December 10, 2003 Ivan Vitev 1 Jet Tomography Jet Tomography Ivan Vitev Iowa State University Iowa...

December 10, 2003 Ivan Vitev 1

Jet Jet TomographyTomography

Ivan VitevIvan Vitev Iowa State UniversityIowa State University


Outline of the TalkOutline of the Talk

Conclusions: Properties of cold and hot nuclear matter Evidence for the creation of the QGP at RHIC

Applications of Jet Tomography

Suppression of hadrons in semi-inclusive DIS Jet quenching in hot nuclear matter, transverse momentum, centrality and rapidity dependence Correlations and di-hadron tomography

Principles of Jet Tomography

Medium-induced gluon bremsstrahlung in QCD Implementations of jet energy loss

Ivan Vitev,Ivan Vitev, ISUISU

Future Experimental Directions

Entropy growth, reappearance of the lost energy Jet cone and intra-jet correlation studies


Principles of Jet Principles of Jet TomographyTomography


The QCD analogue of positron emission tomography

0 0

' / ( ') ' ( ')

0 0

( ')

( )

r r

abs absdr r dr r r

I r I e I e

Radionuclides: 11C, 13N, 15O, 18F

• Calibrated source

• Calculable absorption cross sections

• Interpretation of the results

e+

e+

Prerequisites:e+


• Inclusive hadron distributions – calculable in perturbative QCD


32 *

/

2

/

2

/( , ) ( , ) ( , )a ba A b B

ab cd

h ch cD z

ddt

df x Q f x Q

d pQE

ss ®

ÄÄµ Ä

Leading order pQCD phenomenology Next-to-Leading order pQCD

5 10pT [GeV]

Parton distribution functionsFragmentation functionsPerturbative cross sections

Calibrated ProbesCalibrated Probes

PHENIX Collab., Phys.Rev.Lett. 91 (2003)

I.V., hep-ph/0212109 [in CERN Yellow report]

December 10, 2003 Ivan Vitev 5 Ivan Vitev,Ivan Vitev, ISUISU

M.Gyulassy et al., Nucl.Phys.B594(2001); Phys.Rev.Lett.85 (2000)

(1) R s

3(1)

2

2g

g

2R s

2CE Log ... ,

4

Static medium

9 C 1E Log ... ,

4 A

(L)

dNdy (L

1+1D

)

L 2E

Bjo

L

2EL

L

rken

nz

,n nq a

,n nq a

nznz

,n nq a

,n nq a

nz

,n nq a

,n nq a ++ˆ = R

Exact algebraic recursion(Reaction operator approach)

Effective 2D Schroedinger equation

Path integral formulation

R.Baier et al., Nucl.Phys.B483 (1997); ibid. 484 (1997)

B.Zakharov, JETP Lett. 63 (1996)U.Wiedemann, Nucl.Phys.B588 (2000)

Radiative QCD Energy Radiative QCD Energy Loss Loss

• Elastic energy loss• Radiative energy loss

2 2 /2

46 1 ln jetelastic T

s

E TE T e

TL

J.D.Bjorken, SLAC preprint (1982) unpublished

versus


Gluon Absorption and Mass Gluon Absorption and Mass EffectsEffects


Detailed balance significantly reduces energy loss for at RHIC 2 3jetE GeV

0.5gT GeV

E.Wang, X.-N.Wang, Phys.Rev.Lett. 87 (2001)

(1) 2

2

2

(1) 2

2

2

2

2ln 0.048

4

6 '(2)ln 1

3

rad

ab

g

g

s F

s s FE

L

E

L

E

E C E

E L

E C L

E T

T

M.Djordjevic, M.Gyulassy, nucl-th/0310076

Mass corrections and Ter-Mikayelian plasmon effect in QCD

Reduction of E-loss

11

(1 ) (1 )

2

2 22

2 2

22

2

,g

n ngm x M

m

xE

k k k

x Mx

p Ek k

Heavy quarks


Modified Jet Cross SectionsModified Jet Cross Sections

Ivan Vitev,Ivan Vitev, ISUISUR.Baier et al., JHEP0109 , (2001)

Quenching factor Q(pT) same as

Leading parton RAA(pT)

g* grad

q

0

partond

hadrond• Modified fragmentation functions

• Reduced partonic cross sections

Typical LHC

2 2

2

21,

( ) 2 2

2( ) exp

ˆ

2

vac

TT

T

n

T

cR s

gc

d L L

pdp

Q p Cp

n

q

2 20.045 / , 1 /ˆ ˆcold hotGeV fm GeV mq fq

2

2

( ) /

/

AAT

AA ppbin T

d b dyd pR

N d dyd p


Effective Suppression Effective Suppression of Fragmentation of Fragmentation

Functions Functions


C.Salgado, U.Wiedemann, Phys.Rev.Lett. 89 (2002)

Kniehl, Kramer, Potter fragmentation functions

z=ph/pc1

2 2/ /

0

1( , ) ,

1 1( )med vac

h q h qz

D z Q d D QP

0 1

1

( )1

!

( )

ni

in i

dN ndid

i jet

dNd

n dP

eE

• Independent Poisson approximation for multiple gluon emission

Probability for fractional energy loss / jetE E

Normalized for suppressed leading hadrons (no feedback)


DIS TomographyDIS Tomography

2

2 22

22

/ 2 , 1/

( ) 1( ) 6 ln

2

A A

A

A

B N

s B

c B

x Q p q m

C

x R

x

Q xC Q

N Q xz

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

z zE E E

2L

/ 0.5 0.6 /cold

dE dL GeV fm

E’

E

*

0

F.Arleo, Eur.Phys.J. C30 (2003)

'E E - radiative energy loss fractionz

- energy transfer


QGP TomographyQGP Tomography

I.V., M.Gyulassy, Phys.Rev.Lett. 89 (2002)

PHENIX Collab., Phys.Rev.Lett. 91 (2003)STAR Collab., Phys.Rev.Lett. 91 (2003)

Absolute scale

2 2 2 3 4, ,pl T T T


Centrality DependenceCentrality Dependence

Ivan Vitev,Ivan Vitev, ISUISUX.-N.Wang, nucl-th/0305010

G.G.Barnafoldi et al., hep-ph/0311343

Small number of semihard scatterings

1.5( ) 3.5( )scatn peripheral central 2/3

(1 ) ) ( /AA T

part

T

T

T

nTpR p

N

p

p

p

c

E

E

1+1D GLV


Rapidity DependenceRapidity Dependence


1+1D GLV( ) / ( )0AA AAR RR

(a double ratio)

T.Hirano, Y.Nara, Phys.Rev.C68 (2003)

• Energy loss in a 3+1D hydro

A.Adil, M.Gyulassy, I.V., in preparation

0 0( ) ( ) 1/ /partonA dN dy


g*

grad

2Farh

Di-Hadron TomographyDi-Hadron Tomography


q

1trigh

grad

2Nearh

Near

Far

QGP

J.W.Qiu, I.V., Phys.Lett.B570 (2003)

• Di-jet acoplanarity (insufficient)• Away-side quenching

( )1 2

1 23 3

1

4

2

2 2* */ /

2 2

/ /

( , , ) ( ,

( , ) ( , )

, )

/

c Tc d Tdh c h d

h h a ba A

a cb

c

d

b

b B

a d

f x Q f x Q

D z j Q

dE E

d

p p p

D

d pd

j

p

Q

d

z

p

ts

s

d

®

Ä + -

Ä

µ

Ä

-

Ä

Ä


Near- and Far-Side Near- and Far-Side CorrelationsCorrelations

T.Hirano, Y.Nara, Phys.Rev.Lett.91 (2003)

2

1( )

trig

dNC

N d

• Unaltered near-side correlations

• Disappearance of the away-side correlations

K. Filimonov [STAR Collab.], DNP’03 meeting

x

yz

Out-of-plane

In-plane

Trigger

Trigger


The “Remnants of Lost The “Remnants of Lost Jets”Jets”

d+Au

Ivan Vitev,Ivan Vitev, ISUISUI.V., GLV e-loss simulation

1, |

1

( / )

(1 ) / ), | (

( )

( )

(( 1 (

( )

) ) )

T cut

T cut

Tz E n

z E n

n jen

n

t

n jet

cutp

p

E z E

z

E

P

p P

EE

4 GeV < pTtig < 6 GeV

|y|<1

b=0 fm

y=0

b=0 fm

100% recovered

1 1 ( , )( , )

4 4 ( ,

( )

)trig

Tx

g

x x

EN S

T

rr

r

p d pp p

600 MeV

• Reappearance of the lost energy

• Entropy growth • Momentum sum rules

S.Pal, S.Pratt, Phys.Lett.B574 (2003)


Broadening of the Jet ConeBroadening of the Jet Cone


2 2R

C.Salgado, U.Wiedemann, hep-ph/0310079

Jet cone opening angle

• Intra-jet correlations

( )1( )

( )

( )( ) ( )

+ 1 (

1

)

vac

me

t

jetsjets t

t

td

t

v

vt

ac

ac

RR

R

RR R

E

E

R

E

N E

E

E

- fraction of the total energy within a jet subcone

( )R

Very small effect even at the LHC

5% effec 0.3

5 t

3% effect

0 ,

100 , t

t

E Ge

E GeR

V

V


Summary of Dense Nuclear Summary of Dense Nuclear MatterMatter

SPS 2-3.5 0.8

210-240 1.5-2.5 1.4-2 200-350

RHIC 7-10 0.6

380-400 14-20 6-7 800-1200

LHC 17-28 0.2

710-850 190-400 18-23 2000-3500

SPS RHIC LHC

F.Karsch, Nucl.Phys.A698 (2002)


0[ ]fm [ ]T MeV [ ]tot fm3[ / ]GeV fm /gdN dy

36.8 , 175 , 1 /Au c cR fm T MeV GeV fm

*dE GeV

dz fm

DIS quenching 0.5 0.12

Drell-Yan 0.6 0.45

0.14 0.45

Cronin effect 0.4-0.6 0.1-0.14

Th. estimate 0.2 0.05

dE GeV

dz fm

2 2

g

GeV

fm

F.Arleo, hep-ph/0310274 [CERN Yellow Report]

Hot versus cold nuclear matter

Properties of Dense Nuclear Properties of Dense Nuclear MatterMatter


ConclusionsConclusions


Significant theoretical advances in understanding non-Abelian bremsstrahlung: - Regimes far from asymptopia (E,L) relevant at RHIC - Incorporating mass and gluon absorption corrections

Jet tomographic analysis:

- Cold nuclear matter - Suggests energy density at RHIC (static)

Future directions of high-pT studies in dense nuclear matter:

- Correlations and jet structure, redistribution of - Quantitative studies of open charm and direct photons

Results from Jet Tomography correlated with other theoretical approaches are in strong support of the QGP paradigm at RHIC

315 20 /GeV fm / 0.5 /raddE dz GeV fm

radE

/ 15 /raddE dz GeV fm

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December 10, 2003 Ivan Vitev 1 Jet Tomography Jet Tomography Ivan Vitev Iowa State University Iowa...

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