1. Studies of Spin-Orbit Correlations with CLAS
Harut Avakian (JLab)
Deep PWG, Genova, Feb 27
H. Avakian, DPWG, Feb 27

2. Outline Physics motivation Spin asymmetries from eg1: Summary
spin-orbit correlations and widths of PDFs
Spin asymmetries from eg1:
A1 measurements for pions
Extraction of g1 width from pi+ data
Summary
After an introduction of main transverse momentum dependent parton distributions
accessible with transverse target, I’ll discuss run conditions, CLAS configurations and
Projected results. In the end I’ll present one example of extraction of the Sivers function from
Projected measurements.
H. Avakian, DPWG, Feb 27

3. Transverse Momentum Dependent (TMD) Distributions
Quark polarization
kT – leads to 3D description with 8PDFs
Real and imaginary parts of the DL≠0 interference contributions
Nucleon polarization
Factorization of kT-dependent PDFs proven at low PT of hadrons (Ji et al)
As discussed in the previous presentation, the introduction of the transverse momentum of quarks,
leads to addition transverse degrees of freedom for already existing collinear parton distributions
Describing the momentum, helicity and transversity distributions and appearance of 5 new TMD pdfs.
Columns in the table show the polarization of the parent nucleon and rows show polarizations of corresponding parton distributions. All off diagonal PDFs describe interference of wavefunctions with different orbital momenta.
The new distribution appearing in particular for the longitudinally polarized target, related to the
transversely polarized quarks in the longitudinally polarized nucleon describes the real part of the overlap of wave function, while the BM distribution discussed in previous presentation represents its imaginary part.
In the factorized picture proved to work for SIDIS at low P_T of hadrons, two structure functions defining the cross section in the leading order factorize respectively to convolution of distribution and fragm. Functions, where
D_1 is the unpolarized fragmentation function and H_q the Collins pol. FF.
While the contribution involving the helicity distribution was in the focus recent decades, not much is known about the term involving the transverse spin distribution which is the main focus of the current proposal.
In addition there are two more structure functions, which in case the factorization works will have contributions from all 4 functions listed here, coupled to some twist-3 distribution and fragmentation functions. While I’ll not covere the higher twist effects in this presentation we will measure also them and expect to get important info out of them as well.
Factorization is a major issue and not only for higher twist structure functions but also for
Leading order contribution as the energies we use to study them are relatively low.
One observable that was suggested to check the factorization of the polarized structure
Function was the the P_T-dependence of the double spin asymmetry.
Twist-3
H. Avakian, DPWG, Feb 27

4. Polarized Semi-Inclusive DIS
Cross section is a function of scale variables x,y,z
U unpolarized
L long.polarized
T trans.polarized z
H. Avakian, DPWG, Feb 27

5. CLAS configurations with long.polarized target
ep→e’pX
Inner Calorimeter e p- p+
CLAS detector is uniquely positioned to satisfy requirements of large x coverage and wide acceptance coverage crucial for separation of different azimuthal moments.
Shown here is a typical SIDIS event with scattered electron detected in the detector and
Identified by its signals in the cherenkov -> and calorimeter.
You can see also radiated photon and charged pions.
Detection of multiparticle final states in wide range of kinematics, crucial for understanding of background processes. The most prominent being the diffractive rho-0 production.
Both target and mini-torus will be located upstream.
HD-Ice target (crucial for this experiment) located upstream to increase pi0 detection with ~70cm consistent with DVCS Measurements.
The suggested configuration will require measurements with different orientations of spins of H and D to minimize systematics from acceptance. 15days of polarized only D combined with D from 25 days of hydrogen running will provide comparable error bars for H and D.
Additional 5 days will take measurements with pure H,D and empty targets to keep under control the dilution factors for H and D.
Polarizations:
Beam: ~80%
NH3 proton 80%
Polarized NH3/ND3 (no IC, ~5 days)
Polarized NH3 with IC 60 days
H. Avakian, DPWG, Feb 27

6. Target fragmentation in SIDIS
Use PEPSI MC to define the kinematic region where the partonic description works
Pions from target fragments mainly at low energies, small z and PT
H. Avakian, DPWG, Feb 27

7. SSA with Longitudinal Target
quark polarization
Higher twist in fragmentation/or distribution
In jet SIDIS only contributions ~ D1 survive
With H1┴ (p0)≈0 (or measured) Target (Beam) SSA can be a valuable source of info on HT T-odd distribution functions
H. Avakian, DPWG, Feb 27

8. Polarized target: HERMES vs CLAS at 5.7GeV
ep → e’ p+ X ( Ee =5.7 GeV, MX > 1.1)
x dependence of CLAS A1p (A┴=0) consistent with HERMES data
Du/u from CLAS EG1 is consistent with GRV(GRVS) PDFs
H. Avakian, DPWG, Feb 27

9. A1-kinematic dependences
inbending
outbending
Ratio to inclusive asymmetry will account the x-dependence
H. Avakian, DPWG, Feb 27

10. A1 PT-dependence in SIDIS
m02=0.25GeV2
mD2=0.2GeV2
M.Anselmino et al hep-ph/
Como-2005
constituent quark model (Pasquini et al).
In perturbative limit predicted to be constant
p+ ALL can be explained in terms of broader kT distributions for f1 compared to g1
H. Avakian, DPWG, Feb 27

11. Helicity distributions: Diquark model
Jakob, Mulders, Rodrigues, Nucl. Phys. A 1997 q Dq
Du/u
(dipole formfactor), J.Ellis, D-S.Hwang, A.Kotzinian
JMR model
MR, R=s,a
Indeed the k
For given x the sign of the polarization is changing at large kT
Difference in q+=f1+g1 (quark aligned with proton spin) and q-=f1-g1 - (anti-aligned) kT-dependences may lead to observable effects
H. Avakian, DPWG, Feb 27

12. A1 PT-dependence in SIDIS
0.4<z<0.7
M.Anselmino et al hep-ph/
m02=0.25GeV2
mD2=0.2GeV2
more data in 2009!
p+ A1 suggests broader kT distributions for f1 compared to g1
p- A1 may require non-Gaussian kT-dependence for different helicities and/or flavors
H. Avakian, DPWG, Feb 27

13. cosf moment in A1-PT-dependence
hep-ph/
m02=0.25GeV2
mD2=0.2GeV2
CLAS PRELIMINARY
PT-dependence of cosf moment of double spin asymmetry is most sensitive to kT-distributions of quarks with spin orientations along and opposite to the proton spin.
H. Avakian, DPWG, Feb 27

14. Extracting widths from ALL
Assuming the widths of f1/g1 x,z and flavor independent
Anselmino et al
Collins et al
Fits to unpolarized data
H. Avakian, DPWG, Feb 27

15. A1 PT-dependence
Anselmino
Collins
CLAS data suggests that width of g1 is less than the width of f1
H. Avakian, DPWG, Feb 27

16. Summary
double spin asymmetries measured at CLAS are consistent with HERMES and fits to world data, assuming the factorized picture
PT-dependence of the double spin asymmetry provides access to kT-widths of transverse momentum dependent distributions of quarks.
CLAS data suggests that the kT-width of the momentum distribution is wider than the width of the helicity distribution
The suggestions of the review committee have been applied and the
analysis note has been prepared for the next round of review.
H. Avakian, DPWG, Feb 27

17. Support slides….
H. Avakian, DPWG, Feb 27

18. IC Experimental Setup (CLAS EG1+IC) Polarized target (eg1)
solid NH3 polarized target
proton polarization ~80%
high lumi ~ 21034 s-1cm-2
13o
50o
Major componnents of the proposed experimental setup are the
Polarized target used in the Eg1 run with polarized solid ammonia (${}^{14}$NH$_{3}$),
polarized via Dynamic Nuclear Polarization, which requires cooling the target
to 1 K, and holding it in a uniform ($\Delta B/B=10^{-4}$) magnetic field of 5T.
The polarized target magnetic field shields
the detector from the Moller electrons produced in the target by focusing
them onto the beam line, allowing lumi as high as 2x10^34
The IC designed for the e1-DVCS experiment, used with polarized target will
significantly increase the kinematic coverage for the direct detection of high-energy photons
from the decay of high momentum $\pi^0$.
**The target polarization direction will bereversed many times during the experiment by changing the frequency
**of the microwaves used to polarize the target.
**The cooling system is a ${}^{4}$He evaporation refrigerator.
**The ${}^{4}$He, $N$, and Al endcap contributions to the cross sections and asymmetries will be
**determined using data from the ${}^{12}C$ and empty cell targets.
**Approximately 7 daysof running on these targets will be needed for accurate measurements of the dilution factor **and background asymmetries. For a more accurate determination of the product of target and beam polarizations, **$P_e P_t$, we will use the well-known $ep$ elastic scattering asymmetry, as was done in Eg1b.
**To minimize radiation damage to the target the beam will be rastered over the target surface in a spiral pattern.
** The beam motion is indirectly recorded in the data stream by storing the ADC values of the raster magnet.
** M{\o}ller electrons, which are the vastly dominating source of electromagnetic background, will pass through the ** central penetration in the lead-tungstate wall, and be absorbed in the downstream shielding pipe. The shielding
** arrangement is very similar to the one used during Eg1. IC
Inner Calorimeter (424 PbWO4 crystals) for the detection of high energy photons at forward lab angles (e1-DVCS).
H. Avakian, DPWG, Feb 27

19. Collinear Fragmentationp
quark
Collinear Fragmentation
The only fragmentation function at leading twist for pions in eN→e’pX is D1(z)
Ee =5.7 GeV
No significant variation observed in z distributions of p+ for different x ranges (0.4<z<0.7, MX>1.5) and for A1p as a function of PT
H. Avakian, DPWG, Feb 27

20. p0 multiplicities ep→e’p0X
M.Aghasyan
DSS (Q2=2.5GeV2)
DSS (Q2=25GeV2)
p0 multiplicities consistent with SIDIS predictions
H. Avakian, DPWG, Feb 27

21. sinf SSA analysis for pi0
Measure both for 3 pions and combine to separate different contributions.
With H1┴ (p0)≈0 (or measured) Target (Beam) SSA can be a valuable source of info on HT T-odd distribution functions
H. Avakian, DPWG, Feb 27

22. Dilution factor in SIDIS
Fraction of events from polarized hydrogen in NH3
Nu,Np -total counts from NH3 and carbon normalized by lumi
ru, rp -total areal thickness of hydrogen (in NH3), and carbon target
Cn=Nitr/Carbon ratio (~0.98)
Diff. symbols for diff x-bins p-
Nuclear targed introduces in addition to significant nuclear background, also attennuation effects, which have to be studied separately.
Multiple scattering and attenuation in nuclear environment introduces additional PT-dependence for hadrons
H. Avakian, DPWG, Feb 27