Precision Measurement of Neutron Asymmetry
An1 in the Valence Quark Region
Xiaochao Zheng for The Jefferson Lab Hall A Collaboration
£ Massachusetts Institute of Technology, Cambridge, MA 02139
Address: Jefferson Laboratory, 12000 Jefferson Avenue, MS 16B, Newport News, VA 23606
Email: [email protected]
Abstract. We have measured the neutron virtual photon asymmetry A n1 over the kinematic range
033 x 061 and 27 Q 2 49 (GeV/c)2 . To extract An1 , longitudinal and transverse spin
asymmetries have been measured for inclusive 3Hee e¼ scattering, using a 5.7 GeV longitudinally
polarized electron beam at Jefferson Lab and a high-density polarized 3 He target in Hall A. Preliminary results of A n1 are presented and compared to existing data and various models, including the
predictions of SU(6), broken SU(6) constituent quark models, perturbative QCD based models and
chiral soliton model.
AN1 AT LARGE X
In the scattering of polarized electrons on a polarized target, the virtual photon asymmetry A1 is defined as
A1
σ12 σ32
σ12 σ32
(1)
where σ12 32 is the total virtual photoabsorption cross section for the nucleon with a
projection of 12 (32) for the total spin along the direction of photon momentum. A 1
can be expressed as a ratio of the polarized structure functions g1 , g2 and the unpolarized
structure function F1 as
A1
g1 x Q2 γ 2 g2 x Q2 F1 x Q2 (2)
with γ 2 4M 2 x2 Q2 a kinematic factor, M the nucleon mass, x xB j the Bjorken
variable, and Q2 the four momentum transfer squared.
To first approximation, the constituent quarks in the nucleon are described by SU(6)
wavefunctions as
n «
«
«
1 ¬¬
1 ¬
1¬
d ud S0 ¬d ud S1 ¬d ud S1
2
3
18 ¬
¬
«
«
13 ¬u dd S1 32 ¬u dd S1
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
610
(3)
where the subscript S denotes the total spin of the diquark state. In this limit where SU(6)
is an exact symmetry, both diquark spin states S 1 and S 0 contribute equally to the
observables of interest, leading to the predictions A 1p 59 , An1 0.
However, the SU(6) symmetry is known to be broken. A natural SU(6) symmetry
breaking mechanism based on phenomenological arguments is the hyperfine interaction
among the quarks, described as Si S j δ 3 ri j , where Si is the spin of ith quark. The effect
of this perturbation on the wavefunction is to lower the energy of the S 0 ’diquark’.
This allows the d-quark in the first term of Eq.(3), which has its spin parallel to that of
the neutron, to dominate the high energy tail of the quark momentum distribution that
is probed as x 1. The dominance of this term as x 1 leads to A 1p 1, An1 1.
Hyperfine interaction has been incorporated in the constituent quark model (CQM) in
which A1p and An1 have been calculated in the large x region [1].
Another approach focuses directly on relativistic quarks. Farrar and Jackson [2] in
the early 1970’s, noted that at x 1, the scattering is from a high energy quark, and
the process can be treated perturbatively. They proceeded to show that a quark carrying
nearly all the momentum of the nucleon (i.e. x 1) must have the same helicity as
the nucleon. This is known as hadron helicity conservation. Quark-gluon interactions
cause only the S 1, Sz 1 diquark spin projection component, rather than the full
S=1 diquark system to be suppressed as x 1. This gives d u 0, du 15 as
x 1. Consequently, they obtained the previous limiting value for both the proton and
the neutron, namely A1n p 1 for x 1. This is one of few places where QCD can
make an absolute prediction for the x dependence of the structure functions (here a
ratio of structure functions). How low in x and Q 2 this picture will work is uncertain.
Using this perturbative QCD (pQCD) prediction, A n1 can be calculated from polarized
and unpolarized parton distributions, for example, LSS(BBS) parameterization [3]. An1
have also been calculated using LSS parameterization without pQCD constraint [4].
In addition to SU(6), constituent quark models and pQCD based models, there are
a few other models which can give a prediction for An1 at large x, including statistical
model [5] and local duality method [6]. In contrast to other theories, the chiral soliton
model [7] and the instanton model [8] predict the possibility that A n1 can be negative at
large x. All world data for An1 at x 04 have poor statistics and even cannot determine
the sign of An1 . Therefore, high precision data on An1 at large x are greatly needed.
THE EXPERIMENT E99-117
The experiment E99-117 [9] was carried out in Hall A at JLAB in the summer of 2001
to measure An1 in the x region 033 x 061. The kinematics are shown in Table 1. To
TABLE 1. E99-117 kinematics
xB j
0.331 0.474 0.609
Q2 (GeV/c)2 2.738 3.567 4.887
W2 (GeV/c)2 6.426 4.846 4.023
measure An1 , the asymmetries A and A of polarized e scattering off a polarized 3 He
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target have been measured in the deep inelastic region. They are defined as
A
σ σ σ σ A σ σ σ σ (4)
with σ , σ , σ and σ the electron scattering cross sections with electron spin
anti-parallel, parallel, anti-perpendicular and perpendicular to target spin, respectively.
A1 can be extracted from A and A as
A1
η A
D1 ηξ d 1 ηξ A
(5)
where D, d, η , ξ depend on kinematics and the ratio R σL σT .
The experiment used the JLAB longitudinally polarized electron beam at its highest
available energy 5.7 GeV and with a 81% polarization. The polarized 3 He target in
Hall A was a 25 cm long gas target operated at a density of above 12 atmosphere at 0 Æ C.
During the experiment the average in-beam polarization with an average beam current of
12 µ A was 40%. The scattered electrons were detected by the two standard Hall A High
Resolution Spectrometers (HRS) [10] at symmetric positions. Particle identification is
achieved by using a CO2 gas Cherenkov detector and a double-layered lead-glass shower
counter. The combined pion rejection factor is found to be better than 10 4 for both HRSs,
with a 99% identification efficiency for electrons. This is sufficient regarding pion rates
in this experiment.
The raw and physics asymmetries are extracted from data as
Araw N Q N Q
N Q N Q
A Araw
f Pb Pt
(6)
with N , Q the yield and accumulated beam charge for each beam helicity state, f the
target dilution factor, typically 0.92
0.94, Pb and Pt the beam and target polarizations.
False asymmetries have been checked by measuring asymmetries of polarized e beam
scattering off unpolarized 12 C target. They are found to be negligible compared to the
3
physics asymmetry being measured. A 1He is calculated from physics asymmetries using
3
3
Eq. (5). Radiative corrections have been made to the 3 He asymmetries AHe and AHe
directly. A 3 He model [11] which includes S, S , D states and pre-existing ∆1232
components in the 3 He ground-state wavefunction has been used to extract An1 from
3
A1He .
PRELIMINARY RESULTS
Preliminary results of An1 are shown in Fig. 1, along with world data from HERMES
and SLAC. The error bars in Fig. 1 only include statistical errors. However, a detailed
study has been done for systematic errors showing that the total error is dominated by
statistics.
612
(2)
Preliminary
(6)
(1)
(3)
(4)
(5)
FIGURE 1. Preliminary results of A n1 compared with world data and theoretical predictions. Curves:
g
predictions of F1 from pQCD based model using LSS 2001 parametrization at Q 2 = 5 (GeV/c)2 (1), and
1
n
A1 from constituent quark model (light shaded band), pQCD based model using BBS parameterization
(2), statistical model at Q2 = 4 (GeV/c)2 (3), local duality (4), chiral soliton model at Q 2 = 3 (GeV/c)2 (5),
and E155 fit at Q 2 = 4 (GeV/c)2 (6).
The x 033 datum is in good agreement with existing world data. In the region of
x 04, the statistical errors of An1 have been improved by about one order of magnitude.
Also, the data show a clear trend that An1 turns to positive values at large x. Compared
with theory curves, it is intriguing to note that the constituent quark model gives the
correct sign and trend of An1 at large x. Two other models which use the world data as
input - the LSS parameterization and Soffer’s statistical model can be refined if the data
from this experiment are included in the inputs; Chiral soliton model calculations are
not in agreement with world data at the moment.
Besides An1 and gn1 , the asymmetry An2 and structure function gn2 can also be extracted
from our data. The statistical uncertainties of A n2 and gn2 are comparable to the latest data
from SLAC E155x [12].
Assuming valence quark dominance, one can extract the polarized quark distributions
∆uu and ∆d d from An1 data, d u ratio [13] and a world fit [14] of A1p data. Results
show that ∆d d is negative at all three x points which agrees with CQM prediction but
contradicts the prediction from pQCD based hadron helicity conservation.
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SUMMARY AND OUTLOOK
Experiment E99-117 provided precise data on the neutron spin asymmetry A n1 . Data
on the structure functions gn1 x Q2 , gn2 x Q2 and asymmetry An2 are also available. The
results of this experiment will provide valuable constraints to theoretical calculations. A n1
in the valence quark region is of great interest in the understanding of the valence quark
structure and the constituent quark concept. The measurement of A n1 in the valence quark
region is also an important part of the JLab 12 GeV upgrade [15], in which A n1 will be
measured up to x 08 and within a larger Q2 range of 2 Q2 10 (GeV/c)2 .
ACKNOWLEDGMENTS
The work presented was supported in part by funds provided to the Laboratory for Nuclear Science at the Massachusetts Institute of Technology by the U. S. Department of
Energy(DOE) under contract number DE-FC02-94ER40818. The Southeastern Universities Research Association operates the Thomas Jefferson National Accelerator Facility
for the DOE under contract DE-AC05-84ER40150.
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