New Precision Results on the Spin Structure
Function gd1
P. Lenisa
on behalf of the HERMES Collaboration
Università di Ferrara and INFN - Sez. Ferrara, 44100 Ferrara, ITALY
Abstract. The Hermes experiment studies the spin structure of the nucleon using the 276 GeV
longitudinally polarized positron beam of HERA and an internal target of pure gases. Recently,
HERMES presented preliminary results on the deuteron spin structure function g d1 in the kinematic
range 0002 x 085 and 01 Q 2 20 GeV 2 based on a restricted data set. Here, new, precise
results are presented using the superior statistics of the 2000 data taking period. A reduction of the
systematic uncertainty which could be achieved in this preliminary analysis relies in particular on
the excellent performance of HERA and of the HERMES target.
INTRODUCTION
Deep-inelastic lepton-nucleon scattering is well established as a powerful tool for the
investigation of the nucleon structure. The introduction of polarization variables like in
the scattering of polarized leptons off polarized nucleons provides informations on the
spin composition of the nucleons. This is the case of the polarized structure function g 1
which, in the parton model, is interpreted as a measure of the number of quarks with
same (q ) or opposite (q ) helicity with respect to the nucleon:
g1 x 1
1
e2f qf qf ∑ e2f ∆q f x
2∑
2 f
f
(1)
Recently, HERMES presented preliminary results on the deuteron spin structure function gd1 in the kinematic range 0002 x 085 and 01 Q 2 20 GeV 2 based on a
restricted data set. In this contribution, new, precise results are presented using the superior statistics of the 2000 data taking period.
THE HERMES EXPERIMENT
The HERMES experiment is located in the East straight section of the HERA storage
ring at the DESY laboratory in Hamburg. In 2000 the positron beam of 27.6 GeV with
injected beam currents of about 45 mA has been used. The positrons become transversely polarized by the emission of synchrotron radiation. Longitudinal polarization
at the interaction point is achieved by spin rotators situated upstream and downstream
the HERMES experiment. The beam elicity is usually reversed every 2 3 months to
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
279
account for possible systematic effects. Two Compton-back scattering polarimeters measure the beam polarization [1]. An average polarization value of 0.55 with an uncertainty
of 0.02 has been measured during the year.
Target
A beam of Deuterium atoms is generated in a micro-wave dissociator which forms
part of the atomic beam source (ABS). The beam of nuclear polarized atoms is injected
into the center of a thin-walled storage cell via a side tube and the atoms then diffuse
to the open ends of the cell where they are removed by a high speed pumping system.
A longitudinal magnetic holding field provides a quantization axis for the spins. The
beam emerging from a second side tube is analysed by a Breit-Rabi polarimeter (BRP)
to measure its atom polarization and a target gas analyser (TGA) to determine its atomic
fraction [2]. During the atom diffusion process, relaxation by wall and spin exchange
collisions and wall recombination changes the polarization and the atomic fraction of
the target gas. The atom polarization and atomic fraction values measured by the BRP
and TGA must be corrected for these effects to obtain the average target polarization as
seen by the positron beam which is described by the following expression:
PT
α0 αr 1
αr β Pa
(2)
where α0 is the atomic fraction accounting for unpolarized molecules, α r is the relative
atomic fraction surviving recombination, Pa is the nuclear polarization of the atoms and
β Pm Pa the relative polarization of the recombined molecules respect to the atomic
polarization (0 β 1). In the 2000 data taking period, the target density and thus the
luminosity could be increased by a factor of about 2 respect to 1999, by reducing the
working temperature from 100 K down to 60 K and using a cell with a smaller cross
section. The average polarization was 85 % with a total uncertainty of 3%.
In contrast to the solid targets, the Hermes gaseous target does not suffer from radiation damage (flowed gas), its polarization can be continuously measured and rapidly
reversed, and is not diluted by non-polarizable material. In 2000 the extremely good and
stable performances of both HERA beam and HERMES target allowed the collection of
about 10 million positron DIS candidates, a statistics 5 times higher than in any of the
previous data-taking years.
Spectrometer
The HERMES detector [3] is a forward spectrometer with a dipole magnet providing a
field integral of 1.3 Tm. A horizontal iron plate shields the HERA beam lines against the
field thus dividing the spectrometer into two identical halves with a minimum vertical
acceptance of 40 mrad. The acceptance extends to 140 mrad vertically and to 170
mrad horizontally. Tracking in each detector half is accomplished by 42 drift chamber
planes. Positron identification is accomplished using a probability method based on
signals of three sub-systems: the lead-glass block calorimeter, a transition-radiation
detector and a preshower hodoscope. For positrons in the momentum range of 25 to 27
280
GeV, the identification efficiency exceeds 98 % with a negligible hadron contamination,
the average polar angle resolution is 06 mrad, and the average momentum resolution is
1 2 %.
MEASUREMENT
Extraction Formalism
The kinematic range of this measurement accesses intervals in the Bjorken variables
of 0002 x 085 and 01 y 091. Inclusive events are selected by the requirements: Q2 01 GeV and W 2 324 GeV (where Q2 and W 2 are squared 4-momenta
of the photon and of the hadronic final state). For each of the 2-dimensional [x y] bins
the kinematic range is divided in, the asymmetry between cross-sections of parallel or
antiparallel helicities of the beam and the target is calculated:
meas
A
σ σ
σ
σ
1 N L N L
Pb Pt N L N L
The number of events selected (N) are corrected per spin state for the background
arising from charge symmetric processes. The corresponding luminosities (L) used for
normalization are measured with Bhabha scattering and are corrected for a small cross
section asymmetry caused by residual electron polarization of the target. Pb (Pt ) is the
beam (target) polarization.
The Born asymmetry has been derived from the measured asymmetry by subtraction
of the radiative background according to the formula:
Born
A
where 09 λ
unpol
σbg
1 meas
A λ unpol
λ
σ
DIS
pol
σbg
σ unpol
DIS
unpol are the (un)polarized
112 is a spin independent parameter, σbg
unpol is the unpolarized DIS cross section.
radiative tails, σDIS
The radiative corrections have been calculated using the POLRAD program [4]. The
statistical error had to be enlarged to account for radiative background by about a factor
2 at low x. The structure function ratio gd1 F1d and the spin structure function gd1 have
been extracted according to
gd1
F1d
1
1 γ2
ABorn
D
γ
η Ad2
(3)
and
gd1 gd1
F1d
F1d par gd1
F1d
1 γ F2
2x
1 R
2
d
(4)
The first term in Eq. 3 is the virtual-photon asymmetry, where D is the effective
polarization of the virtual-photon, γ and η are kinematic factors, A d2 is parameterized
281
gd1
Fd1
gd1
0.6
0.2
at measured Q
HERMES PRELIMINARY
0.5
(’00 data, no smearing correction)
0.1
SMC
0.4
(within x range of HERMES)
E143
0.3
2
0
E155
(averaged by HERMES)
0.2
-0.1
exp. systematic uncertainty
0.1
syst. unc. due to R and Fd2
-0.2
0
HERMES PRELIMINARY
(’00 data, no smearing correction)
-0.1
10
-2
10
-1
1
-0.3
2
<Q >
2 10
-0.4
GeV
1
10
-2
10
-1
10
1
-2
10
-1
1
x
x
FIGURE 1. Comparison between different g d1 F1d measurements [9] (left): data are shown at the
measured Q2 and the plotted errors are the quadratic sum of the statistical and systematic uncertainties.
HERMES result on gd1 (right): the error bars are statistical only and the shaded histograms show the
systematic uncertainty estimation.
using the Wandzura-Wilczek relation [5]. F1d in Eq. 4 has been parametrized in terms
d
of the ratio R σL σT [6]
and the structure function F2 , which has been expressed by
F2d F2p 2 1 F2n F2p , using the parameterizations for F2p [7] and F2n F2p [8].
Results
The HERMES result on gd1 is presented in Fig. 1. The contribution to the systematic
uncertainty from the experiment is dominated by the accuracy of the beam and target
polarization measurements. The extraction formalism adds a significant contribution at
lowest x due to the insufficient knowledge of the radiative corrections and at most 1.8
% at highest x due to the knowledge of Ad2 . The uncertainty arising for the unpolarized
structure function F2d is estimated to be at most 3 %, whereas the uncertainty due to R
is as large as 14 % at lowest x and 2.7 % at highest x. Furthermore, the stability of the
results under cut variations were studied and the data have been investigated for nonstatistical fluctuations by division into sub-samples defined by relevant parameters like
dead-time, beam current and time periods. No additional systematic effects could be
detected beyond the statistical accuracy of the data.
The HERMES result is the most precise available measurement of g d1 in the 0002 x 085 and 01 Q2 20 GeV 2 kinematic range (Fig. 2): it will allow the extraction
of gn1 and an accurate test of the Bjorken sum rule.
282
0.06
xg1
0.04
0.02
proton
SMC
HERMES
HERMES ’00 prel.
HERMES prel. rev.
E155
E143
0
deuteron
0.04
0.02
0
3
neutron ( He)
0.02
0
-0.02
E154
E142
-0.04
0.0001
0.001
0.01
0.1
x
1
FIGURE 2. World data on xg 1 [9, 10]. Data are shown at the measured Q 2 and the plotted errors are the
quadratic sum of systematic and statistical uncertainties.
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