July 28, 2004 1 Jets in Nuclear Collisions Ivan Vitev ISMD 2004, July 26 - August 1, 2004 Sonoma County, California, USA Ivan Vitev, LANL

July 28, 2004 1

Jets in Nuclear Collisions

Ivan Vitev

ISMD 2004, July 26 - August 1, 2004 Sonoma County, California, USA

Ivan Vitev, LANL

July 28, 2004 2

Outline of the Talk

Measurements of jets in nuclear collisions: Determination of the jet properties from the near-side and away-side di-hadron correlations.

Ivan Vitev, LANL

Baseline jet results in the vacuum: Quark and gluon jet widths Quark and gluon jet multiplicities

Modification of jet properties in cold and hot nuclear matter :

Elastic: Transverse momentum diffusion. Broadening of the away-side correlation function. Acoplanarity Inelastic: QCD radiative energy loss. Jet quenching Modification of the jet multiplicities and the back-to-back jet correlations Coherent: Power corrections

Conclusions:

July 28, 2004 3

Clean Jets in DIS and e+, e-

Ivan Vitev, LANL

Jets in DIS(Single clean jet)

C.C. example

Jets in p+p

July 28, 2004 4

Jets in A+A Reactions

Ivan Vitev, LANL

Jets in nuclear collisionsThe complication at the Tevatron (D0)

The complication at the RHIC (STAR)

The complication in heavy ion reactions

Infinite multiplicities to deal with Globally correlated underlying event (v2) So far STAR uses a jet reconstruction algorithm

July 28, 2004 5

Di-hadron Correlations

( )

Ivan Vitev, LANL

21yj j

21yk k

yj yk

Relate the widths and the momentum measures

2

2 21 2 2 2

21 ,

2 1tan 2 1 ,

T assoch h

T assoc T trig

T hadrontrig h h

T a

Ty

Ty Tssoc T part

Nea

F ro

r

yn

a

px x

p p

pz x x z

p p

j

k j

• Vacuum: intrinsic, NLO corrections, soft gluon resummation• Medium: transverse momentm diffusion

Hadron 1yj

21 2

2 2 21 2 1 2 1 2/ 2 ( ) / 22

( ) ( ) ( )1( )

2 2Near Far

h hNear

trig N

Far

Fae

ij

rar

d etdN y y A y y y yC e e

N d

A

Di-hadron correlation function:

) 1(Far p pA 1 2( , ) ( )h hFar Tp A A AA R p If then

Hadron 2

Relative to :

• Fragmentation: not collinear, a jT kick to the hadron

G.Altarelli, R.K.Ellis, G.Martinelli, Phys.Lett. 151B (1985)

July 28, 2004 6

Analytic Multiplicity Results

Ivan Vitev, LANL

~2 p

Qt

20

4( )

log( / )s t t

0

( )2log ,

( )s p

s c

t

t

Double ordering

1

ii

i

kz

k

k

• The probability to emit n gluons:

,

8, 6

3q ga

, 00

log (1/ )( , , )

! !

n nq g

c

n

pn

a zP t t z

n n

01

, 00 0

( , , )( )

, 2 log(1/ )( , , ) 2 ( )

nn

nn

c p

g q gc p

P t t zI

N a zP t t z I

n

ct

0 0

3lim

2g jet

q jet

g g Az

q Fg

N a C

a CN

Relative to naive 9

4g jet

q j

gA

Fg et

N C

CN

Key result

• Average gluon number:

0 0 , 0lim log(1/ )2z g q gN a z

Z0 mass scale

Experimentally 1.54 +/- …

See e.g. Field and Feynman, Dokshitzer et al.

July 28, 2004 7

Angular Distribution

Ivan Vitev, LANL

22 2 2 2

2 2 20

1 1( , ) 2 log exp log ( / )

2 2R s R sT

T TT T

C Cd kQ k k Q

dk k Q

The LDLA

• Definite shortcomings2

0

1

T

d

dk

Tk

• The final kT distribution of the jet. Gives by momentum conservation information for the distribution of gluons

(very broad) 2 0Tk

2 22

00

1( , ) 1T T

T

ddk Q k

dk

2

2 222 2 2 202

00

2 1( , ) 1 1 , lim

22R s

s

QC R s

T T TT R sR s

Cdk dk Q k e Erf Q k Q

dk Ck

C

2

0 0 2

3lim lim

2s s

g jet g jet

q j

TA

Fetq e

Tj t

k C

Ck

Key result

• In the limit of small coupling

Normalization and mean kT2

The OPAL experiment:Within 4% of the jet axis17% of g-energy

30% of q-energy

July 28, 2004 8

pT Diffusion in Nuclei

2 22 211 tanh

2 ivac i nucl

ipair

k y kk

22

,

2S

gI

Tq

k L

2

,2

2

0

3 1ln 1+1D

2

2 o d

2

C l

Hot

q g

T gR s

FS

L

kLC dN

A dy

Before the hard scatterAfter the hard scatter

Ivan Vitev, LANL

Summary

† †n n n n nR ˆ ˆD D ˆ ˆV V

( )20 0

2 .

1

( ) ( ) (1

!)ii pp

nn iel

n

n

n i

qi

f q

li e

p d q e ed

pd q

dN dN e dNn

pc

sc s

^ ^

¥ ¥¶Ñ

= =

-- -

=

= = Äå å Õò PP

/n Lc l= =

idNfdN 3

2 2 2

2 2

1

( ) 1( )

4 4( ) 1

2el

b b bK b

dO b

d qmp p

mxm

s-

æ ö÷ç= » + ÷ç ÷÷ççè ø2

2

222

1) , 2

2(

k

edN k k

xcm

xx

cmcmp

-

= =D

log2/ (1.08 )bx m=

Additional approximation for a Gaussian form

Incoherent local Glauber.Elastic application

iL

nz

,n nq a

nznznz

,n nq a ++

,n nq a

,n nq a

,n nq a

,n nq a

July 28, 2004 9

d+Au and Au+Au

pp: <z><|kTy|>

pp: <|jTy|>

2.5pTtrigg4.0, 1.0pTassoc2.5

J.Rak, hep-ex/0403038

P.Constantin, N.Grau

J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068

From: <z> = 0.75, <|kTy|>pp = 1.05 GeV<|kTy|>pA = 1.25 GeV

<z><|kTy|>AA = 1.25 - 1.45 GeV

p+A

A+A

Feedback?

Ivan Vitev, LANL

• The vacuum broadening is large• Cold nuclear matter – only a small effect • Hot nuclear matter – seems insufficient

July 28, 2004 10

nz

,n nq a

,n nq a

nznz

,n nq a

,n nq a

nz

,n nq a

,n nq a ++ˆ = R

Medium Induced Non-Abelian Energy Loss

• Explicitly the Landau- Pomeranchuk-Migdal destructive interference effect in QCD• Incorporates finite kinematics and small number of scatterings

• Applicable for realistic systems

M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594 (2001); Phys.Rev.Lett.85 (2000)

Inverse formation times

Color current propagators

Iterative solution

1,2,...n

Ivan Vitev, LANL

Interplay of formation times and medium size

/ fz l

Also see R. Baier et al., B. Zakharov, U. Wiedemann, X.N. Wang

July 28, 2004 11I.V., nucl-th/0404052

Radiative Spectra3

2

g chdN dN d

dy d dy

Estimate:

550, 850, 1100gdN

dy

17 GeV 62 GeV 200 GeV

Isospin symmetryParton-hadron duality

B.Back et al., Phys.Rev.Lett. 88 (2002)

Ivan Vitev, LANL

Small and finite

(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

00 0ˆ( , ( ))

tE I dt t t x v t t

The basis for jet tomography – the extraction of thedensity of the medium

- transport coefficient

- effective gluon rapidity density

2 / /gdN dy

July 28, 2004 12

The Basic pQCD Process

Ivan Vitev, LANL

P’xbP’

P

xaP

X

0

0

Pc

Pd

Pc / zc

Pd / zd

1

2

2

1

1

2 21 2 1

11/

1 2/1min

2

222

2

1

( ) (( )

) ( )( ) h c

h d

a sb

abcd aT T b

ab cdN

T T z

h hN

D zdz D z

x x

p p x

d

dydy d p d p SM

z x

ffd j p as®

D -= å ò

11

2

1/1

1 1

12

2

2min min 1

( )(

()

))(

a b

sa ab b

ab

h

cd a bx x

ab c

T

dc

hNN

ddx d

D z

zx x x

x x Sd pM

ydas

ff ®= å ò ò

d

d

pdz {

• Double inclusive hadron production (most of what will be discussed)

• Single inclusive hadron production

1/3

2

NA

Q

J.W.Qiu, I.V., hep-ph/0405068

Extended to include power corrections

X

2 21 1( , ) ( ,

1)1

eff Pz zD Q d D Q

: (1 ), 1

hc c

c

p zp p z

p

One way of implementing radiative energy loss:

J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223 (1983)

July 28, 2004 13

The E-loss Connection

Ivan Vitev, LANL

600 MeV

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

2 GeV

The plasmonfrequency forces radiation in fewersemi-hard gluons

25-40% increase in the multiplicity

Poisson approximation

• Increase in the jet multiplicity

• In the approximations used the medium induced multiplicity scales as

• One can hopefully establish the subsequent rescattering and thermalization of the gluons

9

4g jet

q j

gA

Fg et

N C

CN

Factor of2 in mult.

July 28, 2004 14

Jet Quenching and Jet Tomography

I.V., nucl-th/0404052

SPS relative to D.d’Enterria, nucl-ex/0403055 S.S.Adler, et al., Phys.Rev.Lett.91 (2003)

Ivan Vitev, LANL

2

2

/( )

/

AAT

AA T NNbin T

d dp dR p

N d dp d

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

• Attenuation of the inclusive hadron spectra • Extraction of the soft underlying parton density (bulk matter) • In jet algorithms – a need for hard pT cut

July 28, 2004 15X.N.Wang, nucl-th/0305010

2 2/ /

1 1( ), ( )

(

/

)

1

(1 )

eff eff

eff

pp AA

n nT

AA n

n p n

h h

T Tp

T

T T

T p

dN dN

dyd p dy

Rp

D z D zp pd p

Z p

Z

2/3 1, 1partE N D

Ivan Vitev, LANL

peripheral

central

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

Centrality Dependence of

Jet Quenching

July 28, 2004 16

Modification of the Jet-like Correlations

Ivan Vitev, LANL

• Attenuation (disappearance) of the away-side correlation function

• Dependence relative to the reaction plane

1 2

21 2 1 2

21 2 1 2

/( )

/

AAh h T T

AA T NNbin T T

d dp dp d dR p

N d dp dp d d

1 2

2 22 2

1 22

1 2 / 2 ( ) / 2

( )1( )

( )

2 2N area Fr

F

h

ar

Fa

h

trig

Near

Nea

d

r

r

ijetdN y yC

N d

A y ye

Ae

In triggering on the near side all effects are taken by the away side correlationfunction

1 2 1/ ~ 1.5h h hR R• The attenuation of the double inclusive hadron production is between the two naïve limits ,1 2 1/ ~ 1h h hR R 1 2 1/ ~ 2h h hR R

Jet 1Jet 2

July 28, 2004 17

Conclusions

Jet tomographic and jet quenching studies in heavy ion collisions have rapidly developed as one of the most exciting and successful directions in RHIC and LHC physics

Relate to: Spectra, jets and di-hadron correlations

The propagation of jets through cold and hot and dense nuclear matter results in calculable modifications to the pQCD factorization approach

A multitude of novel observable effects are predicted and observed at RHIC and expected at the LHC:

- Strong suppression of the simple and double inclusive hadron cross sections (4-5 times for single), (5-7 times double) - Broadening and disappearance jet-jet correlations. Dependence on centrality and orientation relative to the reaction plane - Redistribution of the lost energy into the system - Increase of the jet multiplicities by 30% to 100% - Broadening of the jet cone (small)

Ivan Vitev, LANL

July 28, 2004 18

A. Predictive Power of pQCD

• Factorization theorem:

Scale of hadron wave function:

Scale of hard partonic collision:

Factorization: Process-dependent:

Process-independent:

• Predictive power: Universality of

Infrared safety of

• Systematically addresses the deviations: Power corrections

Radiative energy loss

J.Collins, D.Soper, G.Sterman,Nucl.Phys.B223 (1983)

1/ 200fm MeV

1 , 1/ 0.2GeV Q mQ f

/( ) ( ) ( )Hadron Parton hadron PartonQ Q

( ), ( )Hadron PartonQ Q / ( )Parton hadron

/ ( )Parton hadron ( )Parton Q

Ivan Vitev, LANL

(dynamical nuclear shadowing)

(jet quenching)

July 28, 2004 19

Basic pQCD Processes (I)

• DIS:

• Drell-Yan:

Ivan Vitev, LANL

PxP

X…

k

k’

P’

xbP’

X

P

xaP

X

0 †0

2 20

2 2

1 0(0) (0) ( ) ( )2

1( , )

2

1 ( , ) ( )

2

if

f

f sf

x

f

Q Q d e p p

Q

x E EFp

x Q

O

Eikonal line. Disappears in A+ = 0

1 1

min min2

( ) 2

2( (( , , )

) )a b

a ab b

BornDYNN

x x

b

f

addx dx x x

d x p x p

q dqd

qff

s s ¢= å ò ò

( )2

2 22

2(

2

) 4( )

3 af

B

ac

orn

Q qd

dp p

Nqx x

qps a

d ¢= - +

J.Collins, D.Soper, G.Sterman,Nucl.Phys.B223 (1983) All orders

All orders

G.Bodwin, Phys.Rev. D31 (1985)

22 1

2( , ) 2 ( , )x x xF FQ Q

Extended to corrections in e()+A1/3

2

NA

Q


July 28, 2004 20

Basic pQCD Processes (II)

• Hadron production in N+N:

Ivan Vitev, LANL

P’xbP’

X

P

xaP

X

0

0

Pc

Pd

Pc / zc

Pd / zd

1

2

2

1

1

2 21 2 1

11/

1 2/1min

2

222

2

1

( ) (( )

) ( )( ) h c

h d

a sb

abcd aT T b

ab cdN

T T z

h hN

D zdz D z

x x

p p x

d

dydy d p d p SM

z x

ffd j p as®

D -= å ò

11

2

1/1

1 1

12

2

2min min 1

( )(

()

))(

a b

sa ab b

ab

h

cd a bx x

ab c

T

dc

hNN

ddx d

D z

zx x x

x x Sd pM

ydas

ff ®= å ò ò

d

d

pdz {

• Double inclusive hadron production (most of what will be discussed)

• Single inclusive hadron production

Factorization: at leading power

and leading power corrections

2

2lnQ

1/3

2

NA

Q

J.Collins, D.Soper, G.Sterman, Adv.Ser.Dir. 5 (1988) J.W.Qiu, G.Sterman, Nucl.Phys.B353 (1991)

2

1

Q


Extended to in p+A corrections

July 28, 2004 21 Ivan Vitev, LANL

Particle Production

• Fragmentation: natural near-side and away-side correlations

• Relativistic hydrodynamics:Cooper-Frye formula

From an uncorrelated evolved fluid

• Coalescence models:2

M

2

M3 3

,

B3 3

, ,B

( , ) ( , (1 ) )

( , ) ( , ' ) ( ,

( )

( ,

(

(1 ') '

2 )

'(2 )

) )

dN P uE d dx

d P

dN P

w R xP w R x P

w R xP w R x Pu

E d dx dxd p

w x P xR x

x

x

After solving

Folding the quark Wignerfunctions and the meson or baryon wave functions

• Saturation gluon fussion models:Folding two gluon distributions into one gluon (particle)

These mechanisms don’t have natural don’t have natural correlations


The FragmentationSeesaw Analogy

Gell-Mann, Slansky, Yanagida0 T

D

D R

M

M M

1T

D R DM M M M

SM + right handed neutrino with large Majorana mass

R

R

LL

A much simpler analog of the interplay between light and heavy, small and large

1 2

1 2

T Tp p

z z

To lowest order and leading twist

Provides a new way of testing the fragmentation picture, the factorizationapproach and the deviations


LO pQCD Example

Calculated as in: J.W.Qiu, I.V., hep-ph/0405068

• Perturbative unbiased calculation

• Clear anti-correlation between pT assoc and ztrig . (Not the naïve expectation that triggering fully fixes the near side.)

• Novel way of studying the pQCD 2 to 2 hadron production mechanism. Distinguish from the alternatives

July 28, 2004 24

2

2

/( )

/

AAT

AA T NNAA T

d N dp dR p

T d dp d

AA

nucleon-nucleon cross section

B. Motivation: Deviations from Hard Scaling

Rapidity dependence, centrality dependence

Examples: 200, 62 GeV Au+Au;

200 GeV d+Au

Ivan Vitev, LANL

<Nbinary>/inelp+p

• Quenching

• Shadowing

• Acoplanarity

July 28, 2004 25

Acoplanarity

0

K

1 2

2 22 2

1 22

1 2 / 2 ( ) / 2

( )1( )

( )

2 2N area Fr

F

h

ar

Fa

h

trig

Near

Nea

d

r

r

ijetdN y yC

N d

A y ye

Ae

• Consider di-hadron correlations associated with hard (approximately) back-to-back scattering

) 1(Far p pA 1 2( , ) ( )h h

Far Tp A A AA R p If

( )

Ivan Vitev, LANL

21yj j

21yk k

yj

yk

Relate the widths and the momentum measures

2

2 21 2 2 2

21 ,

2 1tan 2 1

Ty T assocNear h h

T assoc T trig

Far trig Ty h h TyT assoc

j px x

p p

z k x x jp

Di-hadron correlation function

Vacuum: intrinsic, NLO corrections, soft gluon resummation

Medium: transverse momentm diffusion

July 28, 2004 26

Experimental Results

(Approximate representation of the theoretical calculation in the Figures)

• Qualitative and somewhat quantitative agreement• Indicates the need for a possibly stronger Cronin effect• Systematic error bars should be taken seriously• Beware of baryon/meson ratios (I wouldn’t attempt to fit baryons below 4-5 GeV)

Similar results: (h+,h-) by PHOBOS and STAR. (BRAHMS?)

July 28, 2004 27

Hard part

Matrix element

DIS Coherence

• Lightcone gauge:

• Breit frame:

0A n A

2 2

, ,2 2

Q Qq xp p p xp q n

xnn

pn

xp

[1,0,0 ], [0,1,0 ]nn

2D lightcone dynamics

2

1)

2( i

ix x

xpi i

p Qix p q

Pole – on-shell, long distance

No pole – contact, short distanceJ.W.Qiu, Phys.Rev. D42 (1990)

First coherent calculation

2em

1 22 2

2

4 12 ( , ) 1 ( , )

2 2lh N xx x x

x x

d myF F

d dQ Q

Q

yy

y Ey

Factorization approach: separate the short sistance computable dynamics from the long distance matrix emenets.

Final state effect

Ivan Vitev, LANL

July 28, 2004 28

Resummed Power Corrections

1/3 ( ) 2 22 ( ) 2

2

2 1/

20

3( 1) ( , ) ( 1)( , ) ,

!

n n LTn LTT

T Tnn

NA A d F x Q x

F x Q x F x Qn Q d Q

A AA

x

2 ) 22

2( 2 4

( , ) ( , ) ( , )A AL TLT

LF x Q x Q F QQ

A F x

Simple analytic formula:

x

U-quark, CTEQ5 LO

20

1

0

12ˆ( ) ( )ˆ(0) ( )

2

n

A i i i Ai

P d F PFp

0O ˆ

iO ˆjO

(pole-separated, long-distance)

2

22

0

2 3 ( ) ˆ ( )8s

i

Qp F p

r

20

1lim ,

2 x xG x Q

QM shift operator

Scale of power corrections (geometric and vertex factors, two gluon correlation function)

Ivan Vitev, LANL

Dynamical generation of a parton’smass in the final state

July 28, 2004 29

Numerical Results

J.W.Qiu and I.V., hep-ph/0309094

Q2 dependence, Longitudinal SF

Generated by the multiple final

state scattering of the struck quark

22

21

( , )( , )

( , )L L

T

F

F

x Qx

QR Q

x

• For we impose .(discussion of corrections will follow)

2 0Q 2 2NQ m

( )nsO

• Compares well to the EKS98 scale-dependent shadowing parameterization.

Ivan Vitev, LANL

July 28, 2004 30

• Equations of motion - nuclear enhanced power corrections and mass corrections commute

2 2

( ) 2 2 21,3

, ,

( , ) 2 | | ( ) | | ( ) ,U D

WB DU D B BUD U

DM

U UM

D

F x Q V x V xx x x xA

2 2

( ) 2 2 21,3

, ,

( , ) 2 | | ( ) | | ( ) ,D U

WB UD U B BDU D

UM

D DM

U

F x Q V x V xx x x xA

+A Reactions and Mass Corrections

Special propagator structure:

2

2

2 ( )

( / 2

( )

)

B

B

B M

M B

xiQ

xiQ x x x

p

x p Q p M

x q

i

p

x

p

0

0

p M p M

p p

2 2 2, 2 2

1 2 32 ( , ) 1 ( , ) ( , )2 2 2

W WN Wcc md y yF

xx F y Fx x x x

xQ Q Qy

d E

y

yd

- Axial and vector part (weak current)

- Similarly for the neutral current

- Helps us understand charm and bottom in heavy ion collisions

2

2M B

Mx x

Q

2

2 1/3

2

( 1)B

Ax x

Q

Ivan Vitev, LANL

July 28, 2004 31

F2(x,Q2) and xF3(x,Q2)QCD Sum Rules

Testable at the Fermilab NuMI facility

J. Morfin, J.Phys.G 29, (2003)

) 1.0( ,seasee as a x x

.. .( 0.5) ,val

valval x x 22 0.09 0.12 GeV J.W.Qiu, I.V., Phys.Lett.B 587 (2004)

Valance quark shadowing and QCD sum rules: examples where dipole models will fail

1 10 203Q2

Ivan Vitev, LANL

1

23

2

0

3

1( , ) 3( , ) (1 )

2 GLN N

GLS Sdx x Q x QS x xFx

F

J.W.Qiu, I.V., Phys.Lett.B 587 (2004)

D.J.Gross and C.H Llewellyn Smith , Nucl.Phys. B 14 (1969)

July 28, 2004 32

p+A Collisions

11

1

1 211

1m2

1

/

1i1 mi

1

21n 0n

( ) 1/

) ()

)(

(a

a sa

abcdb

a ab b b

h c

z

hNN

T x

xx

x x S Ux x x F x

D zd

d z Szy pdz

dd

as f-=

+ òå òò

2( )( ) b

ab cdbb

xF x M

x

f®=Isolate all the xb dependence of the

integrand:

11

2

1

21

1/

1 2/1

2

2 2

1

21 2 min 01 2 1 2

(( )

( )( )

((

))

)ha s

abcd

h c

b ba

b

hNN

T Td

zbh

T T

d

dyx

p p xx x x

D zdz D

Sdyd p dF xz

zpd j p fs

da

-D -

= å òò

Resum the multiple final state scattering of the parton “d” with the remnants of the nucleus

p A

+,-

( )

Starting point: LO pQCD

• Maximum coherent rescattering of the small xb parton in the nucleus• Other interactions: less coherent (elastic) and sppressed at forward rapidity by a large scale 1/u, 1/s

Ivan Vitev, LANL

July 28, 2004 33

Numerical Results


• Similar power corrections modification to single and double inclusive hadron production

- increases with rapidity and centrality

- disappears at high pT in accord with the QCD factorization theorems

Ivan Vitev, LANL

2/

0,

1 3

(

( 1)

) ( )

( )

b b b bN

b b b b db x C

dx x x F x

dx F x Ax xt

July 28, 2004 34

Conclusions (II)

This talk is only an introduction to the morning session – the details will be given by the experts:

Jets and di-hadron correlations:

Experimental:

K. Filimonov, “Di-hadron correlations at high pT” J. Jia, “Jets in PHENIX” C. Mironov, “Charged kaons correlations” J. Rak, “Measurement of jet properties and their modification in heavy ion collisions at RHIC” Y. Guo, “Correlations of high-pT particles produced in Au+Au collisions at 200 GeV” Theoretical:

J. Jalilian-Marian, “Two particle production in proton (deuteron) nucleus collisions” A. Majumder, “High pT hadron-hadron correlations”

Ivan Vitev, LANL

July 28, 2004 35

The Single Inclusive Spectra Revisited

Ivan Vitev, ISU

I. Arsene et al., nucl-ex/0403050

• Data is for qualitative comparison

• The power correctionsmodify the ratio from lowpT to high pT

(not vice versa)

(pions versus baryons)

GCG GCG

~ 0.4 – 0.5

Looks like 0.5!

Power corrections

It makes no sense to try and fit the charded hadrons at low pT and these rapidities

July 28, 2004 36

Hard part

Matrix element

The Technology of Power Corrections

Ivan Vitev, ISU

1

2

(1

2

21

)

ˆ ( )Left of cut

Vertex:

Rig

, 2

2

ht of

1

2 ˆ2,

2

(

cut

4( )

)i i i

i

iii

i

x x

i i

sic

F

x x i

i

x x idx

x x

F

i

N

e

Q i

202

2( ) ( )

lim ( , )2 ( )

1( )

2ˆ ( )

i ii

xii i

p F F pdp p

pF xG x Q

The small-x limit of the leading twist gluon distribution function

Note: it is that givesid 1/3 enhancementA

Only one contributing uniquely defined sequence:

... ... ...

July 28, 2004 37

Lowest Order Contributions to

Ivan Vitev, ISU

2( , )LF x Q

0

0

2

0 022 24 1

( , ) 43 2

(0) ( )2

ˆx

fL

isfQ Qx

pd e pF F

Qp

0

0 00 02

( ) ( )( ) (ˆ )

2 ( )n n

nFd d F F

p

(Twist 4)

Short distance, not A1/3-enhanced

1 12 2 2 2 28

( , ) ( , ) ( , ) 2 12 3 2L f gf f

f fx x

s sd x d x xF x Q Q Q Q Q

Tk

Tk

G.Altarelli and G.Martinelli, Phys.Lett. B76 (1978)

M.Gluck and E.Reya, Nucl.Phys. 145 (1978)

Bremsstrahlung diagram

Box diagram

• Genuinely new higher twist contribution

The old and known Leading Twist contribution

July 28, 2004 38

Color Glass Inspired Calculations

Ivan Vitev, ISU

Kharzeev, Kovchegov, Tuchin, High pT workshop at RHIC

Evolves very quickly

Forward d-A

Y=2,3,4J.Jalilian-Marian, nucl-th/0402080

RdAu = 0.5

RdAu = 0.3-0.5

Violate factorization! R.Baier et al., Phys.Rev.D 68 (2003)

The effect never disappears

RdAu = 0.4

Discuss problems

Motivation: pQCD in Nuclear Collisions

• Universal nuclear dependence:

from nuclear wave functions

• Process-dependent nuclear effects:

● Initial-state:

● Final-state:

• Nuclear PDF’s versus medium-induced nuclear effect

Data from: NMC

K.Eskola,V.Kolhinen and C.Salgado,Eur.Phys.J. C9 (1999)

M.Hirari,S.Kumano and M.Miyama,Phys.Rev. D64 (2001)

Shadowing

(Will be discussed)

Ivan Vitev, LANL

July 28, 2004 40

Power Correction Contributions to LO pQCD

Ivan Vitev, ISU

( ) 2 1/ /33 1

,

22

0

1( ) ( 1 ( 1) ( ) ( )

!)

N NN

b b b b b b bbN

db b x C AC

dx x x x A F x dx x xt

F xN t


The results look like LO pQCD with the substitution:

Cd = 1 for quarks, CA/CF = 9/4 for gluons

c

d

• Driven by the Mandelstam invariant (-t) the resulting suppression will be sensitive to pT and rapidity y.

1. Recall that the two gluon ladder generates the scale of higher twist -

0 11

)

1

(

( )

1(

1

!

1

)i b

m N mN

m i jm b

N

Nb

i m m j

bx

m

x

dx x x x

x x

x xN

d

22. For a fixed number of interactions (2N) we take all possible cuts t

3. Sum over all possible N

I.B.P

New contributions to the cross section

July 28, 2004 41

Observing the Acoplanarity and the

Power Corrections0

K

Ivan Vitev, ISU

1 2

2 22 2

1 22

1 2 / 2 ( ) / 2

( )1( )

( )

2 2N area Fr

F

h

ar

Fa

h

trig

Near

Nea

d

r

r

ijetdN y yC

N d

A y ye

Ae

2 22 211 tanh

2 ivac i nucl

ipair

k y kk

22

,

2S

gI

Tq

k L

2

,2

2

0

3 1ln 1+1D

2

2 o d

2

C l

Hot

q g

T gR s

FS

L

kLC dN

A dy

Before the hard scatterAfter the hard scatter

• Consider di-hadron correlations associated with hard (approximately) back-to-back scattering

) 1(Far p pA 1 2 (( ) )h h

Far TA Rp A p If

July 28, 2004 42

Dijet Acoplanarity in d+Au and Au+Au

Ivan Vitev, ISU

pp: <z><|kTy|>

pp: <|jTy|>

(2.5pTtrigg4.0)(1.0pTassoc2.5)

J.Rak, hep-ex/0403038P.Constantin, N.Grau

21yj j

21yk k

J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068Estimate from:

From: <z> = 0.75, <|kTy|>pp = 1.05 GeV<|kTy|>pA = 1.25 GeV

<z><|kTy|>AA = 1.25 - 1.45 GeV

p+A

A+A

Very interesting!

Feedback?

July 28, 2004 43

Nuclear Effects in Inclusive Deeply

Inelastic Lepton-Nucleus Scattering

Ivan Vitev, ISU

2em

1 22 2

2

4 12 ( , ) 1 ( , )

2 2lh N xx x x

x x

d myF F

d dQ Q

Q

yy

y Ey

21 2

2( , ), ( , )x xF Q QF - the DIS structure functions

Used to determine the parton distribution functions (PDFs)

Convenient to calculate in abasis of polarization stares of

2 2

2

2 21

22 22

1

( , ) ( , ),

( , )( , ) ( , ), f

4x1i

2N

T

L

F x Q F x Q

F x mQF x Q F x Q

Qx

00

2 20

2 2

(0) ( )1

( , )2

1 ( , ) ( )

2

2i

ff

f f

x

sf

T Q Q d e px

x

p

Q

F

Q

p

O

2( , ) 0LF x Q

PxP

X…

k

k’

July 28, 2004 44

The Reaction Operator Approach to Multiple Elastic and Inelastic

Scatterings

Reaction Operator = all possible on-shell cuts through a new Double Born interaction with the propagating system

t = ¥

† †n n n n nR ˆ ˆD D ˆ ˆV V

For the elastic scattering case illustrated here byiteration:

( )0

.2

0

2

1

1( ) ( ) 1 ( )

!ii ppn iel

n n iel

nqqf

ii

n

dN dN dNn

dp d q

de

qp e p

c s

s^^

--¥ ¥

¶Ñ

= = =

= = Ä -å å Õò P P

nz

,n nq a

nznznz

,n nq a ++

,n nq a

,n nq a

,n nq a

,n nq a

/n Lc l= =

32 2 2

2 2

1

( ) 1( )

4 4( ) 1

2el

b b bK b

dO b

d qmp p

mxm

s-

æ ö÷ç= » + ÷ç ÷÷ççè ø2

2

2 22

1( ,

2)

k

d k ke

Ncmx

xp cmx

cm-

= =D

log2/ (1.08 )bx m=Mandelstam s,t,u kT kick that helps

idN fdN

Ivan Vitev, ISU

July 28, 2004 45

Dihadron Correlation Broadening and

Attenuation

Ivan Vitev, ISUJ.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068

Midrapidity and moderate pT

Forward rapidity and small pT• Apparently broader

distribution

• Even at midrapidity a small reduction of the area

• Factor of 2-3 reduction of the area at forward rapidity of 4

J.Adams et al., Phys.Rev.Lett. 91 (2003)

• Only small broadening versus centrality • Looks rather similar at forward rapidity of 2 • The reduction of the area is rather modest

1( ) ~ 1/FarA t zTrigger bias can also affect:

July 28, 2004 46

1 10 203Q2

The Gross-Llewellyn Smith and Adler Sum Rules

1

23

2

0

3

1( , ) 3( , ) (1 )

2 GLN N

GLS Sdx x Q x QS x xFx

F

# # 3GLS U DS • To one loop in 2( )s Q2( ) /sGLS Q

• Nuclear-enhanced power corrections are very important

Ivan Vitev, ISU

D.J.Gross and C.H Llewellyn Smith , Nucl.Phys. B 14 (1969)

1

22

22

0

1( , ) ( , ) 1

2 HTn n

A dx Fxx

S Q xF Q

Compatible with the trend in the current data

S.Adler , Phys.Rev. 143 (1964)• Can set a limit on the 4-point parton correlation function

• Leading twist shadowing does not contribute to GLS

July 28, 2004 47

Modifications to the Structure Functions in

ScatteringA

Ivan Vitev, ISU

2 2 2, 2 2

1 2 32 ( , ) 1 ( , ) ( , )2 2 2

W WN Wcc md y yF

xx F y Fx x x x

xQ Q Qy

d E

y

yd

Similarly for the neutral current

The NuTeV experiment claims:

Based on:( )

,( )

( )

( )

v N X

N l X

N X

N l X

R

R

Beware: Monte Carlo with many effects taken on average

• Asymmetric strange sea and violation of the isospin symmetry

G.P.Zeller et al., Phys.Rev.Lett 88 (2002) G.P.Zeller et al., hep-ex/0203004

• deviation from the Standard Model32sin ( ) 0.2227 0.0004W SM 2sin ( ) 0.2277 0.0013 0.0009 ...W NuTeV

Motivation

Axial and vector part (weak current)

Recall the tensorial decomposition ( .) ( .)g g sym g asym

July 28, 2004 48

STARSTAR

Statistical errors only

What the author

concluded

Are suppressed in d+Au relative to p+p at small <xF> and <pT,>

Spp-SdAu= (9.0 ± 1.5) %

Consistent with CGC picture

Are consistent in d+Au and p+p at larger <xF>

and <pT,>

As expected by

HIJING

25<E<35GeV

35<E<45GeV

Ivan Vitev, ISU

Power Corrections at Forward Rapidity

Preliminary:L.Bland, [STAR Colaboration]

X2 = 1.94 x10-4

X2 = 2.51 x10-4

• There may be room for some suppression due to power corrections

• At x2 = 2 x 10-4 and pT = 1.25 GeV hard

scattering issimilar in p+p and p+A

• There isn’t mono jettiness or g-fusion

• I think that the p+A analysis has under and

over estimated theaway-side area CGC logic

July 28, 2004 49 Ivan Vitev, ISU

Analytic Limits For Energy Loss

0

0

1

0

( , ) ( , ) ( , )

( , ) ( ), ( , ) ( , ), ...g gN

n

N

nE E d E

E

P P P

P P E E

E

e e

Ee e e e

e e e

e

d r e

¥¥

=

- -

=

= =

D=å ò

(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

2 2 2 3 4, ,pl T T T

0 0

1( ) ( )

parton

A

dN

dy

00 0ˆ( , ( ))

tE I dt t t x v t t

a) Static medium:

b) Bjorken expanding medium:

M.Gyulassy, I.V., X.N.Wang, Phys.Rev.Lett. 86 (2001)

R.Baier et al., JHEP (2001)M.Gyulassy, P.Levai, I.V., Phys.Lett.B538 (2002)

2

g

transport coefficient

Beyond average : need ansatz

• Independent Poisson emissionGuaranteed to be violated

• By simple kinematics

Usefulness• Allows the system to adjust itself • Minimizes the effect of energy loss

E0 400Npart

July 28, 2004 50 Ivan Vitev, ISU

22( ( / 2 )(2 )

)

( )i B M

BB

Mx p Q x p M

x

QC

xut

x x

( ) 2 2 22

,

2

,2 2

( , ) | | ( ) | | ( )U DM

WL B DU D B BUD U

D UM

U

U D

DF x Q V xMM

Qx

Qx xV

( ) 2 2 2

2

,

2

,2 2

( , ) | | ( ) | | ( )D UM

WL B UD U B BDU D

U DM

D

D U

UF x Q V xMM

Qx

Qx xV

2

2BM xxM

Q

On-shell paricle (M)

New Contribution to 2( , )LF x Q

• Even if one neglects mass effects show up due to the mixing of electroweak and mass eigenstates

2 2( , ), ( , )c cx Q x Q

( , , ), ( , , )u c t D dU s b

J.W.Qiu, I.V., Phys.Lett.B 587 (2004)

|V| - the CKM matrix elements

xi

• Along the way we will develop techniques that may be useful in the discussion of charm production at RHIC

(Cuts fix kinematics)

July 28, 2004 51

Discussion of Jet Quenching at Intermediate RHIC

Energies

Ivan Vitev, ISU

• The result, if confirmed, would not be unexpected• Follow from energy loss jet quenching calculations• Naturally interpolate between the SPS and the top RHIC energies

X.N.Wang, Phys.Lett.B579 (2004) RAA=0.5 at pT=4 GeV

A.Dumitru, R.Pisarski, Phys.Lett.B 525 (2002)

Possible most interesting outcome • Strong deviation from the perturbative prediction • Strong nonlinearity of in dNg/dyEIn a Polyakov loop model

• In their power law behavior the 62 GeV spectra are much closer to the 130 GeV and the 200 GeV cross sections than to the 17 GeV ones

2

2

( ) /

( )( )

/

hT

hAA T

AA

dN b dyd p

T b d dR

yd pb

The nuclear modification ratio

• Sensitively depends on the underlying partonic spectrum

July 28, 2004 52

Experimental Results at 62 GeV

(Approximate representation of the theoretical calculation in the Figures)

• Qualitative and somewhat quantitative agreement• Indicates the need for a possibly stronger Cronin effect• Systematic error bars should be taken seriously• Beware of baryon/meson ratios (I wouldn’t attempt to fit baryons below 4-5 GeV)

July 28, 2004 53

Experimental Results (Continued)

STAR preliminary

PHOBOS(submitted)

May have twiceas many baryons as pions!

• Charged behave differently: factor of 50% enhancement in peripheral but suppression develops at high pt, as expected, in central

July 28, 2004 54

Conclusions (I) Dynamical nuclear shadowing from resummed QCD power

corrections. Results consistent with its x-, Q2- and A- dependence. Neutrino-nucleus DIS. Modification of the QCD sum rules.

First calculations of dynamical power corrections for hadronic collisions, . Results for the centrality and rapidity dependent suppression of single inclusive spectra and the dihadron correlations.

The power corrections disappear at high pT. They are small at 62 GeV and would not affect the extraction of RAA

In central Au+Au collisions at C.M. energy of 62 GeV neutral pions were found to be suppressed by a factor of 2-3 by jet quenching. Relatively weak pT dependence of RAA

Interpretation of the rapidity density in 1+1D Bjorken expansion: at the energy density - already significantly above the current critical value.

Charged hadrons, especially baryons, are expected to be less suppressed and are beyond the reach of the current perturbative techniques

Ivan Vitev, ISU

p A

/ 650 800gdN dy 0 0.8 1 fm 3

0 6 8 /GeV fm

July 28, 2004 55

Conclusions (II) In d+Au collisions midrapidity and moderate pT the dominant

effect is small broadening of the correlations.

At very forward rapidity (y=4) and small pT the power corrections give a factor of 2-3 reduction of the area of the away side correlations.

If the preliminary STAR results at forward y correlations persist – there isn’t monojettines or high density gluon fusion effects at x=2x10-4 (following saturation logic) in Au.

Will be interesting to measure neutral pions at forward y and compare the suppression effect (RAA) to the suppression for charged

Given the results of correlation analysis one can go back and rethink their favorite d+Au suppression scenarios

Ivan Vitev, ISU

July 28, 2004 56

Documents

July 28, 2004 1 Jets in Nuclear Collisions Ivan Vitev ISMD 2004, July 26 - August 1, 2004 Sonoma County, California, USA Ivan Vitev, LANL