility of Dihadron Tomography in High Energy AA Collisions

I. IntroductionII. Numerical analysis on single

hadron and dihadron productionIII. Conclusions

Han-Zhong ZhangInstitute of Particle Physics, Huazhong Normal University, China

Co-authors: J. Owens E. Wang X.-N. Wang

Quark Matter 2006 Nov. 18 , 2006

I. Introduction

Hard Probe Signal of QGP in RHIC and LHC

Jet quenching:

Induced by multiple scattering in QGP medium, a parton

jet will radiate gluon and lose its energy.

Han-Zhong Zhang IOPPQM 2006 Shanghai 2

hadrons

q

q

hadrons

leadingparticle

leading particle

N-N collision

hadrons

q

q

hadrons

Leading particle suppressed

leading particle suppressed

A-A collision

3

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

2

1|)(|)(

2

1

2/

2/

2/

22

)(

cdabEQzDbrQxfrQxf

sxxbrtrtdzdxrdxbdddK

d

d

ccchbAbaAa

baBAcba

eabcd

hAA

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

Han-Zhong Zhang IOPPQM 2006 Shanghai

4

Jet quenching in 2→3 processes

Motivation : 1) contribution for higher order correction?

2) find a robust probe of dense matter

2→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


Jet Quenching effects lead to the modification of FF

Modified Fragmentation Function (FF)

),(

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

2'0/

/

2'0/

'2'0

/

'/2

/

cchL

gghc

gcch

c

cLccch

zDe

zDz

zLzD

z

zeEzD

0000

/1),,,(0

0

nrb

dLg

L

5

KKP

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

,//),/( ''cTgcTcTc EpLzEppz

and the averaged scattering number,

where

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


),,(0

000

0

1

nrbd

dL

dEE g

L

d

)/5.7/()6.1/( 02.1

001

EEdL

dE

d

In 1-demension expanding medium, the total energy loss:

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

6

An energy loss parameter proportional to the initial gluon density


II. Numerical analysis on single hadron and dihadron production

7

1) fix scales and energy loss parameter

2) the centrality dependent of the

suppression factor

3) hadron contour plot

4) fragility of single and dihadron tomography


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

The invariant p_T spectra of single hadron

Th p2.1

8Han-Zhong Zhang IOPPQM 2006 Shanghai

0-10% AuAu data at 200GeV are used to fix the energy

loss parameter (proportional to the initial gluon density):

fmGevGeVAuAu /68.1)200(0


)( partAA NR

10

Centrality Dependence


fmy 0

11

y

xSingle hadron

Color strength = single hadron yield from partons in the square

parton jet

emission surface

completely suppressed

Single hadron is dominated by surface emission

fmGev /68.10

coronathickness


12

1.68

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

loses its effectiveness as a good probe of dense matter


Fit dAu data by pp result to fix scales,

Mhh 2.1

Invariant mass2

212 )( ppM

TtrigTassoTT

hhAA

trigAA

TAA ppzdz

dN

NzD /,

1)( No jet quenching in d+Au,

)()( TppTdAu zDzD

13

of dihadron in Au+Au collisions)( TAA zD

0.3

ppD


14

If no jet quen-ching,

.

)(

const

ND partyieldAA


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

15

PRL95(2005)152301

0.3


partonic di-jet

N

Stangential

fmx 0

16

y

xtriggered hadron

associated hadron

Color strength = dihadron yield from partons in the square

Dihadron is from surface emission + punch-through jets

fmGev /68.10

punch-through jets25% left


LOAA

NLOAA

LOAA

NLOAA IIRR ,

17

3.0AAI

1.68

is a robust probe of dense matter.AAI at 200GeV

Trigger:8GeVat RHIC


18

is a robust probe of dense matter.AAI at 5.5TeV

LOAA

NLOAA

LOAA

NLOAA IIRR ,

Trigger:20GeVat LHC


LHC

III. Conclusions

19

Because of the additional 2→3 processes, NLO contributions

behave with stronger quenching effect than LO contributions: LOAA

NLOAA RR LO

AANLOAA II

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

The dihadron is more sensitive to the initial gluon densitythan the single hadron . When becomes fragile in higher energy AA, is a robust probe of dense matter.

AAIAAR

AAIAAR

Without inputing K factor by hand, NLO results fit data well.

1)

2)

3)


Thank for your attention!

谢谢！


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

2

1|)(|)(

2

1

2/

2/

2/

22

)(

ecdabEQzDbrQxfrQxf

sxxbrtrtdzdxrdxbddd

d

d

ccchbAbaAa

baBAcba

eabcd

hAA

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

2

1|)(|)(

2

1

2/

2/

2/

2/

22

)(

ecdabEQzDEQzDbrQxfrQxf

sxxbrtrtdzdzdxrdxbddd

d

d

dddhccchbAbaAa

baBAdcba

eabcd

hhAA

is the differential 2-body or 3-body phase space elementd

The inclusive cross sections for single hadron production:

The inclusive cross sections for dihadron production:

32~))(( ssecdab is the squared matrix elements


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


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

/)(

/)(


(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)


Nuclear shadowing

effects only

in small pT region

So in large pT,

medium effects

only come from

Jet Quenching !!!


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


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


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

AARAAI

RHIC LHC


is a robust probe of dense matter.AAI at 5.5TeV

LOAA

NLOAA

LOAA

NLOAA IIRR ,

Trigger:20GeVat LHC


A NLO Analysis on Fragility of Dihadron Tomography in High Energy AA Collisions I.Introduction...

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Transcript of A NLO Analysis on Fragility of Dihadron Tomography in High Energy AA Collisions I.Introduction...