W-D. Nowak - INFN

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 1
The Angular Momentum Structure of the Nucleon
Perspectives in Hadronic Physics, May 12-16, 2008
Wolf-Dieter Nowak
DESY, 15738 Zeuthen, Germany
Wolf-Dieter.Nowak@desy.de

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 2
Table of Contents
⊲ 3-dimensional picture of the nucleon
⊲ Proton spin budget in a nutshell
⊲ DIS results: Quark & gluon contributions, QCD fits
⊲ Deeply Virtual Compton Scattering (DVCS)
⊲ Beam-charge and beam-spin asymmetries
⊲ Transverse target-spin asymmetries
⊲ Model-dependent constraints on J u vs. J d
⊲ Summary and Outlook

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 3
3-dimensional Picture of the Proton
Nucleon momentum in Infinite Momentum Frame: (p γ
∗ + p nucl ) z → ∞
• Form factor
y
• Parton density
δ z
⊥
xp
y
• Generalized parton
distribution at =0
δ z
⊥
xp
y
b ⊥
z
b ⊥
x
z
x
z
x
f ( x)
f ( x, b )
⊥
ρ( b ⊥
)
0
b ⊥
x
1
0
x
1
0
b ⊥
Nucleon’s transv.
charge distribution
given by 2-dim.
Fourier transform
of Form Factor:
⇒ Parton’s
transverse
localization b ⊥
Probability density to
find partons of given
long. mom. fraction x
at resol. scale 1/Q 2
(no transv. inform.)
⇒ Parton’s longitudinal
momentum distribution
function (PDF) f(x)
Generalized Parton Distrib. s
(GPDs) probe simultaneously
transverse localization b ⊥
for a given longitudinal
momentum fraction x.
2nd moment by Ji relation:
J q,g = 1 2 lim t→0
R
x dx
[H q,g (x, ξ, t) + E q,g (x, ξ, t)]

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 4
Proton Spin Budget in a Nutshell
NO unique and gauge-invariant decomposition of the nucleon spin:
(A) ‘GPD-based’:
1
2 = J q + J g = 1 2 ∆Σ + L q + ̂∆g + L g
Total angular momenta of quarks (J q ) and gluons (J g ) are
gauge-invariant and calculable in lattice gauge theory
Intrinsic spin contribution and orbital angular momentum are gauge
inv. for quarks ( 1 2 ∆Σ and L q), but not for gluons ( ̂∆g and L g )
Probabilistic interpretation only for 1 2∆Σ (well measured)
J q accessible through exclusive lepton nucleon scattering
J g very difficult to access experimentally
(B) Light-cone gauge:
1
2 = J q + J g = 1 2 ∆Σ + L q + ∆g + L g
All 4 terms have a probabilistic interpretation
∆g is gauge invariant (being measured)
⇒ Results from both decompositions must not be mixed, as
L q ≠ L q , ∆g ≠ ̂∆g, L g ≠ L g , even J g ≠ J g !

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 5
DIS: Kinematics, Cross Sections, Asymmetry
e
N
(E, p)
γ *
(E,
’
p ’)
u
q
u
d
h
h
π
Virtual-photon kinematics:
Q 2 = −q 2 ν = E − E ′
Fraction of nucleon momentum
carried by struck quark: x = Q2
2Mν
fraction of virtual-photon energy
carried by produced hadron h: z = E h
ν
π +
Hadron transverse momentum: P h⊥
Unpolarized cross section: σ UU ≡ 1 2 (σ →⇐ + σ →⇒ )
Cross section (helicity) difference: σ LL ≡ 1 2 (σ →⇐ − σ →⇒ )
Double-spin asymmetry: A || ≡ σ LL
σ UU
≃ g 1
F 1
(neglecting small g 2 contribution)
Measured asymmetry: A || =
1
〈P B 〉〈P T 〉
( N L ) → ⇐−( N
L ) → ⇒
( N L ) → ⇐+( N
L ) → ⇒
with P B (P T ) : longitudinal beam (target) polarization

Direct determination of quark spin contribution ∆Σ
Most precise g d 1 result: Hermes inclusive data [PRD75(2007)012007,hep-ex/0609039]:
x⋅g 1
d
0.03
0.02
HERMES
E143
E155
SMC
COMPASS
Method:
NNLO leading twist analysis in
MS scheme
0.01
assume SU 3 flavor symmetry in
hyperon decay
0
observe saturation of
Γ 1 = ∫ dx g d 1(x) for x < 0.04
-0.01
0.01 0.1 1.0
Data for Q 2 > 1 GeV 2 :
Result at Q 2 = 5 GeV 2 (all data points evolved):
∆Σ = 0.330 ± 0.011 theor. ± 0.025 exp. ± 0.028 evol.
x
assume no significant contribution
of small-x region
evaluate Γ d 1(Q 2 = 5 GeV 2 ) = 0.021
∫ 0.9 dx g
d
1 (x)
where ‘exp.’ includes stat., syst. and parameterization uncertainties
Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 6

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 7
0.5
0.4
0.3
0.2
0.1
Next-to-leading Order QCD Fits
Results by AAC [PRD74(2006)014015,hep-ph/0603213]: NLO in α s , MS scheme
0
0.001 0.01 0.1 1
0
-0.1
Q 2 = 1 GeV 2
x∆u v
(x)
x∆d v
(x)
DIS + π 0 (type 1)
DIS (AAC03)
-0.2
0.001 0.01 0.1 1
x
2
1
0
-1
0.001 0.01 0.1 1
0.01
0
-0.01
-0.02
-0.03
-0.04
DIS + π 0 (type 1)
DIS (AAC03)
x∆g(x)
x∆q(x)
0.001 0.01 0.1 1
x
Assumptions:
Flavor-symmetric ∆q sea
Integrals of ∆qu
val and ∆qd
val fixed
by weak decay constants F and D
Input experimental data:
A p,d
1
from COMPASS,JLAB,HERMES
A π0
LL
from PHENIX
Results at Q 2 = 1 GeV 2 :
∆Σ = 0.25 ± 0.10
∆G = 0.47 ± 1.08 (DIS alone)
∆G = 0.31 ± 0.32 (DIS+PHENIX)
Impact of recent CLAS and COMPASS data [PRD75(2007)074027,hep-ph/0612360]:
Fit with ∆g > 0 : ∆G = 0.13 ± 0.17 Fit with ∆g < 0 : ∆G = −0.20 ± 0.41
Impact of recent PHENIX and STAR data (Q 2 = 10 GeV 2 ) {DSSV, arXiv:0804.0422 [hep-ph]}:
Clear indication for flavor-asymmetric sea. For 0 < x < 1 : ∆G = −0.084
For 0.001 < x < 1 : ∆G = 0.013 with +0.106
−0.120 for ∆χ2 = 1; +0.702
−0.314 for ∆χ2 /χ 2 = 2%

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 8
Determination of Gluon Contribution to Nucleon Spin
High-p t hadron pairs or single hadrons quasi-real photoprod.: 〈Q 2 〉 ≈ 0.1 GeV 2
Sensitivity through γ ∗ g ‘direct’ hard scattering or ‘resolved-photon’ process
left graphs: direct processes; right graphs: resolved-photon processes [COMPASS analysis]
PGF
R
Extraction heavily relies on
PYTHIA simulation (LO only !)
0.3
0.2
0.1
0
QCDC
*
γ
g→qq
*
γ
q→qg
*
γ
q→q
Leading
qq’→qq’
qg→qg
gg→gg
low p
T
Processes:
Hard scale µ 2 ≃ 3 GeV 2
only ‘loosely’ correlated
with x g (〈x g 〉 ≃ 0.1)
COMPASS: Open-charm production (γ ∗ g → c¯c) and hadron pairs
HERMES: Single high-p t hadrons. Pairs in old analysis (all Q 2 , 〈x g 〉 ≃ 0.17
[PRL84 (2000) 2584] ∆g
g = 0.41 ± 0.18 stat ± 0.03 sys−exp (±unknown sys−Model )
RHIC: A LL in inclusive direct γ & π 0 production, inclusive jet production

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 9
Δ g/g
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-2
10
Results on Gluon Helicity Distribution ∆g
g (x)
COMPASS, open charm (this work)
COMPASS, high p
, Q
1 (GeV/c)
T
2
fit with
ΔG>0, µ
=3(GeV/c)
2
fit with
ΔG 1 GeV 2 (〈x g 〉 ≃ 0.13)
= 0.06 ± 0.31 stat ± 0.06 syst
∆g
g
{prel.: K.Kurek,DIS06,hep-ex/0607061}
COMPASS open charm:
∆g
g
= −0.47 ± 0.44 stat ± 0.15 syst
(〈x g 〉 ≃ 0.11) {arXiv:0802.3023[hep-ex]}
Q 2 ≃ 0; (〈x g 〉 ≃ 0.22): ∆g
g = 0.071 ± 0.034 stat ± 0.010 sys−exp ± 0.127
0.105 sys−Models
PHENIX: Confidence limits for fits with different ∆g
g
assumptions

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 10
Deeply Virtual Compton Scattering
e
e ′ e e ′ e e ′
γ
γ ∗ γ
γ
γ ∗ γ ∗
p p ′ p p ′ p p ′
(a)
Same final state in DVCS and Bethe-Heitler ⇒ Interference!
dσ(eN → eNγ) ∝ |T BH | 2 + |T DV CS | 2 + T BH T ∗ DV CS + T ∗ BHT DV CS
} {{ }
I
T BH is parameterized in terms of Dirac and Pauli Form Factors F 1 , F 2 ,
calculable in QED.
T DV CS is parameterized in terms of Compton form factors H, E, ˜H, Ẽ
(which are convolutions of resp. GPDs H, E, ˜H, Ẽ)
(Certain Parts of) interference term I can be filtered out by forming
certain cross section differences (or asymmetries)
(b)
⇒ GPDs H, E,
˜H, Ẽ indirectly accessible via interference term I

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 11
Azimuthal Asymmetries in DVCS
DVCS–Bethe-Heitler Interference term I induces differences or
azimuthal asymmetries A in the measured cross-section:
Beam-charge asymmetry A C (φ) [BCA] :
dσ(e + , φ) − dσ(e − , φ) ∝ Re[F 1 H] · cos φ
Beam-spin asymmetry A LU (φ) [BSA] :
dσ( → e , φ) − dσ( ← e , φ) ∝ Im[F 1 H] · sin φ
z
y
⃗ k
′
⃗ k
⃗q
⃗p γ
x
φ S
φ
uli
Long. target-spin asymmetry A UL (φ) :
dσ( ⇐ P , φ) − dσ( ⇒ P , φ) ∝ Im[F 1 ˜H] · sin φ [LTSA]
Transverse target-spin asymmetry A UT (φ, φ s ) [TTSA]:
dσ(φ, φ S ) − dσ(φ, φ S + π) ∝ Im[F 2 H − F 1 E] · sin (φ − φ S ) cos φ
+ Im[F 2 ˜H − F1 ξẼ] · cos (φ − φ S) sin φ
(F 1 , F 2 are the Dirac and Pauli elastic nucleon form factors)

HERMES Combined BSA & BCA Analysis
Various asymmetry amplitudes A contribute to polarized cross section σ LU :
σ LU (φ; P l , e l ) = σ UU (φ)[1 + e l A C (φ) + e l P l A I LU (φ) + P lA
DV CS
LU
L: longitudinally polarized lepton beam of charge e l & polarization P l ; U: unpolarized proton target
BCA: A C (φ) = 1
σ UU
c I 1 cos φ + · · ·
BSA (interference term): A I LU (φ) = 1
σ UU
s I 1 sin φ + · · ·
BSA (DVCS term):
DV CS
ALU (φ) = 1
DV CS
σ UU
s
(φ)]
c I 1 ∝ √ −t
Q F 1ReH + [· · · ]
s I 1 ∝ √ −t
Q F 1ImH + [· · · ]
1 sin φ (small at HERMES energy)
Unpolarized cross section: σ UU = σ BH + σ DV CS + σ I
F 1 : Dirac elastic nucleon form factor
H : Compton Form Factor (CFF), embodies GPD H
[· · · ] : kinematically suppressed CFFs ( ˜H, E) embodying GPDs ˜H, E
Fit to data: A C (φ) = ∑ 3 nφ
n=0
Acos
C
A I LU (φ) = ∑ 2
A
DV CS
LU
m=1
Asin
mφ
LU,I
cos nφ
sin mφ
(φ) = A sin φ
LU,DV CS sin φ
Fit results: ‘effective’ asymmetry amplitudes: A
cos nφ
C
, A
sin mφ
LU,I
, Asin φ
LU,DV CS
⇒ well defined in theory, can be compared to GPD models !
Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 12

HERMES Combined BSA & BCA Results
cos 0φ
LU,DVCS
A
sin φ
LU,DVCS
A
sin 2φ
LU,DVCS
A
Res. frac
0.2
0
-0.2
0.2
0
-0.2
-0.4
0.4
0.2
0
-0.2
0.4
0.3
0.2
0.1
0
3.4 % scale
uncertainty
overall
0.2
0
-0.2
0.2
cos 0φ
LU,I
0
A
-0.2
-0.4
0.4
0.2
sin φ
LU,I
A
0
-0.2
0.4
0.2
0
-0.2
HERMES PRELIMINARY
3.4 % scale
uncertainty
0 0.2 0.4 0.6
0
-0.2
-0.4
-0.6
0 0.2 0.4 0.60 0.2 0.1 0.4 0.2 0.6 0.3
0.4
0.4
0.2
0
0.3 0
0.3
0.2
0.2 0
-0.2
0.1 -0.2
0.1
0
0 0.2 0.4 0.6 0
-0.2
-0.4
-0.4
2
sin 2φ
LU,I
A
Res. frac
0.4
0.3
0.2
0.1
0
overall
0.4
0.2
0
-0.2
0
-0.2
-0.4
-0.6
cos 0φ
C
A
-t[GeV
0.2
0
-0.2
0.2
0
-0.2
-0.4
0.4
0.2
0
-0.2
]
VGG Regge, D
VGG Fact., D
HERMES PRELIMINARY
0.1 0.2 0.3
0.2
0
-0.2
0.2
0
-0.2
-0.4
0.4
0.2
0
-0.2
Dual Regge/Fact.
2 4 6 8 10
0.1 2 0.24 6 0.3 8 10 2 4 6 8 10
0.4
0.2
VGG Regge, D
0
HERMES 0.3 PRELIMINARY
VGG Regge, no D
0.2
0
0.2
0
0
0.1
-0.2
-0.2
0.1 0.3
0
-0.2
-0.4
x b
2 4
-0.2
6 8-0.4
2
10
2
0 0.2 0.4 0.6
0.4
0.4
0.2
0.2
0.3
0.3
0.2
0.2
0
0
0.1
0.1
0
0
0-0.2
0.2 0.4 -0.2 0.6
2
0.1
0.1
cos φ
C
A
cos 2φ
C
A
cos 3φ
C
A
c
0
-0.1
-0.2
0.1
0
-0.1
-0.2
-t[GeV
0
-0.1
-0.2
0.1
0
-0.1
-0.2
0.4
0.2
0
-0.2
0
-0.2
-0.4
-0.6
]
VGG Regge, no D
VGG Fact., no D
-0.2
Q [GeV
0.1 0.2 0.3
0.4
0.2
0.3
0.2
0
0.1
0
0.1 0.2 -0.2 0.3
0.1 x b
0 0.2 0.4 0.6
0 0.2 0.4 0.6
0 0.2 0.4 0.6
0
-0.1
-0.2
0.1
0
0.4
0.2
0
0
-0.2
-0.4
-0.6
]
Dual Regge
Dual Fact.
2 4 6 8 10
2 4 6 2
-0.2
0.1
10 2
0.1 0.2 0.3
0.1 0.2 0.3
0.1 0.2 0.3
0.2
Dual Regge
Q [GeV
-0.1
-0.1
0 < −t < 0.7 0.03 < x
-0.2 B < 0.35 1 < Q 2 < 10
-0.2
Wolf-Dieter Nowak, 0.4
0.4
0.4
Perspectives 0.4 in Hadronic Physics, May 15, 2008 – p. 13
0
-0.2
0.2
0
-0.1
-0.2
0.1
]
BSA
const.term
∝ F 1 ImH
Dual Fact.
2 4 6 8 10
2 4 6 8 10
2 4 6 8 10
BCA
∝ −A cos φ
C
∝ F 1 ReH
HT
HT

Discussion of Combined BSA & BCA Analysis
!!! Asymmetries of ‘associated (resonance) production’ are unknown !!!
Kinematic dependence of fractions of associated production known from MC:
Average is 12%
Assoc. Prod. (%)
30
20
10
0.5
0 0.2 0.4 0.6
-t (GeV 2 )
0 0.1 0.2 0.3
xB
⇒ In data associated production is part of the signal,
while in models it is not included (still unknown)
5 0 2 4 6 8 10
Q 2 (GeV 2 )
HERMES BSA agrees with Dual model Guzey,(Polyakov),Teckentrup 2006
VGG model Vanderhaeghen, Guichon,Guidal 1999 clearly undershoots HERMES BSA
(Improvement recently proposed Polyakov,Vanderhaeghen arXiv:0803.1271 [hep-ph])
HERMES BCA disfavours factorized t dep., in both models and D-term in VGG
Pure |DVCS| 2 asymmetries found compatible with zero (as models assume)
⇒ HERMES data precise enough to discriminate between models or their variants
⇒ new models eagerly awaited !!!
Müller,Kumericki
Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 14

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 15
Why TTSA Data Expected to be Sensitive to J q
A UT (φ, φ S ) ∝ Im[F 2 H − F 1 E] sin (φ − φ S ) cos φ + Im[F 2 ˜H − F1 ξẼ] cos (φ − φ S) sin φ
ANSATZ: spin-flip Generalized Parton Distribution E is parameterized as follows:
Factorized ansatz for spin-flip quark GPDs: E q (x, ξ, t) =
E q(x,ξ)
(1−t/0.71) 2
(
t-indep. part via double distr. ansatz: E q (x, ξ) = Eq DD
x
(x, ξ) − θ(ξ − |x|)D q ξ
using double distr. K q : E DD
q (x, ξ) =
1∫
−1
dβ
1−|β|
∫
−1+|β|
with K q (β, α) = h(β, α) e q (β) and e q (x) = A q q val (x) + B q δ(x)
based on chiral QSM
where coeff.s A, B constrained by Ji relation, and
A u , A d , B u , B d are functions of J u , J d
⇒ J u , J d are free parameters when calculating TTSA
dα δ(x − β − αξ) K q (β, α)
+1 ∫
−1
dx e q (x) = κ q
Sensitivity to J u (with J d = 0) studied [EPJ C46, 729 (2006), hep-ph/0506264]
)

-0.15 -0.1 -0.05 0 0.05 0.1 0.15
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
0 0.5 0 0.2
0 5 10
0 0.5 0 0.2 0 5 10
0 0.5
0 0.5
0 0.2
0 0.2
0 5 10
Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 16
HERMES: First Measurement of TTSA
A UT (φ, φ S ) = A sin (φ−φ S ) cos φ
UT
A C
cosφ
0.4
0.2
· sin (φ − φ S ) cos φ + A cos (φ−φ S) sin φ
UT
· cos (φ − φ S ) sin φ + ...
PRD75, 011103
this work
DD:Fac,D
DD:Fac,no D
DD:Reg,D
DD:Reg,no D
0
A C
cosφ
0.4
0.2
Dual:Reg
Dual:Fac
0
sin(φ-φ
A s
)
UT
0.2
0
8.1% scale uncertainty
A UT, DVCS
J u
=0.6
0.4
0.2
A UT, I
J u
=0.6
0.4
0.2
-0.2
sin(φ-φ
A s
)cosφ
UT
0.2
0
-0.2
8.1% scale uncertainty
-0.4
overall
0 0.2 0.4 0.6
-t (GeV 2 )
0 0.1 0.2 0.3
x B
5 0 2 4 6 8 10
Q 2 (GeV 2 )

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 17
J u
1
0.5
0
-0.5
Model-dependent constraints on J u vs J d
HERMES Dual
DFJK
JLab DD
QCDSF
LHPC
HERMES DD
-1
-1 -0.5 0 0.5 1
J d
HERMES analysis method:
[arXiv:0802.2499, subm. to JHEP]
Unbinned maximum likelihood fit
to all possible azimuthal asymmetry
amplitudes at average kinematics:
⇒ ‘combined fit’ of HERMES BCA
and TTSA data against various model
calculations, leaving J u and J d
as free parameters ⇒ model-dep.
1-σ constraints on J u vs. J d :
Double-distribution model: J u + J d /2.8 = 0.49 ± 0.17(exp tot )
[Vanderhaghen,Guichon,Guidal]
Dual model [Guzey, Teckentrup]: J u + J d /2.8 = −0.02 ± 0.27(exp tot )
Lattice gauge theory: QCDSF [Göckeler et al.], LHPC [Hägler et al.]
DFJK model: zero-skewness GPDs extracted from nuclear form factor
data using valence-quark contributions only [Diehl et al.])

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 18
Summary and Outlook
⊲ No unique and gauge-invariant decomposition of the nucleon spin
⊲ HERMES and COMPASS results on Deep Inelastic Scattering yield intrinsic
quark and gluon contribution to the nucleon spin (in light-cone gauge)
⊲ Total angular momenta of quarks and gluons accessible in context of
Generalized Parton Distributions
⊲ Deeply Virtual Compton Scattering is prime candidate to constrain total
quark angular momenta (no feasible approach known for gluons)
⊲ Pioneering HERMES results on azimuthal asymmetries, and first promising
JLAB results on cross section differences in DVCS, allow us to severely
constrain GPD models
⊲ Increasing theoretical activities on improved and new GPD models
⊲ Short-term future: for DVCS and other exclusive reactions final HERMES
results and many more very precise JLAB 6 GeV data expected
⊲ Medium-term future: hopefully unique COMPASS BCA data, presumably
many very precise JLAB 12 GeV data

Back-up Slides
Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 19

d 4 σ
d 4 Φ > |BH2 | → BSA and Im I/|BH 2 | are not exactly the same over Φ
Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 20
Lab E00-110 Scaling Test of DVCS Cross Section
5.75 GeV e − beam (76% pol.), unpol. LH 2 target, [PRL 97 (2006) 262002]
Detect e ′ by HRS, γ by EM calorimeter, recoil p by scintillator array
3 different kinematic settings with x Bj = 0.36 fixed:
Q 2 = 1.5, 1.9, 2.3 GeV 2 . For each: −t = 0.17, 0.23, 0.28, 0.33 GeV
Measured separately: d4 Σ
d 4 Φ = 1 2 [ d4 σ +
d 4 Φ
⇒ distinct information on GPDs:
d 4 Σ
∝ Im I: as in BSA numer.
d 4 Φ
d 4 σ
d 4 Φ
∝ Re I: same as in BCA
Fit following terms separately:
|BH 2 | (dot-dot-dashed),
twist-2 int. term (dashed),
twist-3 int. term (dot-dashed)
(|DV CS| 2 found below few %)
Twist-3 terms small
− d4 σ −
d 4 Φ ] and d4 σ
d 4 Φ = 1 2 [ d4 σ +
d 4 Φ
+ d4 σ −
d 4 Φ ]

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 21
LAS E01-113: High-stat. Beam-spin Asymmetry
1st dedicated Hall-B DVCS exp’t: 5.76 GeV e − beam, pol. 76-82%; unpol. LH 2
CLAS spectrometer upgraded by inner calorimeter to detect γ’s at small angles
→ all 3 final state particles (e ′ N γ) detected !
Broad kinematic coverage at medium x (0.1...0.5), combined with high lumi
→ 3-dim. binning possible. Unpublished (White Paper) preview:
)
2
2
One single (x ,Q ) bin
B
2
One (x ,Q ,t) bin out of five
B
(GeV
2
Q
4
3
2
1
0.1 0.2 0.3 0.4 0.5
x B
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
A LU
2
1.5