May 11, 2004 Ivan Vitev, ISU 1

Resummed QCD Power Corrections and Di-Hadron Correlations

Ivan Vitev

Iowa State University, Ames, IA 50011

AGS-RHIC Annual Users’ Meeting May 10 – May 14, 2004

Brookhaven National Lab, Upton NY

Ivan Vitev, ISU

May 11, 2004 Ivan Vitev, ISU 2 Ivan Vitev, ISU

Motivation: Modification of Di-HadronCorrelations in the Nuclear

Environment

J.Rak, hep-ex/0403038

K.Filimonov, nucl-ex/0403060 J.Adams et al., Phys.Rev.Lett. 91 (2003)

Address the (relatively) small effects in d+Au

• Small broadening (and/or attenuation) is observed in d+Au• Large attenuation is observed in Au+Au (sensitive to the orientation relative to the reaction plane) – clearly a final state effect

May 11, 2004 Ivan Vitev, ISU 3

Calculating Power Corrections in DIS

Ivan Vitev, ISUJ.W.Qiu and I.V., hep-ph/0309094

22

1/3( ) 2

2

( 1)( , ) ,LTA

T T

xF x Q FA Q

Ax

Q

2 ) 2

2

2( 2 4

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

LF x Q x Q F QQ

A F x

22

20

2 3 ( ) ˆ ( )8

si

Qp F p

r

Scale of higher twist

Dynamical nuclear shadowing: generated by the multiple final

state scattering of the struck quark

20

1lim ,

2 x xG x Q

x

U-quark, CTEQ5 LO

x = xB

QM shift operator:2 1/3

2

( 1)exp

dxdx

A

Q

Scale of higher twist

May 11, 2004 Ivan Vitev, ISU 4

Results for A- and Bjorken x- Dependence

Ivan Vitev, ISU

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

22

21

( , )( , )

( , )L L

T

F

F

x Qx

QR Q

x

Q2 dependence, Longitudinal structure function

May 11, 2004 Ivan Vitev, ISU 5

1 10 203 Q2

Power Corrections in Neutrino-Nucleus DIS

) 1.0( ,seasee as a x x

.. .( 0.5) ,val

valval x x

Ivan Vitev, ISU

2 2

( ) 2 2 21,3

, ,

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

WB DU D B BUD U

D U UM

D

F x Q V x V xx xA x x

2 2

( ) 2 2 21,3

, ,

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

WB UD U B BDU D

U D DM

U

F x Q V x V xx xA x x

1

23

2

0

3

1( , ) 3( , ) (1 )

2 GLN N

GLS Sdx x Q x QS x xFx

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

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

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

May 11, 2004 Ivan Vitev, ISU 6

Power Corrections in p+A Collisions

Ivan Vitev, ISU

11

1

1 2

1min

11/

1 21mi1 1 0n

1

2

( ) 1/

)) ( )

((

a

a sa

abcd

hNN

a axb b b b

h

T

c

z

xK x

x x S U

d

dyd p

Dx x x F x

S

zdz

z zd

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• Interested in the maximum coherent rescattering of the small xb

parton in the nucleus• Other interactions are less coherent (elastic) and sppressed at forward rapidity by a large scale 1/u, 1/s

( )bxf - standard parton distribution

functions1

1/( )

h cD z - standard parton distribution

functions

May 11, 2004 Ivan Vitev, ISU 7

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

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

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

May 11, 2004 Ivan Vitev, ISU 8

Numerical Results for the Power Corrections

Ivan Vitev, ISU

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

- increases with centrality

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

- increases with rapidity

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

• Dominated by dynamical gluon shadowing- single and double inclusive shift in ~ 2 /t

2

1 22

2

1 22

2

1 22

2 (1 cosh( )),

(1 exp( )),

(1 exp( ))

T

T

T

ps y y

z

pt y y

z

pu y y

z

May 11, 2004 Ivan Vitev, ISU 9

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

May 11, 2004 Ivan Vitev, ISU 10

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?

May 11, 2004 Ivan Vitev, ISU 11

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:

May 11, 2004 Ivan Vitev, ISU 12

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

May 11, 2004 Ivan Vitev, ISU 13

Conclusions Dynamical nuclear shadowing in DIS 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.

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 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

p A