where is the spin of the nucleon hidden?dvcs bethe-heitler (bh) γ + hermes, jlab: dvcs-bh...
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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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 2
-
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�
� ��
�� ��� � � ��� �
�
! "# $
�
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 2
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 3
-
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
Distribution Function
Distribution Function
P P’
qq q
q q
x−ξ +ξ +1-1 0
q
P P’
q q
GPDGPD GPD
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 5
-
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 PDFs� � � � � and � � �� ��� � � � � � � � � � � ���
� � ��� � � � � � � � � � ��� ���
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
Distribution Function
Distribution Function
P P’
qq q
q q
x−ξ +ξ +1-1 0
q
P P’
q q
GPDGPD GPD
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 5
-
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 PDFs� � � � � and � � �� ��� � � � � � � � � � � ���
� � ��� � � � � � � � � � ��� ���
�
� � �� do NOT appear in DIS� � New 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
Distribution Function
Distribution Function
P P’
qq q
q q
x−ξ +ξ +1-1 0
q
P P’
q q
GPDGPD GPD
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 5
-
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 PDFs� � � � � and � � �� ��� � � � � � � � � � � ���
� � ��� � � � � � � � � � ��� ���
�
� � �� do NOT appear in DIS� � New Info !
� Study GPDs
with 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
Distribution Function
Distribution Function
P P’
qq q
q q
x−ξ +ξ +1-1 0
q
P P’
q q
GPDGPD GPD
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 5
-
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 PDFs� � � � � and � � �� ��� � � � � � � � � � � ���
� � ��� � � � � � � � � � ��� ���
�
� � �� do NOT appear in DIS� � New Info !
� Study GPDs
� with spin observablessingle spin azimuthal asymmetries
azimuthal asymmetriesvia cross sections
qqx = ξ
Distribution q(x)Antiquarkξ = 0
Quark Distribution q(x)
H ( x , , t=0)ξu
P P’
qq
Distribution Function
Distribution Function
Distribution Function
P P’
qq q
q q
x−ξ +ξ +1-1 0
q
P P’
q q
GPDGPD GPD
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 5
-
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 PDFs� � � � � and � � �� ��� � � � � � � � � � � ���
� � ��� � � � � � � � � � ��� ���
�
� � �� do NOT appear in DIS� � New Info !
� Study GPDs
� with spin observablessingle spin azimuthal asymmetries
� azimuthal asymmetries
via cross sections
qqx = ξ
Distribution q(x)Antiquarkξ = 0
Quark Distribution q(x)
H ( x , , t=0)ξu
P P’
qq
Distribution Function
Distribution Function
Distribution Function
P P’
qq q
q q
x−ξ +ξ +1-1 0
q
P P’
q q
GPDGPD GPD
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 5
-
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 PDFs� � � � � and � � �� ��� � � � � � � � � � � ���
� � ��� � � � � � � � � � ��� ���
�
� � �� do NOT appear in DIS� � New Info !
� Study GPDs
� with spin observablessingle spin azimuthal asymmetries
� azimuthal asymmetries
� via cross sections
qqx = ξ
Distribution q(x)Antiquarkξ = 0
Quark Distribution q(x)
H ( x , , t=0)ξu
P P’
qq
Distribution Function
Distribution Function
Distribution Function
P P’
qq q
q q
x−ξ +ξ +1-1 0
q
P P’
q q
GPDGPD GPD
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 5
-
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]
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 6
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 7
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 8
-
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
�� ��
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 9
-
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 !
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 12
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 13
-
How to extract exclusive ��
� Production mechanismen: ��� � � �
��� � �� �
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
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 13
-
How to extract exclusive ��
� Production mechanismen: ��� � � �
��� � �� �
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
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 13
-
How to extract exclusive ��
� Production mechanismen: ��� � � �
��� � �� �
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
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 mass� � �
Problematic: difference in relative contribution of resonant andnon-resonant channels to , yield
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 13
-
How to extract exclusive ��
� Production mechanismen: ��� � � �
��� � �� �
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
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 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:
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 14
-
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:
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 14
-
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:
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 14
-
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 by � � � � � �
but
� � � ���
HERMES:
��� � � 0.17
Target Spin Asymmetry:
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 14
-
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 by � � � � � �
but
� � � ���
HERMES:
��� � � 0.17
� Target Spin Asymmetry:
��� � � � ��
� ��� � �� � � � � � � � �
� � � � � � � � � ��
� ��� � �� � � � � � � � �
� � � � � � � � � � � �� �� � �� � � � ��� � �
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 14
-
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
� � � � �
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 15
-
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 �
�
� � �
�� � � � �
�
�
�
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 16
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 18
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 20
-
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
;�� integration
� The others are sensitive to intrinsic �;� � in the nucleon
& in the fragmentation process
: Sivers DF : std. unpol FF: transversity : Collins FF
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 20
-
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
;�� 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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 21
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 22
-
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 ODD
� No Access in Inclusive DIS !!!
L
R
R
L
NEED another chiral-odd object!
semi-inclusive DIS Collins FF
RL
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 22
-
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 ODD
� No Access in Inclusive DIS !!!
L
R
R
L
NEED another chiral-odd object!
semi-inclusive DIS Collins FF
RL
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 22
-
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 ODD
� No Access in Inclusive DIS !!!
L
R
R
L
NEED another chiral-odd object!
� semi-inclusive DIS � ��� Collins FF
RL
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 22
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 24
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 25
-
� � � � ��
-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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 26
-
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’
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 27
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 28
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 28
-
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� � ��� � � > � !� ( � � �� 7 *�
+ ,� 2 � � 9 :( �2 � 4 � :�3< � � � ��� � � = � !� ( � � �� 7 *�
+ ,� 2 � 9 :( �2 � 4 6 � 9 : � < �
x
y
z
φS
φ
~phad
~S⊥
~k
~k′
~q
uli
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 28
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 29
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30
-
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30
-
Summary� Orbital Angular Momentum ���
� GPDs: new avenue to study the structure of the nucleon
� exclusive reactions are experimentaly established
� � many different processes can and have been studiedBUT: 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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30
-
Summary� Orbital Angular Momentum ���
� GPDs: new avenue to study the structure of the nucleon
� 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
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30
-
Summary� Orbital Angular Momentum ���
� GPDs: new avenue to study the structure of the nucleon
� 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
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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30
-
Summary� Orbital Angular Momentum ���
� GPDs: new avenue to study the structure of the nucleon
� 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
� 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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30
-
Summary� Orbital Angular Momentum ���
� GPDs: new avenue to study the structure of the nucleon
� 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
� 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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30
-
Summary� Orbital Angular Momentum ���
� GPDs: new avenue to study the structure of the nucleon
� 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
� 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
E.C. Aschenauer 2003 CTEQ Summer School – Lecture II 30
-
Summary� Orbital Angular Momentum ���
� GPDs: new avenue to study the structure of the nucleon
� 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
� 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 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
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