Measurement of Spin Structure Functions at
Low to Moderate Q2 using CLAS
K.V. Dharmawardane for the CLAS Collaboration
Department of physics, Old Dominion University, Norfolk, VA 23529.
Abstract. Spin structure functions of the nucleon in the region of large x and small to moderate
Q2 continue to be of high current interest. A large experimental program to measure the spin
structure function g 1 and its first moment Γ1 has been concluded at Jefferson Lab. An overview
of the experiment and its kinematic coverage will be discussed. We will also show preliminary
results from the 5.7 GeV and the 1.6 GeV data sets.
INTRODUCTION
The inclusive doubly polarized electron-nucleon cross section for longitudinally polarized target and beam can be written as:
dσ
ΓT σT εσL PePt 1 ε 2A1σT cosψ 2ε 1 ε A2σT sinψ (1)
dΩdE where ΓT is the transverese flux factor, A1 and A2 are the virtual photon asymmetries,
ψ is the angle between the target spin and the virtual photon direction, σ T and σL are
the total absorption cross sections for transverse and longitudinal virtual photons and ε
is the polarization parameter of the virtual photon.
The asymmetry A for longitudinally polarized beam and target is given by:
A d σ dΩdE d σ dΩdE dσ
dΩdE
DA1 η A2 dσ
dΩdE
(2)
dσ
dσ
where dΩdE
( dΩdE ) is the differential cross section for the target spin antiparallel (parallel) to the beam helicity and D and η are:
D
1 ε E E
1 εR
η
ε Q2 E
1 ε E E
(3)
The spin structure function g1 is related to the virtual photon asymmetries A 1 and A2
by:
τ
1
A1 A2 F1 x Q2 (4)
g1 x Q2 1τ
τ
where F1 is the well known unpolarized structure function and τ
ν2
Q2 .
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
601
The first moment of the spin structure function g 1 , Γ1 Q2 g1 x Q2 dx, is a
quantity of great interest. At Q2 ∞ the proton neutron difference of Γ1 is given
by the celebrated Bjorken [1] sum rule, Γ1p Q2 Γn1 Q2 16 gA , where gA is the weak
axial coupling constant. The Bjorken [1] sum rule is based on quark current algebra and
has been verified at the level of 5% accuracy. It can be evolved to finite values of Q2
using pQCD and the Operater-Product-Expansion (OPE).
At the real photon point the Gerasimov-Drell-Hearn (GDH) [2, 3] sum rule predicts:
2 ∞
IGDH
8M
απ 2
σ12 σ32
ν
νthr
dν
14 κ 2
(5)
where κ is the target anomalous magnetic moment. As Q 2 0 the GDH [2, 3] sum
Q2
rule implies a negative slope for Γ1 , Γ1 Q2 2M
IGDH , which goes through a rapid
transition to the deep inelastic limit where it is sensitive to the nucleon spin fraction
carried by quarks. The interesting behavior in the transition region is dominated by
baryon resonance excitations [4]. Recently Ji and Osborn [5] have shown that chiral
perturbation theory can be used to calculate the GDH integral up to Q 2 01 GeV2 .
Further they point out the possibility of using lattice QCD to calculate the integral in
the region Q2 01 05 GeV2 . This is the domain where Jefferson Lab can play an
important role.
The focus of the EG1 experiment, which was carried out in Hall B at Jefferson
Laboratory, is on measuring Γ1 for the proton and deuteron (neutron) in the transition
region. These measurements complement the data at the photoabsorption point and in
the deep inelastic scattering region and cover a Q2 range of 005 Q2 45 GeV2 . This
opens up the possibility of studying the transition from hadronic to quark degrees of
freedom over a wide range of Q2 .
DATA ANALYSIS
A highly polarized electron beam, dynamically polarized 15 NH3 and 15 ND3 targets and
the CEBAF Large Acceptance Spectrometer (CLAS) in Hall B were used to accumulate
over 23 billion triggers with beam energies of 1.6, 2.5, 4.2 and 5.7 GeV. These data are in
addition to the three billion triggers recorded in 1998, the results of which are presented
elsewhere [6]. Calibration and analysis of the data are still under way. Here we present
the asymmetry analysis for the 1.6 and 5.7 GeV data.
In the asymmetry given in equation 2 many factors such as luminosity and acceptance will cancel out. Therefore the experimental raw counting asymmetry A raw can be
converted to the longitudinal electron asymmetry A by :
A Araw
;
Pb Pt f
Araw N N N N (6)
where N (N ) are the raw counting rates normalized to accumulated beam charge for
beam helicity antiparallel (parallel) to the target spin, f is the target dilution factor and
Pb and Pt are the beam and target polarizations.
602
normalized counts
x 10
-3
normalized ND3
0.25
15
simulated N background
deuteron
0.2
0.15
0.1
0.05
0
0.6
0.8
1
1.2
1.4
1.6
1.8
2
W(GeV)
FIGURE 1. The figure above compares the 15 ND3 , simulated 15 N background and deuteron invariant
mass spectra for 1.6 GeV data. The 15 N background has been simulated by the method described in the
text.
To remove the contribution from the 15 N in ammonia as well as the helium and foils
in the target we took extensive data on 12 C and 4 He at several different beam energies.
In addition we were able to take data on a solid 15 N target at some beam energies. The
12 C data were used to simulate the 15 N spectrum parameterizing the 15 N cross section
as a function of the 12 C cross section:
σn
σ15 N a b σ12C (7)
σD
Here σn and σD are the neutron and deuteron cross sections. The parameters a and b
were determined by fitting the limited statistics 15 N data with high statistics 12 C data.
Then a full background spectrum was simulated using the known thicknesses of foils
and the 4 He data. The resulting background spectrum was subtracted from the NH 3 and
ND3 spectra ( Figure 1) to obtain the target dilution factor.
The product of beam and target polarization was extracted by dividing the measured
elastic asymmetry by the product of dilution factor and the theoretical value of the
elastic asymmetry. This greatly reduces the systematic uncertainty of the beam and target
polarization. The product of beam and target polarization for the 1.6 GeV deuteron data
is 019 0004 which gives a target polarization of about 27%. For the 5.7 GeV deuteron
603
N(1650-80)S11/F15
0.4
N(1520-35)D13/S11
N(1440)P11
∆(1232)P33
Asymmetry
0.6
0.2
0
-0.2
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
W(GeV)
FIGURE 2. Preliminary asymmetry in de e¼ at E = 1.6 GeV for the Q 2 range 0.187-0.707 GeV 2 as a
function of invariant mass.
data elastic electron-proton coincidences were used to determine the product of beam
and target polarization to be 0209 0026.
The measured asymmetry for the deuteron at a beam energy of 1.6 GeV is shown in
Figure 2. The asymmetry is negative in the ∆1232 region as expected and is positive
for higher resonances. The asymmetry for the deuteron and proton at a beam energy
of 5.7 GeV is shown in Figure 3. The asymmetry is nearly zero in the ∆1232 region
because of the high Q2 , but becomes positive and large for higher resonances.
SUMMARY AND OUTLOOK
The EG1 experiment is dedicated to study the spin structure of the proton, neutron
and their excited states. The analysis of the data is still in progress but preliminary
asymmetries at beam energies of 1.6 and 5.7 GeV are shown in Figures 2 and 3.
Radiative corrections must still be applied and then g 1 and Γ1 will be extracted in the
near future. This enormous data set is expected to provide detailed information on the
spin structure of the proton and deuteron (neutron) over a large kinematic range in and
above the resonance region.
604
0.4
N(1680)F15
Asymmetry
0.6
N(1520)D13
∆(1232)P33
0.8
ed→e′X
0.2
0
-0.2
0.8
ep→e′X
0.6
0.4
0.2
0
-0.2
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
W(GeV)
FIGURE 3. Preliminary asymmetry in de e¼ (top) and pe e ¼ (bottom) at E = 5.7 GeV for the Q 2
range 1.31-4.16 GeV 2 as a function of invariant mass. The plot represent only 50% of the 5.7 GeV data
set.
ACKNOWLEDGEMENTS
This research is supported by the US Department of Energy under grant DE-FG0296ER40960
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V. Burkert and Z. Li, Phys. Rev. D47, 46 (1993).
X. Ji and J. Osborne, J. of Phys. G57, 127 (2001).
G.E. Dodge, these proceedings.
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