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Updates on Transversity Experiments and Interpretations

Jen-Chieh Peng

Transversity Collaboration Meeting, JLab, March 4, 2005

University of Illinois

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Outline• Recent results of SSA with transversely

polarized targets from HERMES and COMPASS– What are the implications on the transversity, Collins

fragmentation function, and Sivers quark distributions?

– Can existing models explain the SSA data from HERMES for both the longitudinally polarized and the transversely polarized targets?

– What are the implications for the Hall-A experiments?

– What are the implications for polarized and unpolarized Drell-Yan experiments.

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Transversity distribution, Sivers distribution, and Collins fragmentation function in Semi-Inclusive DIS

with transversely polarized target

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26 4

Q

sxd

),()(])1(1{[ 211

,

22 h

qq

qqq PzDxfey

),()()sin()1(||

),()()2sin(4

)1(||

),()()2cos(4

)1(

2

,11

2

2

,1

)1(1

22

2

2

,1

)1(1

22

2

hqq

qqq

lS

lh

h

hT

hqq

qqLq

lh

hN

hL

hqq

qqq

lh

hN

h

PzHxhezM

PyS

PzHxheMMz

PyS

PzHxheMMz

Py

)},()()cos()2

11(||

),()()2

11(||

),()()3sin(6

)1(||

),()()sin()2

11(||

21

)1(1

,

2

21

,1

2

,

21

)2(1

223

3

21

)1(1

,

22

hqq

Tqq

qlS

lh

N

hTe

hq

qq

qqLe

qqh

qqTq

lS

lh

hN

hT

hqq

Tqq

qlS

lh

N

hT

PzDxgezM

PyyS

PzDxgeyyS

PzHxheMMz

PyS

PzDxfezM

PyyS

Unpolarized

Polarized target

Polarzied beam and

target

SL and ST: Target Polarizations; λe: Beam Polarization

Sivers

Transversity

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Observation of Single-Spin Azimuthal Asymmetry

Longitudinally polarized target

ep → e’πx HERMES

<ST> ~ 0.15

Collins effect: Correlation between the quark’s transverse spin with pion’s pT in the fragmentation process.

Sivers effect: Correlation between the transverse spin of the proton with the quark’s transverse momentum.

Other higher twist effects could also contribute.

Origins of the azimuthal asymmetry (correlation between the target nucleon transverse spin and the pion transverse momentum)?

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Model prediction of transversityChiral-quark soliton model

Similar to helicity distributions

Chiral-quark soliton model predicts Sivers distribution is zero!

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Comparison with HERMES longitudinal SSA dataProton data Deuteron data

Chiral-quark soliton model can describe the SSA data very well (by including only the transversity term)

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Makins DNP04 talk

π

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Disfavored Collins function = 0

dis1 ( ) 0H z

Comparison between the HERMES transversely polarized

target SSA data with Chiral-quark soliton model hep-ex/0412420

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Comparison between the HERMES transversely polarized target data with the Chiral-quark soliton model

disf fav1 1( ) 1.2 ( )H z H z

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Comparison between the HERMES transversely polarized data with the Chiral-quark soliton model

disf fav1 1( ) 5 ( )H z H z

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Implications of the HERMES SSA data withtransversely polarized target

• Anselmino et al. showed that the Hermes SSA data for longitudinally polarized data can be explained by Sivers effect alone (without the transversity/Collins effect).

• However, the extracted Sivers function is much larger (and of opposite sign) compare to the HERMES SSA data with transversely polarized data.

hep-ph/0412316

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First results from COMPASS transversely polarized 6LiD

•Effects are expected to be small at small x

•Some cancellations between proton and neutron are expected

hep-ex/0503002

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Extraction of the Sivers distribution

Fits to the HERMES data on Sivers moments

(1) 0.3 51

(1) 51

Dashed curv

Soli

e: (

d curve: ( ) 0.4 (1

0.1 (1 )

)

)

u

T

T

ux

xf x x x

f x x x

(hep-ph/0412353)

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SSA with Transversely Polarized Drell-Yan

• Prediction by Anselmino, D’Alesio, Murgia (hep-ph/0210371) for a negative AN.

• |AN| increases with rapidity, y, and with dilepton mass, M.

Analysing power (AN) is sensitive to Sivers function

q qqqqq

q qqqTqDYN xfxfe

xfxfeA

)()(

)()(2

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Sivers function in Drell-Yan is expected to have a sign opposite to that in DIS!(Brodsky, Hwang, Schmidt, hep-ph/0206259; Collins, hep-ph/0204004)

p↑ + p → l+ l- + X√s = 200 GeV

AN

y

Is this measurement feasible at RHIC?

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Expected statistical sensitivity for Drell-Yan AN

• Might be feasible to determine the sign of the Sivers function at RHIC

• Should consider fixed-target polarized Drell-Yan too

Assuming 400 pb-1 50% polarization

6 < M < 10 GeV

p↑ + p → l+ l- + x √s = 200 GeV

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Sivers functions from SSA in polarized Drell-Yan

(1) 0.3 51

(1) 51

Dashed curv

Soli

e: (

d curve: ( ) 0.4 (1

0.1 (1 )

)

)

u

T

T

ux

xf x x x

f x x x

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Cos2Ф Dependence in Unpolarized Drell-Yan

• RHIC would provide unpolarized p-p Drell-Yan data too

• Fixed-target unpolarized p-p Drell-Yan data also exist

Large cos2Ф dependences have been observed in π – induced Drell-Yan

This azimuthal dependence could arise from a product of KT-dependent distribution function h1

┴

( Boer, hep-ph/9902255; Boer, Brodsky, Hwang, hep-ph/0211110)

In quark-diquark model, h1┴ is identical to Sivers function

No Cos2Ф depenence for unpolarized p-p Drell-Yan has been reported yet (The effect from h1

┴ is expected to be smaller)

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(Conway et al.) 252 GeV π- + W

2 211 cos sin 2 cos sin cos 2

2

d

d

*h N X X

Lam-Tung sum rule : 1 2 0

Lam-Tung rule is violated and can not be explained by pion bound state effect

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Brandenburg, Nachtmann and Mirkes proposed correlation between quark kT and its transverse spin

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0 4 41 2 4 T

T T

Q

Q m

is a measure of the correlation between the transverse spins of the qq

D. Boer pointed out that h1┴ provides such correlation

221 12 2

( , ) ( )T TkC HTT H

T C

M Mh x k c e f x

k M

-2

2.3GeV,

1, 1GeV

C

H T

M

C

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Unpolarized p-p and p-d dimuon production

Fermilab E866, √s = 38.8 GeV

J/Ψ

Ψ’

Υ

~ 2.5 x 105 Drell-Yan events

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Ф – coverage of the E866 dimuon data

J/Ψ events Drell-Yan events

Not corrected for acceptance yet

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Summary• Transversity distribution remains an interesting

frontier in understanding spin structure in nucleon.• Study of the T-odd Sivers structure function and the

Collins fragmentation function are important for their own sake, and for extracting information on transversity.

• First results of SSA using transversely polarized p and d targets are intriguing. The proposed Hall-A measurement on 3He should provide very useful new information.

• New Semi-Inclusive DIS experiments at JLab will continue to probe the flavor structure of unpolarized and polarized parton distributions.