Mauro AnselminoTorino University

and INFN

Theory overview on transversity(The long way to transversity in SIDIS)

Azimuthal asymmetries and PhT dependence in nnunpolarized SIDIS and in dσLL

Learning about the quark intrinsic motion

SSA, Sivers and Collins effects

Collins functions from BELLE data

Coupling Collins function and transversity

JLab, Dec. 14, 2006

Work in collaboration with: M. Boglione, U. D’Alesio, A. Efremov, A. Kotzinian, F. Murgia, B. Parsamyan, A. Prokudin, C. Türk

Polarized SIDIS cross section, up to subleading order in 1/Q

[ ]

( )⎭⎬⎫⎥⎦

⎤⎢⎣

⎡−++−+

+−+

−+++⎩⎨⎧

−+

⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡++++

+++=

151413

12S

11

1098

7654

3210

)2cos( cos1 )cos(

sin )2sin(1

)3sin( )sin( )sin(

cos1 sin1 2sin

sin1 cos1 2cos

LTShLTSLTShe

UTUTSh

UTShUTShUTShT

LLhLLeULhULhL

LUheUUhUUhUU

dΦΦdΦQ

dΦΦ

dΦdΦΦQ

dΦΦdΦΦdΦΦS

dΦQ

ddΦQ

dΦS

dΦQ

dΦQ

dΦdd

σσσλ

σσ

σσσ

σσλσσ

σλσσσσ

Kotzinian, NP B441 (1995) 234

Mulders and Tangermann, NP B461 (1996) 197

Boer and Mulders, PR D57 (1998) 5780

Bacchetta et al., PL B595 (2004) 309

Bacchetta et al., hep-ph/0611265

Unpolarized SIDIS with intrinsic k┴

);,();,(ˆd);,(d 222 QpzDQyQkxf hq

lqlqq q

lhXlp⊥⊥

→⊥

→ ⊗⊗=∑ kσσ

factorization holds at large Q2, and QCDT kP Λ≈≈ ⊥ Ji, Ma, Yuan

qpQxB ⋅

=2

2

22 qQ −=

plqpy

⋅⋅

=

qPPPz h

h ⋅⋅

=

Exact kinematics

struck parton carries 4-momentum k

k

P

k’

02 =k

ql

l′

) ,0 ,0 ,( 00 PPP −=

⎥⎦

⎤⎢⎣

⎡−−=+= ⊥ ϕcos121)(ˆ 2 y

Qksxkls

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−−−−=′−= ⊥ ϕcos

121)1( )(ˆ 2

yQkysxklu

22)(ˆ Qllt −=′−=

neglecting terms one has

PT = p┴ + z k┴hB zzxx ==

⎟⎟⎠

⎞⎜⎜⎝

⎛−−−−+=+∝ ⊥→ ϕσ cos1)2(4)1(1ˆˆˆ 2

2

422 yy

Qky

yQusd lqlq

“Cahn effect”

hh

lhXlp

ΦBAΦ

cosd

d+∝

→σ

assuming:

one finds:

with

clear dependence on (assumed to be constant)and

Find best values by fitting data on Φh and PT dependences

EMC data, µp and µd, E between 100 and 280 GeV

M.A., M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin

Large PT data explained by NLO QCD corrections

EMC data

dashed line: parton model with unintegrated distribution and fragmentation functions solid line: pQCD contributions at LO and a K factor (K = 1.5) to account for NLO effects

Longitudinal polarization (here means along the lepton direction)

γγ ϑϑ cos 12

sin implies , SSQ

yxmSSS L

NT ±=

−±≅±=⇐⇒

helicity-helicity) ,( 76

LLLL dd σσ

helicity-ST

)( 13LTdσ

),( ⊥Δ kxq

),(/ TqS SsxfT

rr⋅Δ +

−+++ − σσ ˆˆ dd

−+++ − σσ ˆˆ dd

⎟⎟⎠

⎞⎜⎜⎝

⎛−−−=−∝− ⊥−+++ ϕσσ cos14)2(ˆˆˆˆ 2

422 yy

Qkyy

yQusdd

Cahn effect

study

assuming

notice: different average for different distributions⟩⟨ ⊥2k

⟩⟨= ⊥22

0 kμ

⟩⟨= ⊥22 pDμ

⟩⟨≤ ⊥22

2,1 kμ

sensitive to the relative values of and , intrinsic k┴ of quarksinside an unpolarized or a longitudinally polarized proton

20μ

22μ

COMPASS: positive (h+), all (h) and negative (h–) hadron production, Q2 > 1.0 (GeV/c)2, W2 > 25 GeV2, 0.1 < x < 0.6, 0.5 < y < 0.9 and 0.4 < z < 0.9

HERMES: π+, π0 and π– production, Q2 > 1.0 (GeV/c)2, W2 > 10 GeV2, 0.1 < x < 0.6, 0.45 < y < 0.85 and 0.4 < z < 0.7

JLab at 6 GeV: π+, π0 and π– production, Q2 > 1.0 (GeV/c)2, W2 > 4 GeV2,0.2 < x < 0.6, 0.4 < y < 0.85 and 0.4 < z < 0.7

M. A., A. Efremov, A. Kotzinian and B. Parsamyan

Predicted dependence of ALL on PhT , for scattering off a proton target, with different choices of μ22:

0.1 (GeV/c)2 – continuous, 0.17 (GeV/c)2 – dashed and 0.25 (GeV/c)2 – dot-dashed lines.

Predicted dependence of ALL on PhT , for scattering off a deuteron (and neutron for JLab) target, with different choices of μ2

2:0.1 (GeV/c)2 – continuous, 0.17 (GeV/c)2 – dashed and 0.25 (GeV/c)2 – dot-dashed lines.

Cahn effect

contains new function, needs assumptions and approximations:

Predicted dependence of on PhT for scattering off a proton target with different choices of μ22:

0.1 (GeV/c)2 – continuous, 0.17 (GeV/c)2 – dashed and 0.25 (GeV/c)2 – dot-dashed lines.Each line splits into three almost overlapping lines corresponding, for each value of μ2

2, to three different values of μ1

2 = (up-down) 0.1, 0.15 and 0.2 (GeV/c)2.

hLLA φcos

Predicted dependence of on x, y and z, for proton, neutron and deuteron targets, for JLab.hLLA φ cos

⊥⊥ −≅ kPp zT

)ˆˆ( ),(21

),(),(

/

//

⊥⊥

⊥⊥

×⋅Δ

+=

↑

↑

kpS

k

kxf

kxfxf

pqN

pqpq

Sivers effect in SIDIS

∑ ∫

∑ ∫

∫∫

⊥

→

⊥⊥

⊥

→

⊥⊥

↓↑

↓↑−

−−Δ=

+

−−≡

↑

qhq

lqlq

pqSh

Shhq

lqlq

SpqN

q Sh

Sh

ShShΦΦUT

pzDdQ

dkxfddΦdΦ

ΦΦpzDdQ

dΦkxfddΦdΦ

dddΦdΦ

ΦΦdddΦdΦA Sh

),(ˆ

),(

)sin( ),(ˆ

)sin( ),(

][

)sin(] [ 2

2/2

2/2

)sin(

σ

σϕ

σσ

σσ

k

k

qTpq

N fMkf ⊥⊥−=Δ

↑ 1/

2

Parameterization of the Sivers function

11 ≤≤− qN

q = u, d. The Sivers function for sea quarks and antiquarksis assumed to be zero.

M.A., M. Boglione, U.D’Alesio, A.Kotzinian, F. Murgia, A Prokudin

from Sivers mechanism)sin( S

UTA Φ−Φ

Deuteron target ( )( )hd

hupd

Npu

NUT DDffA Sh +Δ+Δ∝ ↑↑

Φ−Φ 4 //

)sin(

First p┴ moments of extracted Sivers

functions, comparedwith models

M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin

data from HERMES and COMPASS

),( 4

/2

)1(1

)1(

⊥⊥

⊥

↑Δ

=−=Δ

∫ kxfmkkd

ff

pqN

p

qTq

N

hep-ph/0511017

?11d

Tu

T ff ⊥⊥ −=

The first and 1/2-transverse moments of the Sivers quark distribution functions, defined in Eqs. (3, 9), as extracted in Refs. [20, 21, 23]. The fits were constrained mainly (or solely) by the preliminary HERMES data in the indicated x-range. The curves indicate the 1-σ regions

of the various parameterizations.

),( )( 12)2/1(

1 ⊥⊥⊥

⊥⊥ ∫= kxf

Mkdxf q

Tq

T k

M. Anselmino, M. Boglione, J.C. Collins, U. D’Alesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan

),( 2

12

22)1(

1 ⊥⊥⊥

⊥⊥ ∫= kxf

Mkdf q

Tq

T k

Predictions for π0 production at HERMES

Predictions for K production at HERMES …

… and comparison with data. Role of s quarks?

Predictions for COMPASS, hydrogen target

suggested kinematical cuts:Q2 > 1 (GeV/c)2 W2 > 25 GeV2

PT > 0.1 GeV/c Eh > 4 GeV0.2 < zh < 0.9 0.1 < y < 0.9

predictions for JLab, proton target, 6 GeV

0.4 ≤ zh ≤ 0.7 0.02 ≤ PT ≤ 1 GeV/c 0.1 ≤ xB ≤ 0.6 0.4 ≤ y ≤ 0.85 Q2 ≥ 1 (GeV/c)2 W2 ≥ 4 GeV2 1 ≤ Eh ≤ 4 GeV

predictions for JLab, proton target, 12 GeV

0.4 ≤ zh ≤ 0.7 0.02 ≤ PT ≤ 1.4 GeV/c 0.05 ≤ xB ≤ 0.7 0.2 ≤ y ≤ 0.85 Q2 ≥ 1 (GeV/c)2 W2 ≥ 4 GeV2 1 ≤ Eh ≤ 7 GeV

predictions for JLab, neutron target, 6 GeV

Collins mechanism for SSA

Asymmetry in the fragmentation of a transversely polarized quark )ˆˆ( ),(

21

),(),(

/

//

⊥⊥

⊥⊥

×⋅Δ

+=

↑

↑

ppS

p

qqqhN

qhqh

pzD

pzDzD

initial q spin is transferred tofinal q', which fragments

)sin()ˆˆ( '' Shqq ΦΦ +∝×⋅ ⊥ppS

q

q’

(neglecting intrinsic motionin partonic distributions)

q

hqh

N HMzpD ⊥⊥=Δ ↑ 1/

2

ShC ΦΦΦ −−= π

x

y

α αCΦ

SΦ hΦ

qS

q′S

ll ′−

∫∫

↓↑

↓↑+

+

+−≡

][

)sin( ]d[d 2)sin(

σσ

σσ

dddΦdΦ

ΦΦdΦdΦA

Sh

ShShΦΦUT

Sh

Collins effect in SIDIS

),( ),(

ˆ

)sin(),(ˆ

),(

//22

/212

)sin(

∑ ∫

∑ ∫

⊥⊥

→

⊥

⊥

→

⊥⊥

+

+ΔΔ

=

↑

q pqpq

lqlq

Sh

q ShqhN

lqlq

qSh

ΦΦUT

pzDkxfdQ

dddΦdΦ

ΦΦzDdQ

dkxhddΦdΦ

A Sh

σ

σ

k

pk

:or 1 qh Tq Δ transversity distribution

↓↑↑↑ →→ −=Δ lqlqlqlq ddd σσσ ˆˆˆ

)ˆˆ( ),(),(// ⊥⊥⊥ ×⋅Δ=Δ

↑↑ppSp qqqh

Nqh

N pzDzD

fit to HERMES data on)sin( Sh

UTA Φ+Φ

W. Vogelsang and F. Yuan

Soffer-saturated h1 ( ) ||2 1 qqh +Δ=

A. V. Efremov, K. Goeke and P. Schweitzer(h1 from quark-soliton model)

e+e- CMS frame: GeV 52.10 ,2== s

sEz h

Xhhqqee −+−+ →→

e+

BELLE @ KEK

ϕ1

1hPr

2hPrϕ2−π e-

e+

thrust-axis

z

y

x

1⊥pr

2⊥pr θ

Collins function from e+e- processes (spin effects without polarization, Boer, Jakob, Mulders)

single quark or antiquark are not polarized, butthere is a strong correlation between their spins

θπαθ

σθ

σ 222

sin4

3cosˆ

cosˆ

qesd

ddd

=−↑↑↑↓

),(),( cosˆ

cos 22/11/,2

21

221

21

21

⊥⊥⊥⊥

→

↑↑

−+

∑= pppp

zDzDdd

ddddzdzd

qhqhspinsq

spinsXhhee

θσ

θσ

cross section for detecting the final hadrons inside the jets

contains the product of two Collins functions

∑∑ ↑↑ ΔΔ

++=≡

q qhqhq

q qhN

qhN

q

zDzDe

zDzDe

ddzdzd

dddzdzd

A)()(

)()( )(cos

cos1sin

811

cos 21

cos

2/1/2

2/1/2

02

2

21

0211

21

21ϕθ

θ

θσ

π

θϕσ

∫ ⊥⊥ ↑↑ Δ=Δ etc. ),,( )(/

2/

pzDdzDqh

Nqh

N p 210 ϕϕϕ +≡

Cosine modulationsclearly visible

0210

0 cos)( ϕϕ PPN

N+=

21 ϕϕ +

0

0 )(N

N ϕ

M. Grosse Perdekamp, A. Ogawa, R. Seidl

Talk at SPIN2006

BELLE data

1P

),()cos(1 211 211

1 zzPAA

L

U

ϕϕ ++= U = unlike charged pionsL = like charged pions

⎥⎦

⎤++

ΔΔ+ΔΔ+ΔΔ−

⎢⎣

⎡+

ΔΔ+ΔΔ+

=

)()(2)()(5)()(5)()(2)()(5)()(5

)()(7)()(5)()(7)()(5

cos1sin

81),(

212121

212121

2121

21212

2

211

zDzDzDzDzDzDzDzDzDzDzDzD

zDzDzDzDzDzDzDzDzzP

UUFUUF

UN

UN

FN

UN

UN

FN

UUFF

UN

UN

FN

FN

θθ

etc. , , // UN

uN

FN

uN DDDD Δ≡ΔΔ≡Δ −+ ππ

M.A., M. Boglione, U.D’Alesio, A.Kotzinian, F. Murgia, A. Prokudin, C. Türk, in preparation

Collins functions and transversity distributions from a globalbest fit of HERMES, COMPASS and BELLE data

)]()([21)(N),( /2

/ 22

xqxfk

exkxq pq

kkTqT Δ+

⟩⟨=Δ

⊥

⟩⟨−

⊥

⊥⊥

πSoffer bound

)(2 )( )(N),( /2

/

/

22

zDp

ephzpzD qh

ppCqqh

N

⟩⟨=Δ

⊥

⟩⟨−

⊥⊥

⊥⊥

↑ πpositivity bound

1 |)(N| 1, || )()1()(N)(

≤≥+

−=+

xNxxNx Tq

Tq

Tq

Tq βα

βαβα

βαβα

1 |)(N| 1, || )()1()(N)(

≤≥+

−=+

zNzzNx Cq

Cq

Cq

Cq δγ

δγδγ

δγδγ

22 /2)( hMp

h

eMpeph ⊥−⊥

⊥ =

fit of HERMES data on)sin( Sh

UTA Φ+Φ

fit of COMPASS data on)sin( Sh

UTA Φ+Φ )sin( ShUTA Φ+Φ

fit of BELLE data on ),( 211 zzP

Extracted favoured and unfavoured Collins functions

positivity boundEfremov et al.Vogelsang, Yuan

Extracted transversity distributions

Soffer bound

Predictions for Collins asymmetryat COMPASS, proton target

Collins asymmetry for kaons, HERMES

Predictions for Collins asymmetryat JLab, proton target, 6 GeV

Predictions for Collins asymmetryat JLab, proton target, 12 GeV

Predictions for Collins asymmetryat JLab, neutron target, 6 GeV

Predictions for Collins asymmetryat JLab, neutron target, 12 GeV

Conclusions

Shaping up the nucleon spin and momentumtransverse structure

Information on quark intrinsic motion

Spin-k┴ correlation from Sivers function

Extracting Collins functions

Accessing transversity

Plenty of new data expected from JLab