Spin asymmetries for events with high $p_T$ hadrons in DIS and an evaluation of the gluon polarization

Abstract

We present a measurement of the longitudinal spin cross section asymmetry for deep inelastic muon-nucleon interactions with two high transverse momentum hadrons in the final state. Two methods of event classification are used to increase the contribution of the Photon Gluon Fusion process to above 30%. The most effective one, based on a neural network approach, provides the asymmetries A_p(lN->lhhX)=0.030+/-0.057+/-0.010 and A_d(lN->lhhX)=0.070+/-0.076+/-0.010. From these values we derive an averaged gluon polarization delta(G)/G=-0.20+/-0.28+/-0.10 at an average fraction of nucleon momentum carried by gluons eta=0.07.

Full text

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arXiv:hep-ex/0402010v1 4 Feb 2004
Spin asymmetries for events with high pT hadrons in DIS and an evaluation of the
gluon polarization
In remembrance of Vernon W. Hughes,
initiator of the SMC experiment and spokesman of the collaboration,
who passed away on March 25, 2003
and to whom this article is dedicated.
Spin Muon Collaboration (SMC)
B. Adeva20, E. Arik2, A. Arvidson23,u, B. Bade? lek23,25, G. Baum1, P. Berglund8, L. Betev13,o, R. Birsa22,
N. de Botton19, F. Bradamante22, A. Bravar11,h, A. Bressan22, S. B¨ ultmann1,v, E. Burtin19, D. Crabb24,
J. Cranshaw18,b, T. C ¸uhadar2,15, S. Dalla Torre22, R. van Dantzig15, B. Derro4, A. Deshpande26,ih, S. Dhawan26,
C. Dulya4,15,c, S. Eichblatt18,d, D. Fasching17,e, F. Feinstein19, C. Fernandez20,8, B. Frois19, A. Gallas20,
J.A. Garzon20,9, H. Gilly6, M. Giorgi22, E. von Goeler16, S. Goertz3, G. Gracia20,f, N. de Groot15,g, M. Grosse
Perdekamp26,jh, K. Haft13, D. von Harrach11, T. Hasegawa14,i, P. Hautle5,j, N. Hayashi14,k, C.A. Heusch5,l,
N. Horikawa14, V.W. Hughes26†, G. Igo4, S. Ishimoto14,m, T. Iwata14, E.M. Kabuß11, A. Karev10,
H.J. Kessler6,n, T.J. Ketel15, J. Kiryluk25,o, Yu. Kisselev10, L. Klostermann15, K. Kowalik25, A. Kotzinian10,
W. Kr¨ oger5,l, F. Kunne19, K. Kurek25, J. Kyyn¨ ar¨ ainen1,8, M. Lamanna22,a, U. Landgraf6, J.M. Le Goff19,
F. Lehar19, A. de Lesquen19, J. Lichtenstadt21, M. Litmaath15,a, A. Magnon19, G.K. Mallot11,a, F. Marie19,
A. Martin22, J. Martino19,y, T. Matsuda14,i, B. Mayes9, J.S. McCarthy24, K. Medved10, W. Meyer3,
D. Miller17, Y. Miyachi14, K. Mori14, J. Moromisato16, J. Nassalski25, T.O. Niinikoski5, J.E.J. Oberski15,
A. Ogawa14,h, C. Ozben2,x, H. Pereira19, D. Peshekhonov10,b, R. Piegaia26,p, L. Pinsky9, S. Platchkov19,
M. Plo20, D. Pose10, H. Postma15, J. Pretz11,w, G. R¨ adel5, G. Reicherz3, J. Robertsq, M. Rodriguez23,p,
E. Rondio25, I. Sabo21, J. Saborido20, A. Sandacz25, I. Savin10, P. Schiavon22, E.P. Sichtermann15,26,z, F. Simeoni22,
G.I. Smirnov10, A. Staude13, A. Steinmetz11, U. Stiegler5, H. Stuhrmann7, R. Sulej25,r, F. Tessarotto22,
D. Thers19, W. T? lacza? la25,r, A. Tripet1, G. Unel2, M. Velasco17, J. Vogt13, R. Voss5, C. Whitten4,
R. Windmolders12,w, R. Willumeit7, W. Wi´ slicki25, A. Witzmann6,s, A.M. Zanetti22, K. Zaremba25,r, J. Zhao7,t1
1University of Bielefeld, Physics Department, 33501 Bielefeld, Germany
2Bogazi¸ ci University and Istanbul Technical University, Istanbul, Turkey
3University of Bochum, Physics Department, 44780 Bochum, Germany
4University of California, Department of Physics, Los Angeles, 90024 CA, USA
5CERN, 1211 Geneva 23, Switzerland
6University of Freiburg, Physics Department, 79104 Freiburg, Germany
7GKSS, 21494 Geesthacht, Germany
8Helsinki University of Technology, Low Temperature Laboratory and Institute of Particle Physics Technology, Espoo, Finland
9University of Houston, Department of Physics, and Institute for Beam Particle Dynamics, Houston, 77204 TX, USA
10JINR, Dubna, RU-141980 Dubna, Russia
11University of Mainz, Institute for Nuclear Physics, 55099 Mainz, Germany
12University of Mons, Faculty of Science, 7000 Mons, Belgium
13University of Munich, Physics Department, 80799 Munich, Germany
14Nagoya University, CIRSE and Department of Physics, Furo-Cho, Chikusa-Ku, 464 Nagoya, Japan
15NIKHEF, Delft University of Technology, FOM and Free University, 1009 AJ Amsterdam, The Netherlands
16Northeastern University, Department of Physics, Boston, 02115 MA, USA
17Northwestern University, Department of Physics, Evanston, 60208 IL, USA
18Rice University, Bonner Laboratory, Houston, 77251-1892 TX, USA
19C.E.A. Saclay, DAPNIA, 91191 Gif-sur-Yvette, France
20University of Santiago, Department of Particle Physics, 15706 Santiago de Compostela, Spain
21Tel Aviv University, School of Physics, 69978 Tel Aviv, Israel
22INFN Trieste and University of Trieste, Department of Physics, 34127 Trieste, Italy
23Uppsala University, Department of Radiation Sciences, 75121 Uppsala, Sweden
24University of Virginia, Department of Physics, Charlottesville, 22901 VA, USA
25So? ltan Institute for Nuclear Studies and Warsaw University, 00681 Warsaw, Poland
26Yale University, Department of Physics, New Haven, 06511 CT, USA
∗

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We present a measurement of the longitudinal spin cross section asymmetry for deep inelastic
muon-nucleon interactions with two high transverse momentum hadrons in the final state. Two
methods of event classification are used to increase the contribution of the Photon Gluon Fusion
process to above 30%. The most effective one, based on a neural network approach, provides the
asymmetries AℓN→ℓhhX
p
= 0.030±0.057±0.010 and AℓN→ℓhhX
values we derive an averaged gluon polarization ∆G/G = −0.20±0.28±0.10 at an average fraction
of nucleon momentum carried by gluons ?η? = 0.07.
d
= 0.070±0.076±0.010. From these
PACS numbers: 13.60.Hb, 13.88.+e, 14.70.Dj
I.INTRODUCTION
The Spin Muon Collaboration (SMC) has extensively
studied polarized deep inelastic lepton-nucleon scattering
using the high energy muon beam at CERN and large po-
larized hydrogen and deuterium targets. This program
was initiated by the observation in a previous CERN ex-
periment (EMC) that only a small fraction of the proton
∗† Deceased
aNow at CERN, 1211 Geneva 23, Switzerland
bNow at Texas Technical University, Lubbock TX 79409-1051,
USA
cNow at CIEMAT, Avda Complutense 22, 28040, Madrid, Spain
dNow at Fermi National Accelerator Laboratory, Batavia, 60510
Illinois, USA
eNow at University of Wisconsin, USA
fNow at NIKHEF, 1009 AJ Amsterdam, The Netherlands
gNow at Bristol University, Bristol, UK
hNow at Brookhaven National Laboratory,Upton, 11973 NY, USA
ihNow at Dept. of Physics and Astronomy, SUNY at Stony Brook,
Stony Brook, NY 11974, USA
jhNow at Univ. of Illinois at Urbana-Champaign, 405 North Math-
ews Av. Urbana, Illinois 61801, USA
iPermanent address: Miyazaki University, Faculty of Engineering,
889-21 Miyazaki-Shi, Japan
j
Permanent address:Paul Scherrer Institut, 5232 Villigen,
Switzerland
kPermanent address: The Institute of Physical and Chemical Re-
search (RIKEN), wako 351-01, Japan
lPermanent address: University of California, Institute of Particle
Physics, Santa Cruz, 95064 CA, USA
mPermanent address: KEK, Tsukuba-Shi, 305 Ibaraki-Ken, Japan
nNow at SBC Warburg Dillon Read, CH-4002 Basel, Switzerland
oNow at University of California, Department of Physics, Los An-
geles, 90024 CA, USA
pPermanent address: University of Buenos Aires, Physics Depart-
ment, 1428 Buenos Aires, Argentina
qPermanent address: Rice University, Bonner Laboratory, Hous-
ton, TX 77251-1892, USA
rPermanent address: Warsaw University of Technology, 00-665
Warsaw, Poland
sNow at F.Hoffmann-La Roche Ltd., CH-4070 Basel, Switzerland
t1Now at Oak Ridge National Laboratory, Oak Ridge, TN 37831-
6393, USA
uNow at The Royal Library, 102 41 Stockholm, Sweden
vNow at Old Dominion University, Norfolk, VA 23529, USA
wNow at University of Bonn, 53115, Bonn, Germany
xNow at University of Illinois at Urbana-Champaign, USA
yNow at SUBATECH, University of Nantes, UMR IN2P3/CNRS,
44307, Nantes, France
zNow at Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA
spin is carried by the spin of the quarks [1]. The SMC
results have confirmed this observation for protons and
provided the first measurement of the spin structure of
deuterons which allowed for the verification of the fun-
damental Bjorken sum rule [2, 3].
The high energy polarized data from SMC, combined
with the high precision data from the SLAC [4] and
DESY [5] experiments at lower energy, cover a kinematic
range allowing for a QCD analysis of the spin struc-
ture function g1. Various analyses have been performed
at next-to-leading order with different input parameteri-
zations for the polarized parton densities and different
choices of the fitted parameters [6, 7].
consistent results for the polarized quark densities but
bring little information on the polarized gluon density
∆G. This is an expected feature since g1is sensitive to
gluons only through its Q2evolution and the available g1
data cover only a narrow range in Q2at a given value of
x. In particular it is still not possible to test the hypoth-
esis, formulated many years ago, that the gluon spin may
account for a sizable fraction of the nucleon spin [8].
A direct measurement of the gluon polarisation is pos-
sible via the Photon Gluon Fusion (PGF) process, which
is illustrated in Fig.1, together with the two other lowest
order diagrams: the virtual photon absorption (leading
process ”LP” ) and gluon radiation (QCD Compton scat-
tering ”QCD-C”). Since the contribution of the PGF
diagram is small, the event selection procedure should
be very effective in discriminating the PGF process from
other channels. This can be achieved either by select-
ing events where a charmed particle is produced (e.g. a
D meson) or events with hadrons of large transverse mo-
menta (pT) relative to the virtual photon direction [9, 10].
Both possibilities will be used in the COMPASS experi-
ment presently running at CERN [11].
In this paper we present an evaluation of the gluon
polarization, ∆G/G, from the SMC data. We limit the
analysis to the DIS region (Q2> 1 GeV2) and select
events with high pT hadrons. The SMC experimental
setup was not optimized for the detection of hadrons
produced at large angles, so the precision of the result
is obviously limited. This is, however, the first attempt
to tag PGF with light quark production in a DIS exper-
iment.
A determination of the gluon polarization from events
with high pThadrons has been attempted on the ep data
from the HERMES experiment [12] at lower incident en-
ergy and in a kinematic range where quasi-real photo-
They provide

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production is dominant.
II.FORMALISM
Experimentally observed spin-dependent effects are
small and have to be determined from the cross section
asymmetry defined as the ratio of polarized (∆σ) and
unpolarized (σ) cross sections
AℓN=∆σ
2σ
=σ↑↓− σ↑↑
σ↑↓+ σ↑↑,(1)
where ↑↓ and ↑↑ refer to anti-parallel and parallel con-
figurations of the nucleon and incoming lepton spins. At
the parton level the hard scattering cross section consists
of three terms corresponding to the LP, QCD-C and PGF
processes. According to the factorization theorem σ and
∆σ can be written as convolutions of the parton distri-
butions (F, ∆F), hard-scattering cross sections (ˆ σ,∆ˆ σ)
and fragmentation functions D of partons into hadrons:
σ = F ⊗ ˆ σ ⊗ D
∆σ = ∆F ⊗ ∆ˆ σ ⊗ D. (2)
The parton distributions stand for quarks, antiquarks,
and gluons. The spin dependent distributions are de-
noted ∆q = q↑− q↓for quarks, antiquarks and ∆G =
G↑−G↓for gluons and the corresponding spin-averaged
ones q = q↑+ q↓and G = G↑+ G↓. Here, the up and
down arrows correspond to parallel and anti-parallel con-
figurations of the parton and nucleon spins.
After insertion of the full expression for σ and ∆σ into
Eq. (1), the final expression for the cross section asym-
metry with production of at least two hadrons with large
transverse momenta, AℓN→ℓhhX, reads
AℓN→ℓhhX=
∆q
q
∆G
G
(?ˆ aLL?LPRLP+ ?ˆ aLL?QCD−CRQCD−C) +
?ˆ aLL?PGFRPGF,(3)
where ?ˆ aLL? = ?∆ˆ σ/2ˆ σ? are the average partonic asym-
metries and R the cross section ratios of the different pro-
cesses shown in Fig. 1, with respect to the total cross sec-
tion in the selected sample. The asymmetry AℓN→ℓhhX
thus permits an evaluation of the gluon polarization if all
other elements in Eq. (3) are known. The quark asymme-
try ∆q/q is approximated by the value of A1obtained in
inclusive measurements. The partonic asymmetries ˆ aLL
are calculated for simulated events and averaged over the
selected sample; in the kinematic region covered by the
SMC data, they are found to be positive for the first two
processes and negative for PGF. The ratios R are taken
from the simulated sample to which the same selection
criteria are applied as to the data.
The statistical precision of the gluon polarization de-
termined from Eq. (3) depends on the precision of the
measured asymmetry AℓN→ℓhhXand on the fraction of
PGF events (RPGF) in the final sample. Therefore the
aim of the present analysis is to select a large enough
sample with a maximal contribution of PGF events.
The description of hadron production in DIS muon
data in terms of the three processes of Fig. 1 has
been successfully tested in previous experiments [13, 14].
Other processes, such as those involving resolved pho-
tons, are expected to have small contributions for Q2
above 1 GeV2and are not considered here.
III.THE EXPERIMENT
The experimental setup at the CERN muon beam con-
sisted of three major components: a polarized target, a
magnetic spectrometer and a muon beam polarimeter. A
detailed description of the experiment and of the analysis
of the inclusive data can be found in Refs. [3, 15]. The
muon beam polarization, PB, was determined from the
spin asymmetries measured in polarized muon-electron
scattering and from the energy spectrum of positrons
from muon decays and was found to be −0.795 ± 0.019
for an average beam energy of 187.4 GeV [16].
target consisted of two cells filled with butanol, deuter-
ated butanol or ammonia [17]. The two cells were po-
larized in opposite directions by dynamic nuclear polar-
ization. The average target polarizations, PT, were ap-
proximately 0.90 for protons and 0.50 for deuterons, with
a relative error ∆PT/PT of 3-5%. The polarization was
reversed five times a day.
The counting rate asymmetry, Aexp, is determined
from the number of events counted in upstream and
downstream target cells before and after polarization re-
versal. This is done by solving the resulting second order
equation, as described in [18].
The cross-section asymmetry, AℓN→ℓhhX, is related to
Aexpby:
The
AℓN→ℓhhX=
1
PBPTfAexp, (4)
where f is the effective dilution factor, which takes into
account the dilution of spin asymmetries by the presence
of unpolarizable nuclei in the target and also by radiative
effects on the nucleon. The effect of unpolarizable materi-
als can be expressed in terms of the numbers nAof nuclei
with mass number A and the corresponding total spin-
independent cross sections σtot
on the nucleon [15, 19] are taken into account through
the ratio of one photon exchange to total cross-sections
ρ = σ1γ
p,d. The evaluation of the effective dilution
factor for inclusive events and for events with observed
hadrons is described in Ref. [3]. Polarized radiative cor-
rections are applied to the asymmetries as described in
Refs. [15, 20]. In this analysis polarized radiative cor-
A.The radiative effects
p,d/σtot

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rections and dilution due to radiative effects are reduced
because processes without hadrons are excluded.
IV.SAMPLE SELECTION
The total sample of data collected by the SMC ex-
periment during the years 1993-1996 with muon beam
of E=190 GeV and longitudinally polarized target was
used for the analysis. It consists of samples of similar
size taken on polarized protons and deuterons.
The standard cuts on inclusive kinematic variables [3],
ν = E − E′>15 GeV and E
reject events with poor kinematic resolution and muons
from hadron decay, respectively. The cut y = ν/E <0.9
removes a region where the uncertainty due to radiative
corrections becomes large. Two other cuts were applied
in close relation to the formalism used in the analysis: a
cut Q2>1 GeV2rejects the region dominated by non-
perturbative effects and allows to interpret the results in
terms of partons. A cut y >0.4 removes events which
carry little spin information due to a small virtual pho-
ton polarization. In addition, cuts on the muon scat-
tering angle were applied in order to match the angular
acceptance of the hardware triggers.
In the leading process (LP) most hadrons have small
pT as only the intrinsic kT of quarks in the nucleon [21]
and the fragmentation mechanism contribute to it. A
different situation occurs for QCD-C and PGF, where
hadrons mainly acquire transverse momentum from pri-
marily produced partons. For this reason, the require-
ment of two observed hadrons with large transverse mo-
menta enhances the contribution of the PGF and QCD-C
processes in the selected sample.
In the present analysis, the events of interest include
a reconstructed beam muon, a scattered muon, and at
least two charged hadrons. They represent about 20%
of the total number of events with reconstructed beam
and scattered muons, used for inclusive studies. Hadron
tracks were accepted if they could be associated to the
primary interaction point, i.e. the vertex, defined by the
beam and scattered muons. The same association criteria
as in the SMC analysis of Ref. [3] were applied. In order
to suppress the contribution from the target fragmenta-
tion region, cuts on the reduced longitudinal momentum
of the hadron, xF > 0.1, and on the hadron fractional
energy, z = Eh/ν > 0.1, were applied.
The further requirement of two hadrons with pT >
0.7 GeV selects about 5% of the events passing all pre-
vious cuts. The electron contamination to this sample is
expected to be negligible because electrons are generally
produced at low pT. This is confirmed by the ratio of
the energy deposited in the electromagnetic part of the
calorimeter to the total deposited energy, which does not
show any peak at 1.0 for tracks with pT > 0.5 GeV. Af-
ter all selections the total number of remaining events
amounts to about 80k for the proton and 70k for the
deuteron sample.
′>19 GeV were imposed to
V.MONTE CARLO SIMULATION
A.Conditions for MC generation
The interactions were simulated using the LEPTO 6.5
generator [22] with a leading order parameterization of
the unpolarized parton distributions [23]. The spin de-
pendent effects were calculated using POLDIS [24] with a
consistent set of polarized parton distributions [25]. The
kinematic limits of the MC generation were defined so as
to cover the full kinematic region of the data. Default
values were used for most of the steering parameters of
the LEPTO generator. Below we discuss only the modi-
fied conditions and parameters.
The matrix elements of first order QCD processes ex-
hibit collinear divergences in the cross channel and dif-
ferent schemes are used to avoid such singularities. The
so-called zˆ s scheme, which allows for lower values of the
γ∗-parton center of mass energy
simulation with modified cut-off parameters. The effect
of the cut-off values on any observable distribution for
events with high pT hadrons is only marginal.
The description of interactions requires the choice of
two scales: a factorization scale, which appears in the
parton densities, and a renormalization scale which ap-
pears in expressions depending on the strong coupling
constant αs. Here the usual choice of Q2was made in
both cases. In these conditions, after kinematic cuts on
event variables only, the generated sample contains 8%
PGF events.
In order to describe the data, it was found necessary
to change the values of two fragmentation parameters in
JETSET [26]. The function f(z) = z−1(1 − z)ae−bm2
where m2
Tand m is the mass of the quark,
expresses the probability that a fraction z of the available
energy will be carried away by a newly created hadron.
The parameters (a, b) were modified from their default
values (0.3, 0.58) to (0.5, 0.1), a change making the frag-
mentation softer. This modification was inspired by a
similar study done by the HERMES experiment [27, 28]
and seems to work also in the present case, with smaller
deviations from the default values. However, we are look-
ing here at a particular sample and have no possibility
to check if the Monte Carlo sample generated with these
modifications would correctly describe the full data. The
uncertainty connected with these modifications has been
estimated and included in the systematic error.
√ˆ s, was used in the
T/z,
T= m2+ p2
B.Simulation of experimental conditions
The scattered muon track of each simulated event was
followed through the magnet aperture. Trigger condi-
tions were checked and prescaling factors applied in or-
der to reproduce the relative trigger rates in the simu-
lated sample. Kinematic smearing was applied to muon
and hadron tracks and geometric smearing to the vertex
position. In addition, the loss of tracks due to chamber

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inefficiencies was taken into account by applying detector
plane efficiencies to the simulated events and by removing
the tracks which did not fulfill the minimal requirements
for reconstruction.
Secondary interactions of hadrons have to be taken into
account to reproduce the distribution of interaction ver-
tices along the target axis. Hadrons were rejected from
the sample according to the probability of re-interaction
in the polarized target material. As an example, Fig. 2
shows the agreement obtained for the vertex position
along the beam axis in one of the proton data sets.
The simulation was performed for each year of data
taking separately. To get a good description of the kine-
matic variables it was required to use specific beam pa-
rameters for every year, including small changes in an-
gles, and to take into account the exact target position.
C.Comparison of simulations and data
The distributions of kinematic variables as well as the
particle distributions in detectors were checked with iden-
tical selection criteria applied to data and MC. For the
simulated events the cuts were applied to the smeared
variables. The distributions for data and MC were nor-
malized to the same number of events. The distributions
of x and Q2for interactions on protons are presented in
Fig. 3. The obtained agreement is at the level of 10-25%
for all kinematic event variables. The level of agreement
for deuterons is very similar [29].
The same comparisons were done for hadron variables.
For simulations performed with the unmodified fragmen-
tation function clear discrepancies are observed for the
hadron production angle θ and the longitudinal momen-
tum pL, while satisfactory agreement is obtained for pT,
except at the highest values. The observed differences
at the highest values of pT can be explained by the ap-
proximate description of the non-Gaussian tails of the
distributions used for smearing and by the effects of real
photon radiation, which are not taken into account in
the present analysis. It was checked that the discrep-
ancy for the θ angle could not be removed by using dif-
ferent smearing parameterizations or even by an artifi-
cial increase of smearing. Agreement between data and
simulation could only be achieved by applying a cut on
the hadron production angle θ > 0.02 rad. This cut,
however, removes about 25% of the selected sample and
cannot be justified since there is no reason why the sim-
ulation should not describe the hadrons produced at low
θ. Therefore modified simulation conditions providing a
better description of the data were searched for.
When the modifications of the fragmentation function
parameters are applied (cf.
ment becomes satisfactory over a wide range of θ and
pL.The comparison of the pL and θ distributions is
shown in Fig. 4 for the hadron with highest pT. The
second hadron is also well described by the MC [29]. We
concluded that the parameters of the longitudinal frag-
Section V.A), the agree-
mentation function f(z) have to be modified in order to
obtain a good description of the data over the full range
of hadron production angle θ. Since it is difficult to check
if the modified set of parameters correctly describes the
semi-inclusive hadron distributions, the analysis has been
performed in parallel with modified fragmentation as well
as with the standard fragmentation and an additional cut
on θ > 0.02 rad.
VI.SELECTION OF THE PGF PROCESS
In order to compare the merits of various selections of
PGF events, we will use the efficiency ǫ, which is the
ratio of the number of PGF events accepted by the se-
lection criteria to the total number of PGF events, and
the purity RPGF(Eq.3), which is the ratio of the number
of selected PGF events to the total number of selected
events. The optimal selection is obviously the one pro-
viding the highest values of ǫ and RPGF but, in general,
an increase of the former will result in a decrease of the
latter.
The purity is 0.11 for the full sample of events with
at least 2 charged hadrons. The additional requirement
of two hadrons with pT > 0.7 GeV defines our reference
sample for which RPGF= 0.24 and, by definition, ǫ = 1.
The effects of cuts were studied for the following vari-
ables: pT1, the sum p2
or opposite sign), the azimuthal angle φ between the mo-
menta of the two hadrons with respect to the virtual pho-
ton direction, and the invariant mass of the two hadrons
(see also Ref. [30]). It was found that the selection on
?p2
further requirements on the hadron charges do not bring
any significant improvement. Fig. 5 shows the variation
of RPGF with ǫ when the cut on?p2
4 GeV2. It is seen that the purity increases only very
slowly when the cut is made more restrictive while the
efficiency drops very rapidly. This can be understood by
the fact that one of the background processes (QCD-C)
has a similar dependence on the?p2
approximation made in Eq. (3) by the use of A1for the
asymmetry on quarks is only valid if the fraction of PGF
events in the selected sample is much higher than in the
inclusive one, i.e. close to the maximum value of 0.33.
The efficiency also needs to be sufficiently high to allow
a meaningful analysis. As a compromise, we have fixed
the cut at 2.5 GeV2, which corresponds to ǫ = 0.30 and
RPGF = 0.31.
The combination of several variables into a single pa-
rameter has also been investigated in a classification pro-
cedure based on a neural network [29, 31]. We considered
the variables which characterize the DIS event (x, Q2, y,
and the multiplicity of tracks) and those which describe
the two selected hadrons with highest pT(transverse and
longitudinal hadron momenta, charges of the hadrons,
energy fraction of the hadrons, and the azimuthal an-
gle φ).The classification procedure was trained on a
T1+ p2
T2, hadron charges (same
Tis optimal for enhancing the PGF purity and that
Tis varied up to
Tcut as PGF. The

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Monte Carlo sample where the actual process is known
for each event. As a result, the procedure provides a sin-
gle value, called ”NN response”, within the range (0,1).
High values of this response correspond to events which,
according to the classification algorithm, are more likely
to be PGF than background processes. A threshold on
the network response can thus be used to select a PGF
enriched sample.
The variation of RPGF vs.
the NN response threshold is also shown in Fig. 5. It
is observed that at equal efficiency the NN approach al-
ways provides samples with higher purity than the selec-
tion based on?p2
0.26 was chosen, which corresponds to RPGF= 0.33 and
ǫ = 0.56. A similar purity is obtained with the?p2
at 2.5 GeV2but with an efficiency of 30%. Therefore a
better statistical precision on the measured asymmetry
will be obtained with the neural network method. Alter-
natively, a higher NN threshold corresponding to a PGF
efficiency of 30% would yield a sample where the purity
is about 37%, i.e. 6% higher than the value obtained
with the?p2
samples shows that the NN procedure selects a large frac-
tion of events with?p2
lower range of?p2
tributions of NN responses are compatible for data and
Monte-Carlo events.
ǫ for various choices of
T. For further analysis, a threshold of
Tcut
Tcut. The comparison of the two selected
T> 2.5 GeV2but also covers the
T. It was also checked that the dis-
VII.SPIN ASYMMETRIES AℓN→ℓhhX
The SMC data taken from 1993 to 1996 were split into
periods of data taking, corresponding to about 15 days
each. The asymmetry for a given year is the weighted
average of the asymmetries calculated for each period of
data taking. Splitting the data into smaller subsamples
gives identical results within the expected statistical fluc-
tuations. The distribution of the vertex position along
the beam axis, as presented in Fig. 2, shows that the ra-
tio of acceptances for the upstream to downstream target
cells is about 0.7. The method used for asymmetry calcu-
lation, described in [18], is suited for such an acceptance
difference.
The asymmetry calculations were done for the entire
sample which has a purity RPGF= 0.24 and for the two
selection methods with enhanced RPGF (?p2
GeV2and NN response > 0.26). The results given in
Fig. 6 and Table I show that the asymmetries do not
change significantly with the selection. Also the asym-
metries obtained for proton and deuteron are compatible
within errors. The statistical error is larger for the selec-
tion based on?p2
is selected (28 % vs. 42 %).
The errors of the measured AℓN→ℓhhXasymmetry
for the selected samples are dominated by statistics.
The contributions to the systematic uncertainty on
AℓN→ℓhhXare detailed in Table II for the two selec-
tions with enhanced RPGF. The most significant ones
T> 2.5
Tbecause a smaller fraction of events
come from the false asymmetries, the fraction of radia-
tive processes (ρ) and the polarized radiative corrections.
For the false asymmetries an upper limit from the time
variation of the acceptance was taken under the assump-
tion that the reconstruction for each of the three tracks
(scattered muon and two hadrons) is affected indepen-
dently. The method used for estimating these effects is
described in Ref.[30]. The radiative corrections are small
due to the limited phase space for real photon emission in
events where a significant fraction of the available energy
is taken by the two hadrons with large pT. The uncertain-
ties in ρ and polarized radiative corrections were taken
equal to the full size of the inelastic contribution. The
effect of real photon radiation on the event kinematics
and, in particular, on the value of pT itself has not been
taken into account in view of the limited precision of the
present analysis.
VIII.DETERMINATION OF THE GLUON
POLARIZATION
The gluon polarization is evaluated from Eq. (3) us-
ing the measured AℓN→ℓhhXasymmetry, obtained for the
samples with enhanced RPGF, quoted in Table 1. In view
of the strong dependence of the resulting gluon polariza-
tion on the information obtained from the Monte Carlo,
special attention was given to the agreement of data and
simulated events (Figs.2-4).
The asymmetry A1(x) for each event is taken from a
fit to all experimental data and averaged for the full pro-
ton and deuteron samples. The partonic asymmetries
ˆ aLLfor each sub-process are calculated for each Monte-
Carlo event and averaged.
LP and QCD-C are very similar for the two selections
namely, ?ˆ aLL?LP= 0.8 and ?ˆ aLL?QCD−C= 0.6. The
values for PGF are ?ˆ aLL?PGF= −0.44 and −0.49 for
the Σp2
Tcut and the NN selection, respectively. After
selection on Σp2
Tthe final proton sample consists of 26%
LP, 43% QCD-C and 31% PGF, while for the neural net-
work the fractions are RLP= 38%, RQCD−C= 29% and
RPGF = 33%. The contributions of different processes
for the proton and deuteron samples differ by less than
2%.
The gluon polarization is determined for the kinematic
region covered by the selected sample and corresponds to
a given fraction of nucleon momentum carried by gluons
η:
Their averaged values for
η = x(ˆ s
Q2+ 1).(5)
This quantity is known for simulated events but cannot
be directly determined from the data. Nevertheless, ˆ s
can be approximately calculated from the virtual photon
energy in the laboratory system and from the angles (θ1,
θ2) defined by the directions of the two hadrons with
respect to the virtual photon:
ˆ s ≈ ν2tgθ1tgθ2.(6)

Page 7

7
To check the validity of this approximation in our kine-
matic conditions, we have compared the generated η and
the one calculated from the above equation for selected
PGF events. The calculated values are on average 25%
higher than the generated ones. The averaged value of
the generated η for the selected PGF events in the Monte
Carlo is used as the reference value for the result on
∆G/G. We have also checked the average values of η
calculated for all simulated events and obtained the val-
ues 0.15 for the cut?p2
NN response > 0.26. For both selection methods the val-
ues of η calculated for all simulated events and for data
are very close. The results on the gluon polarization and
the values of ?η? are presented in Table III.
In addition to the systematic errors on the measured
asymmetry discussed in Section 7 and given in Table II,
the asymmetry A1, the fractions R, and the partonic
asymmetries ?ˆ aLL? contribute to the systematic error on
∆G/G. The contribution due to the asymmetry A1 is
determined from the uncertainty on A1at the averaged
value of x and thus from the errors on the fit parameters.
The value of A1at the average x agrees with the average
A1calculated from the fit for each event to within 0.001.
The dominant contributions to the systematic error are
due to the uncertainties on the values of R and ?ˆ aLL?.
They are estimated by comparing the results obtained
from Monte Carlo simulations with different parameters.
For this purpose, a sample of LEPTO events was gener-
ated with the same kinematic and hadron selections but
with modified renormalization and factorization scales,
cut-offs and fragmentation function parameters. Scales of
Q2/2 and 2 Q2were used for comparison and provide an
estimate of the stability of the leading order approxima-
tion used here. Results with standard and modified pa-
rameters (see Section 5.1) in the fragmentation function
were compared. Since only the simulations which repro-
duce the data should be considered, a cut on the hadron
angle θ was applied, as explained in Section 5.3. The
value of the gluon polarization calculated with this new
Monte Carlo sample was compared to the one obtained
under the conditions described in Section 5.1. This pro-
cedure was repeated several times with slightly different
cuts and with different neural network thresholds. For
the neural network the procedure is complicated by the
fact that any change in the simulation procedure leads to
a different selection on the data. To avoid the fluctuation
of the gluon polarization due to variation of the measured
asymmetry, the value of this asymmetry was artificially
frozen when comparing results for different MC samples.
The individual contributions to the systematic error are
given, for both selection methods, in Table IV. It was
checked that the effect of combined modifications in the
Monte Carlo is smaller than the sum of the individual un-
certainties. The maximal variation of RPGF and ?ˆ aLL?
was found to be 20% and 4% respectively.
As discussed before, the neural network selection pro-
vides a more accurate result than the selection based on
Σp2
Tcuts. However, the statistical error is too large to
T> 2.5 GeV2and 0.10 for the
draw definitive conclusions on the contribution of ∆G to
the nucleon spin. The systematic uncertainty is small
compared to the statistical error. The demand of a good
agreement of the simulation with the data sets an impor-
tant limitation on the estimated systematic uncertain-
ties. For this reason, an increase in statistical precision
is expected also to lead to further improved systematic
uncertainty estimates.
Averaging the results for proton and deuteron obtained
with the neural network classification we obtain ∆G/G =
−0.20± 0.28 ± 0.10.
IX. CONCLUSIONS
We have evaluated for the first time the gluon polar-
ization from the spin asymmetries measured in lepton-
nucleon DIS events with Q2> 1 GeV2including two
hadrons with large transverse momentum in the final
state. The analysis is performed at leading order in QCD
and based on the comparison of selected data samples
with simulated events provided by the LEPTO genera-
tor. The partonic asymmetry ˆ aLLis mostly negative for
the photon-gluon fusion process while it is positive for
the two competing processes, leading process and gluon
radiation. The relative contribution of photon-gluon fu-
sion is enhanced to about 30% by applying a cut on
Σp2
fication.
The average gluon polarization obtained for the SMC
data is close to zero with a large statistical error (∼ 0.30).
The accuracy is limited by the reduction to less than 1%
of the DIS sample by the hadron selection requirements.
It is thus expected to be improved by higher counting
rates and larger hadron acceptance in ongoing and future
experiments.
T> 2.5 GeV2or by using a neural network classi-
ACKNOWLEDGMENT
This work was supported by Bundesministerium
f¨ ur Bildung, Wissenschaft, Forschung und Technolo-
gie, partially supported by TUBITAK and the Center
for Turkish-Balkan Physics Research and Application
(Bogzi¸ ci University), supported by the U.S. Department
of Energy, the U.S. National Science Foundation, Mon-
busho Grant-in-Aid for Science Research (International
Scientific Research Program and Specially Promoted Re-
search), the National Science Foundation (NWO) of the
Netherlands, the Commisariat ` a l’Energie Atomique,
Comision Interministerial de Ciencia y Tecnologia and
Xunta de Galicia, the Israel Science Foundation, and Pol-
ish State Committee for Scientific Research (KBN) SPUB
no. 134/E-365/SPUB-M/CERN/P-03/DZ299/2000 and
621/E-78/SPB/CERN/P-03/DWM 576/2003-2006 and
Grant No. 2/P03B/10725.

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8
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privatecommunication

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9
FIG. 1: Lowest order diagrams for DIS γ∗absorption: a) leading process (LP), b) gluon radiation (QCD-C), c) photon-gluon
fusion (PGF).
vertex position [ m ]
-5.8-5.6-5.4-5.2-5-4.8-4.6-4.4-4.2 -4-3.8
number of events
0
2000
4000
FIG. 2: Distribution of vertices along the beam axis. Points correspond to the proton data from 1993 and the histogram to
the corresponding MC simulation.

Page 10

10
]
2
[GeV
2
Q
510 1520 253035 4045
number of events
10
2
10
3
10
4
x
0.050.10.150.20.250.30.35
number of events
10
2
10
3
10
4
FIG. 3: The x and Q2distributions for the proton case: points correspond to the data and histograms to the Monte Carlo
simulation.
[ GeV ]
L
p
1020 3040 5060 708090100
number of events
0
5000
10000
[ rad ]
θ
0 0.01 0.020.030.04 0.05 0.060.070.08 0.09
number of events
0
2000
4000
6000
8000
FIG. 4: Distributions of longitudinal momentum and scattering angle for the hadron with the highest pT. Points correspond
to the proton data collected in 1993, histograms to the Monte Carlo simulations with the modified fragmentation function.

Page 11

11
Efficiency [%]
020406080100
Purity [%]
10
15
20
25
30
35
40
45
50
55
0.26
2.5
]
2
[GeV
2
T2
+p
2
T1
p
NN
1.7
1.2
0.33
0.19
FIG. 5: Comparison of purity and efficiency for the selection methods based on the cut on?p2
Simulations correspond to the proton sample.
Tand the NN response.
-0.2
0
0.2
> 0.7 GeV
T1,2
p
2
> 2.5 GeV
T2
2
+ p
2
T1
p
NN response > 0.26
Proton
Deuteron
lhhX
→
lN
A
All events
FIG. 6: Measured asymmetry AℓN→ℓhhX, for proton and deuteron, for events with pT1,2 > 0.7 GeV cut and after additional
selections on?p2
Tand neural network threshold to increase the purity.

Page 12

12
TABLE I: Measured cross-section asymmetries AℓN→ℓhhXfor proton and deuteron events with pT1,2 > 0.7 GeV and in the
samples selected with the?p2
errors.
Tcut and with the neural network response threshold, each given with statistical and systematic
SelectionAℓN→ℓhhX
p
AℓN→ℓhhX
d
All
?p2
NN response>0.26
0.041±0.037±0.011
0.018±0.071±0.010
0.030±0.057±0.010
0.063±0.050±0.011
0.054±0.093±0.008
0.070±0.076±0.010
T>2.5 GeV2
TABLE II: The contributions to the systematic error of AℓN→ℓhhXwith the?p2
response >0.26 for SMC proton and deuteron data. The first and last contributions are additive; the others are proportional
to the asymmetry.
T>2.5 GeV2cut and with the neural network
Contributions to the
systematic error on AℓN→ℓhhX
proton datadeuteron data
Σp2
T
NNΣp2
T
NN
False asymmetries
Target polarization
Beam polarization
Dilution factor
Target composition
ρ factor
Polarized rad. corr.
0.0049
0.0005
0.0007
0.0049
0.0008
0.0011
0.0044
0.0016
0.0021
0.0044
0.0023
0.0029
0.0003
0.0018
0.0083
0.0001
0.0030
0.0083
0.0002
0.0054
0.0020
0.0001
0.0076
0.0020
Total systematic error0.00980.01020.00770.0097
TABLE III: Gluon polarization for proton and deuteron for the Σp2
Tcut and the neural network selection.
Selection
?∆G
G
?
p
?∆G
G
?
d
?η?
?p2
NN response> 0.26
T> 2.5 GeV2
0.11±0.51±0.12
–0.06±0.35±0.10
–0.37±0.66±0.12
–0.47±0.49±0.10
0.09
0.07

Page 13

13
TABLE IV: Contributions to the systematic error on gluon polarization for two methods of event selection.
Source of the uncertaintyΣp2
T
NN
systematic error
on AℓN→ℓhhX
precision of A1 fit
scale change
from Q2/2 to 2 Q2
fragmentation paramr.
cut-offs in matrix elem.
0.072(p) 0.057(d)
0.042(p) 0.042(d)
0.061(p) 0.063(d)
0.026(p) 0.028(d)
0.008
0.036
0.015
0.010
0.034
0.008