Measurement of single-spin azimuthal asymmetries in semi-inclusive electroproduction of pions and kaons on a longitudinally polarised deuterium target
ABSTRACT Single-spin asymmetries have been measured for semi-inclusive electroproduction of π+, π−, π0 and K+ mesons in deep-inelastic scattering off a longitudinally polarised deuterium target. The asymmetries appear in the distribution of the hadrons in the azimuthal angle φ around the virtual photon direction, relative to the lepton scattering plane. The corresponding analysing powers in the sinφ moment of the cross section are 0.012±0.002(stat.)±0.002(syst.) for π+, 0.006±0.003(stat.)±0.002(syst.) for π−, 0.021±0.005(stat.)±0.003(syst.) for π0 and 0.013±0.006(stat.)±0.003(syst.) for K+. The sin2φ moments are compatible with zero for all particles.
arXiv:hep-ex/0212039v2 21 Feb 2003
Measurement of single-spin azimuthal asymmetries in semi-inclusive
electroproduction of pions and kaons on a longitudinally polarised deuterium target
A. Airapetian,33N. Akopov,33Z. Akopov,33M. Amarian,7,33V.V. Ammosov,25A. Andrus,16E.C. Aschenauer,7
W. Augustyniak,32H. Avakian,11R. Avakian,33A. Avetissian,33E. Avetissian,11P. Bailey,16V. Baturin,24
C. Baumgarten,22M. Beckmann,6S. Belostotski,24S. Bernreuther,30N. Bianchi,11H.P. Blok,23,31H. B¨ ottcher,7
A. Borissov,20M. Bouwhuis,16J. Brack,5A. Br¨ ull,19V. Bryzgalov,25G.P. Capitani,11H.C. Chiang,16
G. Ciullo,10M. Contalbrigo,10G.R. Court,17P.F. Dalpiaz,10R. De Leo,3L. De Nardo,1E. De Sanctis,11
E. Devitsin,21P. Di Nezza,11M. D¨ uren,14M. Ehrenfried,9A. Elalaoui-Moulay,2G. Elbakian,33F. Ellinghaus,7
U. Elschenbroich,13J. Ely,5R. Fabbri,10A. Fantoni,11A. Fechtchenko,8L. Felawka,29B. Fox,5J. Franz,12
S. Frullani,27Y. G¨ arber,9G. Gapienko,25V. Gapienko,25F. Garibaldi,27E. Garutti,23D. Gaskell,5G. Gavrilov,24
V. Gharibyan,33G. Graw,22O. Grebeniouk,24L.G. Greeniaus,1,29W. Haeberli,18K. Hafidi,2M. Hartig,29
D. Hasch,11D. Heesbeen,23M. Henoch,9R. Hertenberger,22W.H.A. Hesselink,23,31A. Hillenbrand,9Y. Holler,6
B. Hommez,13G. Iarygin,8A. Ivanilov,25A. Izotov,24H.E. Jackson,2A. Jgoun,24R. Kaiser,15E. Kinney,5
A. Kisselev,24K. K¨ onigsmann,12H. Kolster,19M. Kopytin,24V. Korotkov,7,25V. Kozlov,21B. Krauss,9
V.G. Krivokhijine,8L. Lagamba,3L. Lapik´ as,23A. Laziev,23,31P. Lenisa,10P. Liebing,7T. Lindemann,6K. Lipka,7
W. Lorenzon,20B.-Q. Ma,4N.C.R. Makins,16H. Marukyan,33F. Masoli,10F. Menden,12V. Mexner,23N. Meyners,6
O. Mikloukho,24C.A. Miller,1,29Y. Miyachi,30V. Muccifora,11A. Nagaitsev,8E. Nappi,3Y. Naryshkin,24
A. Nass,9W.-D. Nowak,7K. Oganessyan,6,11H. Ohsuga,30G. Orlandi,27S. Potashov,21D.H. Potterveld,2
M. Raithel,9D. Reggiani,10P.E. Reimer,2A. Reischl,23A.R. Reolon,11K. Rith,9G. Rosner,15A. Rostomyan,33
D. Ryckbosch,13I. Sanjiev,2,24I. Savin,8C. Scarlett,20A. Sch¨ afer,26C. Schill,11,12G. Schnell,7K.P. Sch¨ uler,6
A. Schwind,7R. Seidl,9J. Seibert,12B. Seitz,1R. Shanidze,9T.-A. Shibata,30V. Shutov,8M.C. Simani,23,31
K. Sinram,6M. Stancari,10M. Statera,10E. Steffens,9J.J.M. Steijger,23J. Stewart,7U. St¨ osslein,5H. Tanaka,30
S. Taroian,33B. Tchuiko,25A. Terkulov,21S. Tessarin,22E. Thomas,11A. Tkabladze,7A. Trzcinski,32M. Tytgat,13
G.M. Urciuoli,27P. van der Nat,23G. van der Steenhoven,23R. van de Vyver,13M.C. Vetterli,28,29
V. Vikhrov,24M.G. Vincter,1J. Visser,23C. Vogel,9M. Vogt,9J. Volmer,7C. Weiskopf,9J. Wendland,28, 29
J. Wilbert,9T. Wise,18S. Yen,29S. Yoneyama,30B. Zihlmann,23H. Zohrabian,33and P. Zupranski32
(The HERMES Collaboration)
1Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1, Canada
2Physics Division, Argonne National Laboratory, Argonne, Illinois 60439-4843, USA
3Istituto Nazionale di Fisica Nucleare, Sezione di Bari, 70124 Bari, Italy
4Department of Physics, Peking University, Beijing 100871, China
5Nuclear Physics Laboratory, University of Colorado, Boulder, Colorado 80309-0446, USA
6DESY, Deutsches Elektronen-Synchrotron, 22603 Hamburg, Germany
7DESY Zeuthen, 15738 Zeuthen, Germany
8Joint Institute for Nuclear Research, 141980 Dubna, Russia
9Physikalisches Institut, Universit¨ at Erlangen-N¨ urnberg, 91058 Erlangen, Germany
10Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara and
Dipartimento di Fisica, Universit` a di Ferrara, 44100 Ferrara, Italy
11Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, 00044 Frascati, Italy
12Fakult¨ at f¨ ur Physik, Universit¨ at Freiburg, 79104 Freiburg, Germany
13Department of Subatomic and Radiation Physics, University of Gent, 9000 Gent, Belgium
14Physikalisches Institut, Universit¨ at Gießen, 35392 Gießen, Germany
15Department of Physics and Astronomy, University of Glasgow, Glasgow G128 QQ, United Kingdom
16Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
17Physics Department, University of Liverpool, Liverpool L69 7ZE, United Kingdom
18Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
19Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
20Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA
21Lebedev Physical Institute, 117924 Moscow, Russia
22Sektion Physik, Universit¨ at M¨ unchen, 85748 Garching, Germany
23Nationaal Instituut voor Kernfysica en Hoge-Energiefysica (NIKHEF), 1009 DB Amsterdam, The Netherlands
24Petersburg Nuclear Physics Institute, St. Petersburg, Gatchina, 188350 Russia
25Institute for High Energy Physics, Protvino, Moscow region, 142284 Russia
26Institut f¨ ur Theoretische Physik, Universit¨ at Regensburg, 93040 Regensburg, Germany
27Istituto Nazionale di Fisica Nucleare, Sezione Roma 1, Gruppo Sanit` a
and Physics Laboratory, Istituto Superiore di Sanit` a, 00161 Roma, Italy
28Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
29TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
30Department of Physics, Tokyo Institute of Technology, Tokyo 152, Japan
31Department of Physics and Astronomy, Vrije Universiteit, 1081 HV Amsterdam, The Netherlands
32Andrzej Soltan Institute for Nuclear Studies, 00-689 Warsaw, Poland
33Yerevan Physics Institute, 375036 Yerevan, Armenia
(Dated: February 18, 2003)
Single-spin asymmetries have been measured for semi-inclusive electroproduction of π+, π−, π0
and K+mesons in deep-inelastic scattering off a longitudinally polarised deuterium target. The
asymmetries appear in the distribution of the hadrons in the azimuthal angle φ around the virtual
photon direction, relative to the lepton scattering plane. The corresponding analysing powers in the
sinφ moment of the cross section are 0.012±0.002(stat.)±0.002(syst.) for π+, 0.006±0.003(stat.)±
0.002(syst.) for π−, 0.021 ± 0.005(stat.) ± 0.003(syst.) for π0and 0.013 ± 0.006(stat.) ± 0.003(syst.)
for K+. The sin2φ moments are compatible with zero for all particles.
PACS numbers: 13.87.Fh, 13.60.-r, 13.88.+e, 14.20.Dh
Deep-inelastic lepton scattering (DIS) on polarised nu-
cleons has provided much of our present understanding
of the spin structure of the nucleon. Recently, measure-
ments of single-spin azimuthal asymmetries have been
recognised as a powerful source of information about the
spin structure of the nucleon , complementary to in-
clusive deep-inelastic scattering. Significant azimuthal
target-spin asymmetries in electroproduction of π+and
π0mesons on a longitudinally polarised hydrogen tar-
get have been reported in Refs. [2, 3]. Evidence for azi-
muthal asymmetries of pions has also been reported for
deep-inelastic lepton scattering off transversely polarised
It has been suggested  that these single-spin asym-
metries may provide information on the transversity dis-
tribution, which describes in a transverse polarisation
basis the probability to find a quark with its spin par-
allel or antiparallel to the spin of the nucleon that is po-
larised transversely to its (infinite) momentum [6, 7, 8].
Transversity is a chiral-odd distribution function, which
implies that it is not observable in an inclusive measure-
ment, because chirality is conserved in electromagnetic
and strong interactions in the limit of massless on-shell
quarks. Therefore, a second chiral-odd object has to be
involved in the process [9, 10]. In semi-inclusive scatter-
ing this can be a chiral-odd fragmentation function —
for example the Collins-function .
The HERMES results on target single-spin asymme-
tries [2, 3] have elicited a number of phenomenological
studies to evaluate these asymmetries in the framework
of the Collins mechanism using various models as input
for the chiral-odd distribution and fragmentation func-
tions [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. The-
oretical predictions have also been made for single-spin
asymmetries in DIS off the nucleons in a deuterium tar-
get [21, 22].
Recently, it has been shown that another mechanism
can also cause a single-spin azimuthal asymmetry in
semi-inclusive deep-inelastic scattering . In this case,
the observed asymmetry is attributed to the interaction
of the struck quark with the target remnant through the
exchange of a single gluon. This mechanism was shown
to be identical  to the Sivers effect known already for
a long time , involving a chiral-even time-odd distri-
bution function. Other theoretical studies [26, 27, 28, 29]
have revealed that factorisation applies to this process,
which leads to gauge-invariant momentum dependent
parton distributions. In the case of a longitudinally po-
larised target the Collins and the Sivers mechanism can-
not be distinguished. However, for the two mechanisms a
different kinematic dependence on the fractional energy
z of the hadron has been predicted .
This paper reports the first observation of target-spin
azimuthal asymmetries for semi-inclusive pion and kaon
production on a longitudinally polarised deuterium tar-
get. The data were recorded during the 1998, 1999 and
2000 running periods of the HERMES experiment. The
experiment was performed with a beam of 27.6 GeV po-
larised electrons/positrons from the HERA storage ring
at DESY and polarised nucleons in a deuterium gas tar-
get.The average target polarisation was 0.84 with a
fractional uncertainty of 5%. The data were taken with
an electron beam in 1998 and with a positron beam in
1999 and 2000. The measured single-spin asymmetries
show no dependence on the beam charge. Therefore, all
datasets were combined. In the following, electrons and
positrons will be jointly referred to as positrons.
The process considered is the production of a pseu-
doscalar meson (m = π or K) in deep-inelastic positron
scattering off a longitudinally polarised deuterium target:
e +− →
d → e + m + X.(1)
The kinematics of this scattering process are illustrated
in Fig. 1. The relevant variables are the squared four-
momentum −Q2= q2= (k − k′)2and the energy ν =
E −E′of the virtual photon in the target rest frame and
its fractional energy y = ν/E, the invariant mass of the
virtual-photon nucleon system W =
the Bjorken variable x = Q2/2Mν and the fractional en-
?2Mν + M2− Q2,
inclusive deep-inelastic scattering: Lepton scattering plane
(white) and the meson production plane (shaded).
Kinematic planes for meson production in semi-
ergy z = Em/ν of the produced meson. Here, k (k′)
and E (E′) are the 4-momenta and the energies of the
incident (scattered) positron and M is the nucleon mass.
The energy and momentum of the meson in the target
rest frame are given by Em and Pm, respectively. The
transverse momentum P⊥of the produced meson is de-
fined with respect to the virtual-photon direction. The
angle φ is the azimuthal angle of the scattered meson
around the virtual photon direction with respect to the
lepton scattering plane. Its magnitude is evaluated by
cosφ =(− →q ×− →k ) · (− →q ×− →
|− →q ×− →
k | |− →q ×− →Pm|
and its sign by (− →q ×− →
of a target polarised longitudinally with respect to the in-
cident positron direction, the target polarisation vector
has components parallel and orthogonal with respect to
the virtual photon. The longitudinal and the transverse
component of the target polarisation vector are given by
cosθγ and sinθγ, respectively. Here, θγ is the angle be-
tween the incident positron and the virtual photon in the
photon-nucleon centre-of-mass system. In the HERMES
acceptance, the mean values of ?cosθγ? and ?sinθγ? are
0.98 and 0.16, respectively.
For the measurement of a single target-spin asym-
metry the positron beam has to be unpolarised. The
positrons in the HERA storage ring are naturally trans-
versely polarised by the emission of synchrotron radi-
ation . The transverse beam polarisation is trans-
formed into longitudinal polarisation and back to trans-
verse polarisation by two spin-rotators  upstream
and downstream of the HERMES experiment, respec-
tively. The sign of the beam polarisation is changed
about every two months, which requires moving the
magnets of the spin rotators and inverting their mag-
netic field direction. The transverse and the longitudinal
positron polarisation are continuously monitored by two
Compton-backscattering polarimeters [32, 33]. To ob-
k )·− →Pm/|(− →q ×− →k )·− →Pm|. In the case
tain an unpolarised beam, a polarisation and luminosity
weighted average is formed from data of periods with op-
posite beam spin orientations. The averaged luminosity
weighted beam polarisation in the analysed data sample
is 0.0%±0.1%(stat.) ± 2.0%(syst.).
The scattered positrons and associated mesons are de-
tected by the HERMES spectrometer  in the range
0.04 rad < θ < 0.22 rad of the polar angle. Positron
and hadron separation is based on the information from
four detectors: a transition-radiation detector, a dual-
radiator ring imagingˇCerenkov detector (RICH) , a
preshower scintillation detector and a lead-glass electro-
magnetic calorimeter . This system provides an aver-
age positron identification efficiency exceeding 98% with
a hadron contamination below 1%.
Events are required to contain only one electron or
positron track with the same charge as the beam particle
and in addition at least one meson. If more than one
meson is detected in the spectrometer, only the meson
with the largest momentum is considered. Identification
of charged pions or kaons in the momentum range 2 GeV
< Pm< 15 GeV is accomplished using the information
from the RICH. Based on a Monte Carlo simulation of
the RICH, detection efficiencies and contaminations for
charged pions and kaons are determined as a function
of the hadron momentum and the hadron multiplicity.
The average identification efficiency in the RICH is 97%
for pions and 88% for kaons. The detector properties
are used to unfold the true hadron populations from the
Neutral pions are identified by the detection of two
photons in the electromagnetic calorimeter.
constructed energy for each photon is required to be
at least 1.0 GeV and each photon hit in the calorime-
ter is required not to be associated with any charged
particle track going in the same direction. The recon-
structed photon-pair invariant mass Mγγ distribution
shows a clear π0mass peak with a mass resolution of
about 0.012 GeV, as displayed in Fig. 2. Neutral pions
are selected within the invariant mass range 0.10 GeV
< Mγγ< 0.17 GeV. The background contribution from
uncorrelated photons to the reconstructed invariant mass
spectrum decreases with increasing z of the hadron and
ranges from 35% for the lowest z bin to less than 5% for
the highest bin. The asymmetry of this background is de-
termined outside of the mass window of the π0mass peak
and is found to be compatible with zero. A correction is
applied to account for this dilution.
The requirements imposed on the kinematics of the
scattered positron are the same as those in the previous
analyses of the hydrogen data [2, 3]: 1 GeV2< Q2<
15 GeV2, W > 2 GeV, 0.023 < x < 0.4 and y < 0.85.
Contributions from target fragmentation are suppressed
by requiring z > 0.2 and exclusive meson production is
suppressed by the cut z < 0.7. A lower limit of 50 MeV
is imposed on P⊥to ensure an accurate measurement of
number of events
FIG. 2: Invariant mass (Mγγ) spectrum of photon pairs mea-
sured in the electromagnetic calorimeter. A fit to the data
using a Gaussian function for the peak plus a second order
polynomial (solid curve) for the background of uncorrelated
photons is shown as the dotted curve. The two vertical lines
embrace the invariant mass interval used for π0identification.
the azimuthal angle φ.
The target-spin asymmetry AULin the cross section of
scattering an unpolarised beam (U) on a longitudinally
polarised target (L) is evaluated as
N→(φ)/L→+ N←(φ)/L←, (3)
where N→(←)is the number of pions or kaons detected for
target spin antiparallel (parallel) to the direction of the
beam momentum, L→(←)is the respective dead-time cor-
rected luminosity, and PLthe average longitudinal target
polarisation. The asymmetry for π0mesons is corrected
for the dilution from the background of uncorrelated pho-
tons using the equation
Acorr(φ) =Nπ0 + Nbg
· Ameas(φ) −Nbg
Nπ0· Abg(φ). (4)
Here Nπ0 and Nbgare the number of neutral pions and
background-photon pairs, respectively, in each kinematic
bin. The asymmetries for π0mesons Ameasand for the
background of uncorrelated photons Abgare calculated as
defined in Eq. (3). The background asymmetry is found
to be consistent with zero.
In Fig. 3, the azimuthal asymmetries AUL(φ) for the
mesons π+, π0, π−and K+are displayed as a function
of φ, integrated over the experimental acceptance in the
kinematic variables x, P⊥, z, y and Q2. The average
→ → e π+ X
P1 * sin φ
P1 * sin φ + P2 * sin 2φ
P1 = 0.012 ± 0.002
P2 = 0.004 ± 0.002
→ → e π0 X
P1 = 0.021 ± 0.005
P2 = 0.009 ± 0.005
→ → e π- X
P1 = 0.006 ± 0.003
P2 = 0.001 ± 0.003
→ → e K+ X
P1 = 0.013 ± 0.006
P2 = -0.005 ± 0.006
duction of π+, π0, π−and K+mesons.
P0+P1sinφ (solid line) and P0+P1sinφ+P2sin2φ (dashed
line) are also displayed in the figure. The error bars give the
statistical uncertainties of the measurements. The values of
the coefficients P0 are all compatible with zero and the coeffi-
cients P1 and P2 for the various hadrons and their statistical
uncertainties are listed in each panel.
Target spin asymmetries AUL(φ) for electropro-
Fits of the form
values are ?x? = 0.09, ?P⊥? = 0.40 GeV, ?z? = 0.38,
?y? = 0.53 and ?Q2? = 2.4 GeV2.
The asymmetries defined in Eq. (3) were alternatively
fit with the functions
f1(φ) = P0+ P1sinφ
f2(φ) = P0+ P1sinφ + P2sin2φ ,
which are indicated as curves in Fig. 3. All coefficients
P0 are compatible with zero. The sinφ and sin2φ am-
plitudes P1 and P2, obtained from the fit (6) to the
data, are displayed in the figure as well. They repre-
sent the analysing powers Asinφ
muthal asymmetry. The numerical values are given in
and Asin 2φ
of the azi-
proton target [2, 3]
TABLE I: Analysing powers Asin φ
muthal target-spin asymmetry for the electroproduction of
pions and kaons on the deuteron, integrated over the exper-
imental acceptance in x, P⊥, z, y and Q2. Also listed are
earlier results obtained on the proton from Ref. [2, 3]. The
first uncertainty is the statistical and the second is the sys-
tematic uncertainty of the measurement.
for the azi-
Tab. I for the various mesons, together with the previ-
ously reported analysing powers for pion production on
longitudinally polarised protons [2, 3].
The effects of smearing and spectrometer acceptance
are estimated using a Monte Carlo simulation. For this
purpose, a Monte Carlo simulation is carried out with
various x, P⊥or z dependent sinφ and sin2φ amplitudes.
Within the statistical accuracy, the reconstructed event
distributions show the same sinφ and sin2φ amplitudes
as the generated distributions. It is concluded from the
Monte Carlo simulation that the measured asymmetries
are not affected by acceptance or smearing effects of the
detector in any significant way within the statistical pre-
cision of the Monte Carlo simulation of 0.001 (0.002) for
charged mesons (π0).
An additional test of possible acceptance effects was
performed using measurements with unpolarised hydro-
gen and deuterium gas targets.
were regularly done after a few hours of data taking
with polarised targets.The data were analysed with
the kinematic requirements described above and the sinφ
and sin2φ moments Asinφ
cross section are extracted.
spectively as Asinφ
unpolarised target gas. The moments Asin φ
were found to be consistent with zero as expected 
for pions (kaons) within a statistical uncertainty of 0.002
The analysing powers Asinφ
the asymmetry AUL(φ) have been compared to those ob-
tained as moments:
of the unpolarised
They were calculated re-
i=1sinφi and Asin2φ
i=1sin2φi, summed over all N events taken with
extracted from a fit to
?Q2? in GeV2
0.039 0.068 0.115 0.179 0.276
0.47?P⊥? in GeV 0.36
TABLE II: Mean values of Q2for each x bin (upper table)
and mean values of P⊥ for each bin of z (lower table).
source of systematic uncertainty
determination of target polarisation
upper limit on acceptance effects
meson identification (RICH)
TABLE III: Contributions to the systematic uncertainty of
the experimental results for the target spin analysing powers
listed in Tab. I for π+, π−, π0and K+mesons. The
total systematic uncertainty is calculated as the quadratic
sum of the individual contributions.
using the weighting functions W(φ) = sinφ and W(φ) =
sin2φ, respectively. This type of analysis is more sen-
sitive to the experimental acceptance . Based on a
Monte Carlo simulation, corrections of about 15% had to
be applied to account for a cross-contamination between
the sinφ and sin2φ moments. After these corrections,
the analysing powers extracted as moments according to
Eq. (7) and those extracted using a fit to the cross section
asymmetry AUL(φ) agree within the systematic uncer-
tainty assigned to effects of the spectrometer acceptance
(see Tab. III).
In Fig. 4, the analysing powers Asinφ
are shown as a function of x, P⊥ and z together with
earlier results obtained on the proton [2, 3]. The mean
values of Q2for each x bin and the mean values of P⊥
for each z bin are given in Tab. II.
The various contributions to the systematic uncer-
tainty of the experimental results in Tab. I, integrated
over x, P⊥ and z, are listed in Tab. III. For charged
pions, the largest contributions originate from the de-
termination of the target polarisation and from the up-
per limit for possible acceptance effects evaluated in a
Monte Carlo simulation. For kaons the uncertainty in the
hadron identification with the RICH detector also con-
tributes significantly. For pions the RICH efficiency is
larger and the contamination by other hadrons is smaller
so that the contribution to the systematic uncertainty is
small. The charged pion sample can be contaminated by
pions from the decay of heavier mesons. The main contri-
bution originates from the decay of exclusively produced
ρ0vector mesons and is estimated using a Monte Carlo
on the deuteron
→ → e π+ X
→ → e π+ X
→ → e π0 X
→ → e π0 X
→ → e π- X
→ → e π- X
→ → e K+ X
FIG. 4: Target spin analysing powers Asinφ
and on the proton (open squares). The latter are taken from Refs. [2, 3]. The data are shown as a function of one of the
kinematic variables x, P⊥ and z while integrating over the other variables. The error bars give the statistical uncertainties of
the measurements and the bands in the lower parts of each panel give the systematic uncertainties for the deuteron (hashed
band) and for the proton measurement (open band).
for semi-inclusive π+, π0, π−and K+production on the deuteron (filled circles)
simulation. It is found to be smaller than 5%. In addi-
tion, it is shown from the experimental data that there
is no asymmetry in their azimuthal distribution. A con-
tribution is added to the systematic uncertainty for this
dilution. For π0mesons there is a significant contribution
to the systematic uncertainty due to the uncertainty in
the determination of the background yield and its asym-
The analysing power Asinφ
deuteron is greater than zero, but smaller than that ob-
tained on the proton (see Tab. I). In the context of mod-
els based on transversity, the different size of the asymme-
tries for π+production on the proton and deuteron can
be attributed to the dominant role of the u-quark con-
tribution to the observed asymmetry . The analysing
powers for π0production are positive for both deuteron
and proton and of similar size. For π−production, only
the deuteron data suggest an asymmetry different from
zero. The result for K+production on the deuteron is
compatible with that of π+production, which may indi-
cate the dominant contribution from u-quarks fragment-
ing into kaons.
The results for the two targets show a similar be-
haviour in their kinematic dependences on x, P⊥and z.
The observed increase of Asinφ
ULwith increasing x suggests
that the single-spin asymmetries are associated with va-
lence quark contributions.
Two mechanisms have been proposed to explain the
measured single-spin asymmetries. One is the combina-
tion of transversity-related chiral-odd distribution func-
tions and chiral-odd fragmentation functions like the
Collins fragmentation function. The other one is a final-
state interaction of the struck quark with the target rem-
nant (Sivers Effect) [23, 26]. There are no calculations
for a deuterium target available for the latter scenario
that can be compared with the present data.
Recent model calculations in the context of transver-
sity [21, 22] predict Asinφ
for scattering on the deuteron
within the kinematic range of the HERMES experiment.
These calculations are performed in the same frame-
work than those mentioned in our earlier publications
of the proton results [2, 3], but take into account a re-
cently detected sign error in the earlier theoretical calcu-
lations [19, 20]. The transversity distributions calculated
in the chiral quark soliton model (χQSM) , in the
SU(6) quark spectator diquark model  and in a per-
turbative QCD model  have been used as an input.
The results of three of these calculations are displayed in
Fig. 5 together with the experimental data. As can be
seen from Fig. 5, the experimental data are well described
by these calculations.
The analysing power Asin2φ
observable, since it appears as a leading term in the ex-
pansion of the cross section for scattering electrons off a
longitudinally polarised target, while the sinφ moment
appears only at order 1/Q . The dependence of Asin2φ
for π+production on the
is an additional important
→ → e π+ X
→ → e π0 X
→ → e π- X
→ → e K+ X
FIG. 5: Comparison of the measured analysing powers Asin φ
on the deuteron for π+, π0, π−and K+production with pre-
dictions from theoretical calculations in the chiral quark soli-
ton model (χQSM, solid lines ), the quark-diquark model
(QdQ, dashed lines ) and a perturbative QCD model
(pQCD, dotted lines . The shown curves refer to “ap-
proach 2” of the models in Ref. . The error bars give the
statistical uncertainties of the measurements, and the bands
in the lower part of the panels show the systematic uncertain-
ties of the measurements.
→ → e π X
→ → e K+ X
FIG. 6: The sin2φ analysing powers Asin 2φ
π−(upper panel) and for K+production (lower panel) on the
deuteron. The error bars give the statistical uncertainties of
the measurements. The systematic uncertainties for π+and
π−are represented by the hatched band and those for π0by
the open band. The points for π0and π−are slightly shifted in
x for better visibility. Included as curves are predictions from
a transversity-related calculation in the chiral quark soliton
for π+, π0and
on x is presented in Fig. 6. Integrated over the measured
x-range, it is compatible with zero for all mesons (see
Tab. I). Also shown are corresponding values calculated
in the χQSM . For pions, the data do not favour the
predicted trend towards negative asymmetries at large x.
The data presented so far are evaluated in the semi-
inclusive kinematic range 0.2 < z < 0.7. In Fig. 7, the
z-dependencies of the single spin asymmetries Asinφ
the proton and on the deuteron are shown up to z = 1.
The results on the proton have been obtained from ex-
perimental data taken with a longitudinally polarised hy-
drogen target as described in Ref. , neglecting the up-
per z < 0.7 cut, however. The mean experimental resolu-
tion in z is ∆z = 0.02 (0.04) for charged (neutral) pions in
the semi-inclusive regime and ∆z = 0.07 (0.06) for z → 1.
It has to be pointed out that the experimental data shown
as open symbols in Fig. 7 have not been corrected for this
→ → e π X
→ → e π X
FIG. 7: The dependence on z of the analysing powers Asinφ
for π+, π0and π−production on the deuteron (upper panel)
and on the proton (lower panel). The filled symbols show the
semi-inclusive measurements on the deuteron from Fig. 4 and
on the proton from Ref. , respectively. Shown as filled star
is the exclusive measurement for π+production from Ref. .
For the data at high z (open symbols), no corrections for the
experimental resolution in z or possible contaminations by
pions from the decay of exclusive ρ0vector mesons have been
applied. The error bars indicate the statistical uncertainty
of the measurements. The points for π0and π−are slightly
shifted in z for visibility.
variation in ∆z. Also, the results for charged pions have
not been corrected for a possible contamination by pions
from the decay of exclusively produced ρ0vector mesons.
At large z, a transition from the semi-inclusive regime
to the exclusive regime is observed. In the exclusive limit
(z → 1), the scattering process can be interpreted in
terms of generalised parton distributions [37, 38, 39, 40].
The data show an inversion of the sign and an increase
in absolute size of the single spin asymmetries, similar
for both π−and π+.The size of the asymmetry for
π0mesons increases but it remains positive for all z.
A large asymmetry in the exclusive limit has already
been reported for exclusive π+production on the pro-
ton . As shown in the lower panel of Fig. 7, there is a
large analysing power for π0production on the proton as
well, while no significant asymmetry for π−production
is found. No theoretical explanation yet exists for this
In summary, single-spin azimuthal asymmetries for
electroproduction of π+, π0, π−and K+mesons on a
longitudinally polarised deuterium target have been mea-
sured for the first time. The dependences of these asym-
metries on x, P⊥ and z have been investigated.
results show positive asymmetries for π+and π0and
an indication of a positive asymmetry for π−mesons.
The asymmetry for K+is compatible with that for π+
mesons. These findings can be well described by model
calculations where the asymmetries are interpreted in the
context of transversity as the effect of combinations of
chiral-odd distribution functions and chiral-odd fragmen-
tation functions. Here, the observed asymmetries for π+
and K+are consistent with the assumption of u-quark
dominance in the quark distribution and the fragmenta-
tion process. Together with earlier measurements on the
proton [2, 3], the results support the existence of non-
zero chiral-odd distribution functions that describe the
transverse polarisation of quarks. However, it cannot be
excluded that a part of the observed asymmetry is due to
an additional exchange of a gluon in the final state (Sivers
effect) as discussed in Ref. . Furthermore, the data
show an increase of the magnitude of the asymmetries for
charged and neutral pions at large z when approaching
the exclusive regime.
Kotzinian, P.J. Mulders and P. Schweitzer for many in-
teresting discussions on this subject. We gratefully ac-
knowledge the DESY management for its support, the
staffs at DESY and the collaborating institutions for
their significant effort. This work was supported by the
FWO-Flanders, Belgium; the Natural Sciences and En-
gineering Research Council of Canada; the ESOP, IN-
TAS and TMR network contributions from the Euro-
pean Union; the German Bundesministerium f¨ ur Bildung
und Forschung; the Italian Instituto Nazionale di Fisica
Nucleare (INFN); Monbusho International Scientific Re-
search Program, JSPS and Toray Science Foundation of
Japan; the Dutch Foundation for Fundamenteel Onder-
zoek der Materie (FOM); the U.K. Particle Physics and
Astronomy Research Council; and the U.S. Department
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