where is the spin of the nucleon hidden?dvcs bethe-heitler (bh) γ + hermes, jlab: dvcs-bh...

Where is the Spin of the Nucleon hidden?

E.C. Aschenauer

DESY-ZEUTHEN

E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 1

The Spin Structure of the Nucleon

Naive Parton Model:��

� � ��

� ��

BUT

1988 EMC measured:�� = 0.123 � 0.013 � 0.019

� � Spin Puzzle

F � from HERA tells:Gluons are important !

� � sea quarks ��

� � ��

��

��

� �� ! "# $ ! "# $

% � %&

� '( � ' � '( � ') * +

Full description of J & Jneeds

orbital angular momentum


The Spin Structure of the Nucleon

Naive Parton Model:��

� � ��

� ��

BUT

1988 EMC measured:�� = 0.123 � 0.013 � 0.019

� � Spin Puzzle

F � from HERA tells:Gluons are important !

� � sea quarks ��

� � ��

Full description of J� & J �

needsorbital angular momentum�

� ��

��

�

! "# $

�


The Hunt for% �

Study of hard exclusive processes leads toa new class of PDFs

Generalised Parton Distributions��

� possible access toorbital angular momentum

� � � ��

� � ��

exclusive processes: all products of a reaction are detected� � missing energy ( �� ) and missing Mass ( �� ) = 0


GPDs Introductionquantum numbers of final state � select different GPDs

∆2

P +∆P - 2

x - ξ ξx +

γ∗ γ

GPD

0+

P - ∆2

P + ∆2

π , π

x - ξ ξx +

γ∗

GPD

q 0ρ , Φ , ωq

P + ∆2

P - ∆2

x - ξ ξx +

GPD

γ∗

DVCS: pseudo-scalar mesons vector mesons��

What does GPDs characterize?unpolarized polarized�� conserve nucleon helicity�� flip nucleon helicity

�, �, � defined on the light cone

�: longitudinal momentum fraction �: momentum transfer ( � � � � )

�

: exchanged longitudinal momentum fraction (

� � �� )E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 4

GPDs Introduction II

� Link to DIS:

P

Im

Forward DVCS

x

2

DIS ∆, ξ −−> 0

∆2

P +∆P - 2

x - ξ ξx +

γ∗ γ

GPD

γ∗

standard PDFsand

do NOT appear in DISNew Info !

Study GPDswith spin observablessingle spin azimuthal asymmetriesazimuthal asymmetriesvia cross sections

qqx = ξ

Distribution q(x)Antiquarkξ = 0

Quark Distribution q(x)

H ( x , , t=0)ξu

P P’

qq

Distribution Function



P P’

qq q

q q

x−ξ +ξ +1-1 0

q

P P’

q q

GPDGPD GPD



� Link to DIS:

P

Im

Forward DVCS

x

2

DIS ∆, ξ −−> 0

∆2

P +∆P - 2

x - ξ ξx +

γ∗ γ

GPD

γ∗

� standard PDFs� � � � � and � � ��

� � ��

do NOT appear in DISNew Info !


qqx = ξ



H ( x , , t=0)ξu

P P’

qq




P P’

qq q

q q

x−ξ +ξ +1-1 0

q

P P’

q q

GPDGPD GPD



� Link to DIS:

P

Im

Forward DVCS

x

2

DIS ∆, ξ −−> 0

∆2

P +∆P - 2

x - ξ ξx +

γ∗ γ

GPD

γ∗


� � ��

�

� � �� do NOT appear in DIS� � New Info !


qqx = ξ



H ( x , , t=0)ξu

P P’

qq




P P’

qq q

q q

x−ξ +ξ +1-1 0

q

P P’

q q

GPDGPD GPD



� Link to DIS:

P

Im

Forward DVCS

x

2

DIS ∆, ξ −−> 0

∆2

P +∆P - 2

x - ξ ξx +

γ∗ γ

GPD

γ∗


� � ��

�


� Study GPDs

with spin observablessingle spin azimuthal asymmetriesazimuthal asymmetriesvia cross sections

qqx = ξ



H ( x , , t=0)ξu

P P’

qq




P P’

qq q

q q

x−ξ +ξ +1-1 0

q

P P’

q q

GPDGPD GPD



� Link to DIS:

P

Im

Forward DVCS

x

2

DIS ∆, ξ −−> 0

∆2

P +∆P - 2

x - ξ ξx +

γ∗ γ

GPD

γ∗


� � ��

�


� Study GPDs

� with spin observablessingle spin azimuthal asymmetries

azimuthal asymmetriesvia cross sections

qqx = ξ



H ( x , , t=0)ξu

P P’

qq




P P’

qq q

q q

x−ξ +ξ +1-1 0

q

P P’

q q

GPDGPD GPD



� Link to DIS:

P

Im

Forward DVCS

x

2

DIS ∆, ξ −−> 0

∆2

P +∆P - 2

x - ξ ξx +

γ∗ γ

GPD

γ∗


� � ��

�


� Study GPDs


� azimuthal asymmetries

via cross sections

qqx = ξ



H ( x , , t=0)ξu

P P’

qq




P P’

qq q

q q

x−ξ +ξ +1-1 0

q

P P’

q q

GPDGPD GPD



� Link to DIS:

P

Im

Forward DVCS

x

2

DIS ∆, ξ −−> 0

∆2

P +∆P - 2

x - ξ ξx +

γ∗ γ

GPD

γ∗


� � ��

�


� Study GPDs


� azimuthal asymmetries

� via cross sections

qqx = ξ



H ( x , , t=0)ξu

P P’

qq




P P’

qq q

q q

x−ξ +ξ +1-1 0

q

P P’

q q

GPDGPD GPD


DVCS � � ��

e’e

γ

p + ∆

γ∗

p

ee’

γγ∗

p ∆p +

DVCS Bethe-Heitler (BH)

��

+

� � � ��

HERMES, JLAB:DVCS-BH interference:

� � use BH as a vehicle to study DVCSH1, ZEUS:measure DVCS cross section directly

HERMES / JLAB kinematics:BH cross section larger than DVCS

10 2

10 3

10 4

10 5

10 6

-10 0 10 20

10 2

10 3

10 4

10 5

10 6

-10 0 10 20

10 2

10 3

10 4

10 5

10 6

-10 0 10 20

10 2

10 3

10 4

10 5

10 6

-10 0 10 20

Θγγ*, deg

x = 0.1

Q2 = 2 GeV2

Θγγ*, deg

x = 0.3

Q2 = 2 GeV2

DVCSBH

Θγγ*, deg

x = 0.1

Q2 = 5 GeV2

Θγγ*, deg

x = 0.3

Q2 = 5 GeV2

d σ

/ d

pe

dΩ

e d

Ωγ (

pb

/ G

eV s

r2)

[Korotkov, Nowak, hep-ph/0108077]


DVCS azimuthal asymmetries

�� + � � � � � �� isolate BH-DVCS interference term � � non-zero azimuthal asymmetries

� imaginary part � beam helicity asymmetry:��

� � � � � � ��

� asymmetry measured by HERMES and JLAB

� real part � beam charge asymmetry:��

� ��

� asymmetry measured by HERMES

� no polarized target needed

k

k’

q

φθγ∗

PγP

�

: azimuthal angle between

lepton scattering plane

and the � � � - plane

(Detected)(Not Detected)

(Detected)(Not Detected)

GPDX

eγ∗

γe’

p


DVCS at HERMES

(Not Detected)

(Detected)(Detected)

GPDX

eγ∗

γe’

p

� � Exclusivity has to be ensured bymissing mass: M

�� Energy resolution in exclusive region:� � � �� 0.8 GeV

��

0

1000

2000

3000

4000

5000

6000

-5 0 5 10 15 20 25 30 35 40 45Mx

2 ( GeV2 )

Co

un

ts

0

200

400

600

800

1000

1200

-4 -2 0 2 4 6 8Mx

2 ( GeV2 )C

ou

nts

Improve Exclusivity: detect recoil proton � planned for 2005/2006 data taking


DVCS beam charge asymmetry (BCA)

�

�� sensitive to ��

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-3 -2 -1 0 1 2 3

Φ (rad)

AC

HERMES PRELIMINARY

P1 + P2 cos Φ

P1 = -0.05 ± 0.03 (stat.) ± 0.03 (sys.)

P2 = 0.11 ± 0.04 (stat.) ± 0.03 (sys.) -0.2

-0.1

0

0.1

0.2

0.3

0.4

-1 0 1 2 3 4 5 6

M x [GeV]

AC

co

s φ

e± p → e±γ X

HERMES PRELIMINARY

AC cos φ |M < 1.7 GeV = 0.11 ± 0.04 (stat) ± 0.03 (sys)x

-1.5

�

M � � 1.7 GeV

��

��

� azimuthal asymmetry appears at

��


DVCS single beam-spin asymmetry (BSA)

�

�� sensitive to

� � � � � � ��

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-3 -2 -1 0 1 2 3

φ (rad)

AL

U

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 50 100 150 200 250 300 350φ, deg

A

HERMES CLAS

-1.5

�

M � � 1.7 GeV

96/97: [PRL87 (2001), 182001] [PRL87 (2001), 182002]� � ��

��

at

�� , �� GeV

�

,

�� GeV

�

at � � �� , �� GeV

�

,

� � � �� GeV

�

GPD-calculation: [Kivel et al. Phys. Rev. D 63 (2001), 114014]E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 10

Much more data!

�

�� sensitive to

� � � � � � ��

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-3 -2 -1 0 1 2 3

φ (rad)

AL

U

HERMES 2000 (refined)PREL.e→ + p → e+ γ X (Mx< 1.7 GeV)

P1 + P2 sin φ + P3 sin 2φ

= 0.18 GeV2, = 0.12, = 2.5 GeV2

P1 = -0.04 ± 0.02 (stat)P2 = -0.18 ± 0.03 (stat)P3 = 0.00 ± 0.03 (stat)

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-1 0 1 2 3 4 5 6

Mx (GeV)

AL

U s

in

φ

e→ + p → e+ γ X

HERMES 2000(refined analysis)

PRELIMINARY

ALU sin φ M < 1.7 GeV = -0.18 ± 0.03 (stat) ± 0.03 (sys)x

= 0.18 GeV2, = 0.12, = 2.5 GeV2

� all azimuthal asymmetries (BCA & BSA) appear at

� � �

� enough statistics to study kinematic dependencies of GPDs

� DVCS data on polarized proton / deuterium target � � access to

� � � ��

� DVCS data on nuclear targets (D,

�

He, Ne, Kr)� � coherent scattering on a nucleus ?!E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 11

Exclusive PS meson production e p e

�

n ��

� cross section: � � � � � � ��

� � has an interference between pole and non-pole amplitudes:�� - FF

� � � � ��

� � large single spin asymmetry expected for transverse polarized H-target

γ*L p → π+ n, π+ ∆0

-0.5

-0.3-0.1

π+ n

-0.5-0.35-0.2

π+ ∆0

xB

SPIN

ASY

MM

ET

RY

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

[ K. Goeke et al., hep-ph/0106012 ]

0+

P - ∆2

P + ∆2

π , π

x - ξ ξx +

γ∗

GPD

Lets see what the data say !


How to extract exclusive ��

� Production mechanismen: ��

��

not detected

no exclusive production at a proton targetTrick: exclusive

π+

Normalisationregion

Missing Mass [GeV]

Cou

nts

Cou

nts

π-

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5 3 3.5 4

Exclusive MCArbitrary Norm.

Data

Fit to data

Missing Mass [GeV] N

π+ -

Nπ-

0

100

200

300

400

0 0.5 1 1.5 2 2.5 3 3.5 4

clear peak at missing massProblematic: difference in relative contribution of resonant and

non-resonant channels to , yield




��

not detected

� no exclusive � � production at a proton target

Trick: exclusive

π+

Normalisationregion

Missing Mass [GeV]

Cou

nts

Cou

nts

π-

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5 3 3.5 4


Data

Fit to data


π+ -

Nπ-

0

100

200

300

400

0 0.5 1 1.5 2 2.5 3 3.5 4






��

not detected


� � Trick: exclusive � � � � � � � � � � � � � π+

Normalisationregion

Missing Mass [GeV]

Cou

nts

Cou

nts

π-

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5 3 3.5 4


Data

Fit to data


π+ -

Nπ-

0

100

200

300

400

0 0.5 1 1.5 2 2.5 3 3.5 4






��

not detected



Normalisationregion

Missing Mass [GeV]

Cou

nts

Cou

nts

π-

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5 3 3.5 4


Data

Fit to data


π+ -

Nπ-

0

100

200

300

400

0 0.5 1 1.5 2 2.5 3 3.5 4

clear peak at missing mass� � �

Problematic: difference in relative contribution of resonant andnon-resonant channels to , yield




��

not detected



Normalisationregion

Missing Mass [GeV]

Cou

nts

Cou

nts

π-

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5 3 3.5 4


Data

Fit to data


π+ -

Nπ-

0

100

200

300

400

0 0.5 1 1.5 2 2.5 3 3.5 4

clear peak at missing mass� � �� Problematic: difference in relative contribution of resonant andnon-resonant channels to �

�

, � � yieldE.C. Aschenauer 2003 CTEQ Summer School – Lecture II 13

Exclusive ��

target - SSA

� until 2001 no data with transverse polarized proton target available� � use longitudinal polarized proton target

x

y

z φ

~phad

~S⊥

~S

~k

~k′

~q

uli

transverse component to

cross section:

unpolarized polarizedbeam target

suppressed bybut

HERMES: 0.17

Target Spin Asymmetry:


Exclusive ��

target - SSA


x

y

z φ

~phad

~S⊥

~S

~k

~k′

~q

uli

� � transverse component to � �

cross section:


suppressed bybut

HERMES: 0.17



Exclusive ��

target - SSA


x

y

z φ

~phad

~S⊥

~S

~k

~k′

~q

uli


� cross section:

� � � ��

�


suppressed bybut

HERMES: 0.17



Exclusive ��

target - SSA


x

y

z φ

~phad

~S⊥

~S

~k

~k′

~q

uli


� cross section:

� � � ��

�


� � � suppressed by � � � � � �

but

� � � ��

HERMES:

�� 0.17



Exclusive ��

target - SSA


x

y

z φ

~phad

~S⊥

~S

~k

~k′

~q

uli


� cross section:

� � � ��

�


� � � suppressed by � � � � � �

but

� � � ��

HERMES:

�� 0.17

� Target Spin Asymmetry:

��

� ��

� � � � � � � � � ��

� ��

� � � � � � � � � � � ��


Exclusive ��

target - SSA-Results

MX [GeV]

AU

L

sin

φ

-0.5

-0.25

0

0.25

0 1 2

φ [rad]

A(φ

)

-3 -2 -1 0 1 2 3-0.6

-0.4

-0.2

0

0.2

0.4

0.6

� Asymmetry appears at

�� = Nucleon mass

�

� � � � �� at � � � � � � � � � ��

� more data needed � � transverse polarized target to study

� � � � �


Exclusive VM-production � � ��

0

200

400

600

800

Eve

nts

γ*p ρ0p4 < W < 5 GeV

-2 0 2 4 6 8 10 12 0

200

400

600

800

∆E [GeV]

5 < W < 6 GeV� � � � � �

� �

� Recoiling proton is notdetected

� good determination ofexclusive channelusing

��

� DIS-‘background‘well described by Monte Carlo

� deduce longitudinalcross section fromdecay angular distributions �

�

� � �

��

�

�

�


Exclusive �� for ��

-Production

101

10-1

100

W [GeV]

σ L(γ

* p

ρ0 p

) [µ

b] = 2.3 GeV2

HERMES

E665

101

= 4.0 GeV2

γ* + p → ρ0L + p

10

10 2

10 3

10 102

Q2 = 5.6 GeV2

10

10 2

10 3

10 102

dσL/d

t(t=

t min

) (n

b/G

eV2 )

Q2 = 9 GeV2

10-1

1

10

10 2

10 102

Q2 = 27 GeV2

W (GeV)

[ K. Goeke et al., hep-ph/0106012 ]

GPD calculations: � quark exchange mechanism dominates

� � �� p �� p) at low W �

� 2-gluon exchange mechanism dominates

� � �� p �� p) at high W � and in � � �� p � �p)E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 17

Deep Inelastic Scattering Cross Section

Cross Section:

� � ��

� � � ��

leptonic hadronic

�� purely electromagnetic � � calculable in QED

�

= � �� ! � " # $% $ &

� �� ! � "

# ')( � * � +,

� � � � � �� ! � " #�

�.-0/ � � � � �/ �- � � � � � � ! � " "

(for spin 1) + quadrupole terms

�1 � 1 � 132 154 �

6 � , 687 � , 7 9 : Un- / Polarized Structure Functions

BUTQuarks are relativistic, have intrinsic

;8< , masses and correlations


DIS and SIDIS Cross Section

�� 9 �� < � ��

�� 7��

� �

� � � � � � � � ��

��

� � � � �

� �< � � � � � � �� < � � � � � � �� < � � � � � � � � � �� < � � � � <

� � �< � �� < � � � �� < � � <

� non zero Single Spin Azimuthal Asymmetries��

Beam Target polarization Mulders and Tangermann (NP B 461 (1996) 197)E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 19

Twist-2 Quark DF & FF

Distribution Functions (DF) Fragmentation Functions (FF)

=

=

=

f1

h1T

g1L g1T=

f1T =

h1 =

h1T =h1L =

=

=1L

1

G

=H1T

=1TG

D

D1T

1H

=

=

H1L= H1T =

survive integrationThe others are sensitive to intrinsic in the nucleon& in the fragmentation process

: Sivers DF : std. unpol FF: transversity : Collins FF




=

=

=

f1

h1T

g1L g1T=

f1T =

h1 =

h1T =h1L =

=

=1L

1

G

=H1T

=1TG

D

D1T

1H

=

=

H1L= H1T =

� survive

;�� integration

� The others are sensitive to intrinsic �;� � in the nucleon

& in the fragmentation process

: Sivers DF : std. unpol FF: transversity : Collins FF




=

=

=

f1

h1T

g1L g1T=

f1T =

h1 =

h1T =h1L =

=

=1L

1

G

=H1T

=1TG

D

D1T

1H

=

=

H1L= H1T =

� survive

;�� integration

� The others are sensitive to intrinsic �;� � in the nucleon

& in the fragmentation process

� � ��< : Sivers DF � �: std. unpol FF

� �< : transversity � � �: Collins FFE.C. Aschenauer 2003 CTEQ Summer School – Lecture II 20

... surviving

�� integration

1f =q

g =1 -q

1h = -q

Unpolarizedquarks and nucleons

vector charge:

� � � � ��

� ��

q(x): spin averagedwell known

H1, ZEUS

Longitudinally polarizedquarks and nucleons

axial charge:

� � � � ��

�

q(x): helicity differenceknown

SMC, HERMES,COMPASS, RHIC

Transversely polarizedquarks and nucleons

tensor charge :

� � � � ��

�

q(x): helicity flipunmeasured

SMC, HERMES,COMPASS, RHIC


Characteristics of Transversity

� Non-relativistic quarks:

� � � � � � � � � � �

� � � probes relativistic nature of quarks

� Angular momentum conservation� Transversity has no gluon component� different � � evolution than � � � � �

� � and �� contribute with opposite sign to � � � � �� predominantly sensitive to valence quark polarization

� Bounds:� � � � � � � ��

� Soffer bound: � � � � � � ��

Transversity distribution CHIRAL ODDNo Access in Inclusive DIS !!!

L

R

R

L

NEED another chiral-odd object!

semi-inclusive DIS Collins FF

RL




� � � � � � � � � � �




� Bounds:� � � � � � � ��

� Soffer bound: � � � � � � ��

� Transversity distribution CHIRAL ODD

� No Access in Inclusive DIS !!!

L

R

R

L


semi-inclusive DIS Collins FF

RL




� � � � � � � � � � �




� Bounds:� � � � � � � ��

� Soffer bound: � � � � � � ��

� Transversity distribution CHIRAL ODD

� No Access in Inclusive DIS !!!

L

R

R

L


� semi-inclusive DIS � �� Collins FF

RL


How can one measure Transversity

Single spin azimuthal asymmetries with a transverse polarized target� � � � ��

x

y

z

φS

φ

~phad

~S⊥

~k

~k′

~q

uli

� � � � �� Collins angle� � � � � � �

� � ��

� �

chiral-odd chiral-oddDF FF

� �� ! � "� � � � � � �� # � �# " �

� � � �� $�

� %'& (*) + �-, �. (*/ +

� $ �� & () + � .(*/ +

Can only measure

�10 �32 �54 6 �87 9;: �3< �6 �87 9;: � < � from e =e > collider experiments, like BelleE.C. Aschenauer 2003 CTEQ Summer School – Lecture II 23

First glimpse on Transversity?!HERMES:

� until 2001 no data with transverse polarized proton target available� � like for exclusive pion production� � use longitudinal polarized proton and deuterium target

�� 4 � � � � � � � � ��

�� transverse componentof target spin w.r.t. virtual photon:� � � �� 2� � ��

� � �� !� � �#" " 4 � � $ %'& � � � � � � � $ % & � � � � (x

y

z φ

~phad

~S⊥

~S

~k

~k′

~q

uli

� � transverse component to )

� � �� !� � � �#" " � � 97 * 9 +, 9 2 - .0/ � � �123 4 6 � 9 : �3< � � � 97 * 9 +, 9 2 - . � � � � � � �� 65 �1 23 4

sub-leading transversity4 Collins FForder


ResultsPROTON DEUTERON

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 π-π

A(φ

)

φ

π+P1 + P2 sin(φ)

P1 = 0.004 ± 0.003P2 = 0.020 ± 0.004

0 π-π

A(φ

)

φ

π-

P1 = 0.003 ± 0.004P2 = -0.001 ± 0.005

0 π-π

A(φ

)

φ

π0

P1 = -0.001 ± 0.005P2 = 0.019 ± 0.007

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-0.04

-0.02

0

0.02

0.04

-3.14 -1.57 0 1.57 3.14

-0.04

-0.02

0

0.02

0.04

-3.14 -1.57 0 1.57 3.14

-0.04

-0.02

0

0.02

0.04

-3.14 -1.57 0 1.57 3.14

-0.04

-0.02

0

0.02

0.04

-3.14 -1.57 0 1.57 3.14

-0.02

0

0.02

0.04

e d→

→ e π+ X

P1 * sin φP1 * sin φ + P2 * sin 2φP1 = 0.012 ± 0.002P2 = 0.004 ± 0.002

A(φ

)

-0.02

0

0.02

0.04

e d→

→ e π0 X

P1 = 0.021 ± 0.005P2 = 0.009 ± 0.005

A(φ

)

-0.02

0

0.02

0.04

e d→

→ e π- X

P1 = 0.006 ± 0.003P2 = 0.001 ± 0.003

A(φ

)

-0.02

0

0.02

0.04

-0.04

e d→

→ e K+ X

P1 = 0.013 ± 0.006P2 = -0.005 ± 0.006

A(φ

)

-π -π/2 0 π/2 π

φ


� � � � ��

-0.04

-0.02

0

0.02

0.04

0.06

0.08

-0.04

-0.02

0

0.02

0.04

0.06

0.08

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.1 0.2 0.3

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.25 0.5 0.75 1

AU

L

sin

φA

UL

sin

φe p

→ → e π+ X

e d→

→ e π+ XA

UL

sin

φ

e d→

→ e π0 Xe p

→ → e π0 X

AU

L

sin

φ

e d→

→ e π- Xe p

→ → e π- X

x

AU

L

sin

φ

e d→

→ e K+ X

P⊥ (GeV) z0.2 0.3 0.4 0.5 0.6 0.7

Original predictions by Collins:

� Proton TargetLarger for � = , � �than for � >

( �-quark dominance )

� Rise with x ��

(valence quark dominance)� Grow with � � , peak around 1 GeV

(

� �� = � � with �� 1 GeV)� First SSA for Kaons


What does theory tell?

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3

AU

L

sin

φ

e d→

→ e π+ X

χQSM

QdQ

pQCDA

UL

sin

φ

e d→

→ e π0 X

χQSM

QdQ

pQCD

AU

L

sin

φ

e d→

→ e π- X

χQSM

QdQ

pQCD

x

AU

L

sin

φ

e d→

→ e K+ X

χQSM

QdQ

pQCD

� - �calculated in: �QSM, QdQ, pQCD models

� sub-leading order terms� 0

� Collins FF� � �:

�QSM:� � 6 � :�� :� � � � � � � � � � � �

QdQ, pQCD: ’Collins guess’


Challenges in Interpretation

Problem:

�have neglected the Sivers - DF� � �� !� � � � �� 7 *�

+ ,� 2 � � 9 :( �32 �54 � :�3< �

longitudinally polarized target

Sivers and Collins effect indistinguishable

Transversely polarized target needed

becomes dominant

Sivers and Collins distinguishable

moment moment

x

y

z

φS

φ

~phad

~S⊥

~k

~k′

~q

uli



Problem:


+ ,� 2 � � 9 :( �32 �54 � :�3< �


� Sivers and Collins effect indistinguishable


becomes dominant

Sivers and Collins distinguishable

moment moment

x

y

z

φS

φ

~phad

~S⊥

~k

~k′

~q

uli



Problem:


+ ,� 2 � � 9 :( �32 �54 � :�3< �


� Sivers and Collins effect indistinguishable


� �� becomes dominant

� Sivers and Collins distinguishable� �� moment �� moment� � �� > � !� ( � � �� 7 *�

+ ,� 2 � � 9 :( �2 � 4 � :�3< � � � �� = � !� ( � � �� 7 *�

+ ,� 2 � 9 :( �2 � 4 6 � 9 : � < �

x

y

z

φS

φ

~phad

~S⊥

~k

~k′

~q

uli


Results from SMC

-20

-10

0

10

20

all (h++ h−)

h+ (π+)h− (π−)

a)

prot deut

AN

(%

)

SMC P

relimin

ary

-20

-10

0

10

20

h+: pT > 0.1 GeV/c

h+: pT > 0.5 GeV/c

b)

prot deut

AN

(%

)

SMC P

relimin

ary

-20

-10

0

10

20

h−: pT > 0.1 GeV/c

h−: pT > 0.5 GeV/c

c)

prot deut

AN

(%

)

SMC P

relimin

ary

Data with transversely polarized target

�� $ % & � ��

� � � �� ( � � � ��

�$ % & � ��

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-180 -120 -60 0 60 120 180

φC

AN

SMC Preliminar

y

h+ (π+)

Need more data � � COMPASS, HERMES, RHIC


Summary� Orbital Angular Momentum ��

GPDs: new avenue to study the structure of the nucleon

exclusive reactions are experimentaly establishedmany different processes can and have been studied

BUT: not yet enough data to

deduce kinematic dependences of GPDsdetermine GPDs as accurate as standard PDFs

The transverse spin structure of the nucleon

nothing definite known till now

data from longitudinally polarized targets suggest

BUT: Collins versus Sievers

need data with transversely polarised targetsCOMPASS, HERMES, RHIC



� GPDs: new avenue to study the structure of the nucleon

exclusive reactions are experimentaly establishedmany different processes can and have been studied

BUT: not yet enough data to










� exclusive reactions are experimentaly established

� � many different processes can and have been studiedBUT: not yet enough data to












� deduce kinematic dependences of GPDs

determine GPDs as accurate as standard PDFs












� determine GPDs as accurate as standard PDFs













� The transverse spin structure of the nucleon













� nothing definite known till now













� data from longitudinally polarized targets suggest

� � � � � ��

� � �BUT: Collins versus Sievers











� data from longitudinally polarized targets suggest

� � � � � ��

� � �BUT: Collins versus Sievers

� need data with transversely polarised targets

� � COMPASS, HERMES, RHICE.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30

The Spin Structure of the NucleonThe Hunt for $displaystyle mathbf {L_q}$GPDs IntroductionGPDs Introduction IIDVCS $ep ightarrow e^{prime } gamma p$DVCS azimuthal asymmetriesDVCS at HERMESDVCS beam charge asymmetry (BCA)

DVCS single beam-spin asymmetry (BSA)Much more data!Exclusive PS meson production e p $ightarrow $ e$^prime $ n $pi ^+$How to extract exclusive $pi ^+$Exclusive $pi ^+$ target - SSAExclusive $pi ^+$ target - SSA-ResultsExclusive VM-production $e p ightarrow e^{prime } ho ^0/phi p$Exclusive $displaystyle mathbf {sigma _L}$ for $displaystyle mathbf {ho ^0}$-ProductionDeep Inelastic Scattering Cross SectionDIS and SIDIS Cross SectionTwist-2 Quark DF & FF{}... surviving $k_�ot $ integrationCharacteristics of TransversityHow can one measure TransversityFirst glimpse on Transversity?!Results$A^{sin phi }_{UL}$What does theory tell?Challenges in InterpretationResults from SMCSummary

where is the spin of the nucleon hidden?dvcs bethe-heitler (bh) γ + hermes, jlab: dvcs-bh...

Documents