a nlo analysis on fragility of dihadron tomography in high energy aa collisions

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

Documents

total energy loss

dihadron yield

single hadron production

single hadron yield

invariant massno jet

fragility of single

dihadron production7

lhcjet quenching