EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN–PH–EP/2007–009
(revised author list)
2 April 2007
Double spin asymmetry in exclusive ρ0
muoproduction at COMPASS
Abstract
The longitudinal double spin asymmetry A
1 for exclusive leptoproduction of ρ
mesons, µ + N → µ + N + ρ, is studied using the COMPASS 2002 and 2003
data. The measured reaction is incoherent exclusive ρ0 production on polarised
deuterons. The Q2 and x dependence of A
1 is presented in a wide kinematical
range 3 · 10−3 < Q2 < 7 (GeV/c)2 and 5 · 10−5 < x < 0.05. The presented results
are the first measurements of A
1 at small Q
2 (Q2 < 0.1 (GeV/c)2) and small x
(x < 3 · 10−3). The asymmetry is in general compatible with zero in the whole
kinematical range.
(to be submitted to Eur. Phys. J. C)
http://arxiv.org/abs/0704.1863v2
The COMPASS Collaboration
M. Alekseev29), V.Yu. Alexakhin8), Yu. Alexandrov18), G.D. Alexeev8), A. Amoroso29),
A. Arbuzov8), B. Bade lek30), F. Balestra29), J. Ball25), G. Baum1), J. Barth4),
Y. Bedfer25), C. Bernet25), R. Bertini29), M. Bettinelli19), R. Birsa28), J. Bisplinghoff3),
P. Bordalo15,a), F. Bradamante28), A. Bravar16), A. Bressan28), G. Brona30), E. Burtin25),
M.P. Bussa29), A. Chapiro27), M. Chiosso29), A. Cicuttin27), M. Colantoni29,b),
S. Costa29), M.L. Crespo27), N. d’Hose25), S. Dalla Torre28), S. Das7), S.S. Dasgupta6),
R. De Masi20), N. Dedek19), O.Yu. Denisov29,c), L. Dhara7), V. Diaz27),
A.M. Dinkelbach20), S.V. Donskov24), V.A. Dorofeev24), N. Doshita21), V. Duic28),
W. Dünnweber19), P.D. Eversheim3), W. Eyrich9), M. Fabro28), M. Faessler19),
V. Falaleev11), A. Ferrero29), L. Ferrero29), M. Finger22), M. Finger jr.8), H. Fischer10),
C. Franco15), J. Franz10), J.M. Friedrich20), V. Frolov29,c), R. Garfagnini29),
F. Gautheron1), O.P. Gavrichtchouk8), R. Gazda30), S. Gerassimov18,20), R. Geyer19),
M. Giorgi28), B. Gobbo28), S. Goertz2,4), A.M. Gorin24), S. Grabmüller20),
O.A. Grajek30), A. Grasso29), B. Grube20), R. Gushterski8), A. Guskov8), F. Haas20),
J. Hannappel4), D. von Harrach16), T. Hasegawa17), J. Heckmann2), S. Hedicke10),
F.H. Heinsius10), R. Hermann16), C. Heß2), F. Hinterberger3), M. von Hodenberg10),
N. Horikawa21,d), S. Horikawa21), C. Ilgner19), A.I. Ioukaev8), S. Ishimoto21), O. Ivanov8),
Yu. Ivanshin8), T. Iwata21,32), R. Jahn3), A. Janata8), P. Jasinski16), R. Joosten3),
N.I. Jouravlev8), E. Kabuß16), D. Kang10), B. Ketzer20), G.V. Khaustov24),
Yu.A. Khokhlov24), Yu. Kisselev1,2), F. Klein4), K. Klimaszewski30), S. Koblitz16),
J.H. Koivuniemi13), V.N. Kolosov24), E.V. Komissarov8), K. Kondo21),
K. Königsmann10), I. Konorov18,20), V.F. Konstantinov24), A.S. Korentchenko8),
A. Korzenev16,c), A.M. Kotzinian8,29), N.A. Koutchinski8), O. Kouznetsov8,25),
N.P. Kravchuk8), A. Kral23), Z.V. Kroumchtein8), R. Kuhn20), F. Kunne25), K. Kurek30),
M.E. Ladygin24), M. Lamanna11,28), J.M. Le Goff25), A.A. Lednev24), A. Lehmann9),
J. Lichtenstadt26), T. Liska23), I. Ludwig10), A. Maggiora29), M. Maggiora29),
A. Magnon25), G.K. Mallot11), A. Mann20), C. Marchand25), J. Marroncle25),
A. Martin28), J. Marzec31), F. Massmann3), T. Matsuda17), A.N. Maximov8),
W. Meyer2), A. Mielech28,30), Yu.V. Mikhailov24), M.A. Moinester26), A. Mutter10,16),
O. Nähle3), A. Nagaytsev8), T. Nagel20), J. Nassalski30), S. Neliba23), F. Nerling10),
S. Neubert20), D.P. Neyret25), V.I. Nikolaenko24), K. Nikolaev8), A.G. Olshevsky8),
M. Ostrick4), A. Padee31), P. Pagano28), S. Panebianco25), R. Panknin4), D. Panzieri29,b),
S. Paul20), B. Pawlukiewicz-Kaminska30) , D.V. Peshekhonov8), V.D. Peshekhonov8),
G. Piragino29), S. Platchkov25), J. Pochodzalla16), J. Polak14), V.A. Polyakov24),
J. Pretz4), S. Procureur25), C. Quintans15), J.-F. Rajotte19), V. Rapatsky8),
S. Ramos15,a), G. Reicherz2), A. Richter9),F. Robinet25), E. Rocco28,29), E. Rondio30),
A.M. Rozhdestvensky8) , D.I. Ryabchikov24), V.D. Samoylenko24), A. Sandacz30),
H. Santos15), M.G. Sapozhnikov8), S. Sarkar7), I.A. Savin8), P. Schiavon28), C. Schill10),
L. Schmitt20), P. Schönmeier9), W. Schröder9), O.Yu. Shevchenko8), H.-W. Siebert12,16),
L. Silva15), L. Sinha7), A.N. Sissakian8), M. Slunecka8), G.I. Smirnov8), S. Sosio29),
F. Sozzi28), V.P. Sugonyaev24), A. Srnka5), F. Stinzing9), M. Stolarski30,10), M. Sulc14),
R. Sulej31), N. Takabayashi21), V.V. Tchalishev8), S. Tessaro28), F. Tessarotto28),
A. Teufel9), L.G. Tkatchev8), G. Venugopal3), M. Virius23), N.V. Vlassov8), A. Vossen10),
R. Webb9), E. Weise3), Q. Weitzel20), R. Windmolders4), S. Wirth9), W. Wíslicki30),
K. Zaremba31), M. Zavertyaev18), E. Zemlyanichkina8), J. Zhao16), R. Ziegler3), and
A. Zvyagin19)
1) Universität Bielefeld, Fakultät für Physik, 33501 Bielefeld, Germanye)
2) Universität Bochum, Institut für Experimentalphysik, 44780 Bochum, Germanye)
3) Universität Bonn, Helmholtz-Institut für Strahlen- und Kernphysik, 53115 Bonn, Germanye)
4) Universität Bonn, Physikalisches Institut, 53115 Bonn, Germanye)
5) Institute of Scientific Instruments, AS CR, 61264 Brno, Czech Republicf)
6) Burdwan University, Burdwan 713104, Indiah)
7) Matrivani Institute of Experimental Research & Education, Calcutta-700 030, Indiai)
8) Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
9) Universität Erlangen–Nürnberg, Physikalisches Institut, 91054 Erlangen, Germanye)
10) Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germanye)
11) CERN, 1211 Geneva 23, Switzerland
12) Universität Heidelberg, Physikalisches Institut, 69120 Heidelberg, Germanye)
13) Helsinki University of Technology, Low Temperature Laboratory, 02015 HUT, Finland and University
of Helsinki, Helsinki Institute of Physics, 00014 Helsinki, Finland
14) Technical University in Liberec, 46117 Liberec, Czech Republicf)
15) LIP, 1000-149 Lisbon, Portugalg)
16) Universität Mainz, Institut für Kernphysik, 55099 Mainz, Germanye)
17) University of Miyazaki, Miyazaki 889-2192, Japanj)
18) Lebedev Physical Institute, 119991 Moscow, Russia
19) Ludwig-Maximilians-Universität München, Department für Physik, 80799 Munich, Germanye)
20) Technische Universität München, Physik Department, 85748 Garching, Germanye)
21) Nagoya University, 464 Nagoya, Japanj)
22) Charles University, Faculty of Mathematics and Physics, 18000 Prague, Czech Republicf)
23) Czech Technical University in Prague, 16636 Prague, Czech Republicf)
24) State Research Center of the Russian Federation, Institute for High Energy Physics, 142281 Protvino,
Russia
25) CEA DAPNIA/SPhN Saclay, 91191 Gif-sur-Yvette, France
26) Tel Aviv University, School of Physics and Astronomy, 69978 Tel Aviv, Israelk)
27) ICTP–INFN MLab Laboratory, 34014 Trieste, Italy
28) INFN Trieste and University of Trieste, Department of Physics, 34127 Trieste, Italy
29) INFN Turin and University of Turin, Physics Department, 10125 Turin, Italy
30) So ltan Institute for Nuclear Studies and Warsaw University, 00-681 Warsaw, Polandl)
31) Warsaw University of Technology, Institute of Radioelectronics, 00-665 Warsaw, Polandm)
32) Yamagata University, Yamagata, 992-8510 Japanj)
a) Also at IST, Universidade Técnica de Lisboa, Lisbon, Portugal
b) Also at University of East Piedmont, 15100 Alessandria, Italy
c) On leave of absence from JINR Dubna
d) Also at Chubu University, Kasugai, Aichi, 487-8501 Japan
e) Supported by the German Bundesministerium für Bildung und Forschung
f) Suppported by Czech Republic MEYS grants ME492 and LA242
g) Supported by the Portuguese FCT - Fundação para a Ciência e Tecnologia grants
POCTI/FNU/49501/2002 and POCTI/FNU/50192/2003
h) Supported by DST-FIST II grants, Govt. of India
i) Supported by the Shailabala Biswas Education Trust
j) Supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan; Daikou
Foundation and Yamada Foundation
k) Supported by the Israel Science Foundation, founded by the Israel Academy of Sciences and Human-
ities
l) Supported by KBN grant nr 621/E-78/SPUB-M/CERN/P-03/DZ 298 2000, nr 621/E-
78/SPB/CERN/P-03/DWM 576/2003-2006, and by MNII reasearch funds for 2005–2007
m) Supported by KBN grant nr 134/E-365/SPUB-M/CERN/P-03/DZ299/2000
1 Introduction
In this paper we present results on the longitudinal double spin asymmetry A
1 for
exclusive incoherent ρ0 production in the scattering of high energy muons on nucleons.
The experiment was carried out at CERN by the COMPASS collaboration using the
160 GeV muon beam and the large 6LiD polarised target.
The studied reaction is
µ + N → µ′ + ρ0 + N ′, (1)
where N is a quasi-free nucleon from the polarised deuterons. The reaction (1) can be
described in terms of the virtual photoproduction process
γ∗ + N → ρ0 + N ′. (2)
The reaction (2) can be regarded as a fluctuation of the virtual photon into a quark-
antiquark pair (in partonic language), or an off-shell vector meson (in Vector Meson
Dominance model), which then scatters off the target nucleon resulting in the production
of an on-shell vector meson. At high energies this is predominantly a diffractive process and
plays an important role in the investigation of Pomeron exchange and its interpretation
in terms of multiple gluon exchange.
Most of the presently available information on the spin structure of reaction (2)
stems from the ρ0 spin density matrix elements, which are obtained from the analysis
of angular distributions of ρ0 production and decay [1]. Experimental results on ρ0 spin
density matrix elements come from various experiments [2–6] including the preliminary
results from COMPASS [7].
The emerging picture of the spin structure of the considered process is the following.
At low photon virtuality Q2 the cross section by transverse virtual photons σT dominates,
while the relative contribution of the cross section by longitudinal photons σL rapidly
increases with Q2. At Q2 of about 2 (GeV/c)2 both components become comparable and
at a larger Q2 the contribution of σL becomes dominant and continues to grow, although
at lower rate than at low Q2. Approximately, the so called s-channel helicity conservation
(SCHC) is valid, i.e. the helicity of the vector meson is the same as the helicity of the
parent virtual photon. The data indicate that the process can be described approximately
by the exchange in the t-channel of an object with natural parity P . Small deviations from
SCHC are observed, also at the highest energies, whose origin is still to be understood. An
interesting suggestion was made in Ref. [8] that at high energies the magnitudes of various
helicity amplitudes for the reaction (2) may shed a light on the spin-orbital momentum
structure of the vector meson.
A complementary information can be obtained from measurements of the double
spin cross section asymmetry, when the information on both the beam and target polari-
sation is used. The asymmetry is defined as
σ1/2 − σ3/2
σ1/2 + σ3/2
, (3)
where σ1/2(3/2) stands for the cross sections of the reaction (2) and the subscripts denote
the total virtual photon–nucleon angular momentum component along the virtual photon
direction. In the following we will also use the asymmetry ALL which is defined for reaction
(1) as the asymmetry of muon–nucleon cross sections for antiparallel and parallel beam
and target longitudinal spin orientations.
In the Regge approach [9] the longitudinal double spin asymmetry A
1 can arise due
to the interference of amplitudes for exchange in the t-channel of Reggeons with natural
parity (Pomeron, ρ, ω, f , A2 ) with amplitudes for Reggeons with unnatural parity (π,A1).
No significant asymmetry is expected when only a non-perturbative Pomeron is exchanged
because it has small spin-dependent couplings as found from hadron-nucleon data for cross
sections and polarisations.
Similarly, in the approach of Fraas [10], assuming approximate validity of SCHC, the
spin asymmetry A
1 arises from the interference between parts of the helicity amplitudes
for transverse photons corresponding to the natural and unnatural parity exchanges in
the t channel. While a measurable asymmetry can arise even from a small contribution of
the unnatural parity exchange, the latter may remain unmeasurable in the cross sections.
A significant unnatural-parity contribution may indicate an exchange of certain Reggeons
like π, A1 or in partonic terms an exchange of qq̄ pairs.
In the same reference a theoretical prediction for A
1 was presented, which is based
on the description of forward exclusive ρ0 leptoproduction and inclusive inelastic lepton-
nucleon scattering by the off-diagonal Generalised Vector Meson Dominance (GVMD)
model, applied to the case of polarised lepton–nucleon scattering. At the values of Bjorken
variable x < 0.2, with additional assumptions [11], A
1 can be related to the A1 asymmetry
for inclusive inelastic lepton scattering at the same x as
1 + (A1)2
. (4)
This prediction is consistent with the HERMES results for both the proton and deuteron
targets, although with rather large errors.
In perturbative QCD, there exists a general proof of factorisation [12] for exclu-
sive vector meson production by longitudinal photons. It allows a decomposition of the
full amplitude for reaction (2) into three components: a hard scattering amplitude for
the exchange of quarks or gluons, a distribution amplitude for the meson and the non-
perturbative description of the target nucleon in terms of the generalised parton distri-
butions (GPDs), which are related to the internal structure of the nucleon. No similar
proof of factorisation exists for transverse virtual photons, and as a consequence the in-
terpretation of A
1 in perturbative QCD is not possible at leading twist. However, a model
including higher twist effects proposed by Martin et al. [13] describes the behaviour of
both σL as well as of σT reasonably well. An extension of this model by Ryskin [14] for
the spin dependent cross sections allows to relate A
1 to the spin dependent GPDs of
gluons and quarks in the nucleon. The applicability of this model is limited to the range
Q2 ≥ 4 (GeV/c)2. More recently another pQCD-inspired model involving GPDs has been
proposed by Goloskokov and Kroll [15,16]. The non-leading twist asymmetry ALL results
from the interference between the dominant GPD Hg and the helicity-dependent GPD H̃g.
The asymmetry is estimated to be of the order k2T H̃g/(Q
2Hg), where kT is the transverse
momentum of the quark and the antiquark.
Up to now little experimental information has been available on the double spin
asymmetries for exclusive leptoproduction of vector mesons. The first observation of a non-
zero asymmetry A
1 in polarised electron–proton deep-inelastic scattering was reported by
the HERMES experiment [11]. In the deep inelastic region (0.8 < Q2 < 3 (GeV/c)2)
the measured asymmetry is equal to 0.23 ± 0.14 (stat) ± 0.02 (syst) [17], with little
dependence on the kinematical variables. In contrast, for the ‘quasi-real photoproduction’
data, with 〈Q2〉 = 0.13 (GeV/c)2, the asymmetry for the proton target is consistent with
zero. On the other hand the measured asymmetry A
1 for the polarised deuteron target
and the asymmetry A
1 for exclusive production of φ meson either on polarised protons
or deuterons are consistent with zero both in the deep inelastic and in the quasi-real
photoproduction regions [17].
The HERMES result indicating a non-zero A
1 for the proton target differs from the
unpublished result of similar measurements by the SMC experiment [18] at comparable
values of Q2 but at about three times higher values of the photon-nucleon centre of mass
energy W , i.e. at smaller x. The SMC measurements of ALL in several bins of Q
2 are
consistent with zero for both proton and deuteron targets.
2 The experimental set-up
The experiment [19] was performed with the high intensity positive muon beam from
the CERN M2 beam line. The µ+ beam intensity is 2·108 per spill of 4.8 s with a cycle time
of 16.8 s. The average beam energy is 160 GeV and the momentum spread is σp/p = 0.05.
The momentum of each beam muon is measured upstream of the experimental area in a
beam momentum station consisting of several planes of scintillator strips or scintillating
fibres with a dipole magnet in between. The precision of the momentum determination
is typically ∆p/p ≤ 0.003. The µ+ beam is naturally polarised by the weak decays of
the parent hadrons. The polarisation of the muon varies with its energy and the average
polarisation is −0.76.
The beam traverses the two cells of the polarised target, each 60 cm long, 3 cm in
diameter and separated by 10 cm, which are placed one after the other. The target cells are
filled with 6LiD which is used as polarised deuteron target material and is longitudinally
polarised by dynamic nuclear polarisation (DNP). The two cells are polarised in opposite
directions so that data from both spin directions are recorded at the same time. The
typical values of polarisation are about 0.50. A mixture of liquid 3He and 4He, used to
refrigerate the target, and a small amount of heavier nuclei are also present in the target.
The spin directions in the two target cells are reversed every 8 hours by rotating the
direction of the magnetic field in the target. In this way fluxes and acceptances cancel
in the calculation of spin asymmetries, provided that the ratio of acceptances of the two
cells remains unchanged after the reversal.
The COMPASS spectrometer is designed to reconstruct the scattered muons and
the produced hadrons in wide momentum and angular ranges. It is divided in two stages
with two dipole magnets, SM1 and SM2. The first magnet, SM1, accepts charged particles
of momenta larger than 0.4 GeV/c, and the second one, SM2, those larger than 4 GeV/c.
The angular acceptance of the spectrometer is limited by the aperture of the polarised
target magnet. For the upstream end of the target it is ±70 mrad.
To match the expected particle flux at various locations in the spectrometer, COM-
PASS uses various tracking detectors. Small-angle tracking is provided by stations of
scintillating fibres, silicon detectors, micromesh gaseous chambers and gas electron mul-
tiplier chambers. Large-angle tracking devices are multiwire proportional chambers, drift
chambers and straw detectors. Muons are identified in large-area mini drift tubes and
drift tubes placed downstream of hadron absorbers. Hadrons are detected by two large
iron-scintillator sampling calorimeters installed in front of the absorbers and shielded to
avoid electromagnetic contamination. The identification of charged particles is possible
with a RICH detector, although in this paper we have not utilised the information from
the RICH.
The data recording system is activated by various triggers indicating the presence of
a scattered muon and/or an energy deposited by hadrons in the calorimeters. In addition
to the inclusive trigger, in which the scattered muon is identified by coincidence signals
in the trigger hodoscopes, several semi-inclusive triggers were used. They select events
fulfilling the requirement to detect the scattered muon together with the energy deposited
in the hadron calorimeters exceeding a given threshold. In 2003 the acceptance was further
extended towards high Q2 values by the addition of a standalone calorimetric trigger in
which no condition is set for the scattered muon. The COMPASS trigger system allows us
to cover a wide range of Q2, from quasi-real photoproduction to deep inelastic interactions.
A more detailed description of the COMPASS apparatus can be found in Ref. [19]
3 Event sample
For the present analysis the whole data sample taken in 2002 and 2003 with the
longitudinally polarised target is used. For an event to be accepted for further analysis it
is required to originate in the target, have a reconstructed beam track, a scattered muon
track, and only two additional tracks of oppositely charged hadrons associated to the
primary vertex. The fluxes of beam muons passing through each target cell are equalised
using appropriate cuts on the position and angle of the beam tracks.
The charged pion mass hypothesis is assigned to each hadron track and the invariant
mass of two pions, mππ, calculated. A cut on the invariant mass of two pions, 0.5 < mππ <
1 GeV/c2, is applied to select the ρ0. As slow recoil target particles are not detected, in
order to select exclusive events we use the cut on the missing energy, −2.5 < Emiss <
2.5 GeV, and on the transverse momentum of ρ0 with respect to the direction of virtual
photon, p2t < 0.5 (GeV/c)
2. Here Emiss = (M
X−M2p )/2Mp, where MX is the missing mass
of the unobserved recoiling system and Mp is the proton mass. Coherent interactions on
the target nuclei are removed by a cut p2t > 0.15 (GeV/c)
2. To avoid large corrections for
acceptance and misidentification of events, additional cuts ν > 30 GeV and Eµ′ > 20 GeV
are applied.
The distributions of mππ, Emiss and p
t are shown in Fig. 1. Each plot is obtained
applying all cuts except those corresponding to the displayed variable. On the left top
panel of Fig. 1 a clear peak of the ρ0 resonance, centred at 770 MeV/c2, is visible on the
top of the small contribution of background of the non-resonant π+π− pairs. Also the
skewing of the resonance peak towards smaller values of mππ, due to an interference with
the non-resonant background, is noticeable. A small bump below 0.4 GeV/c2 is due to
assignment of the charged pion mass to the kaons from decays of φ mesons. The mass cuts
eliminate the non-resonant background outside of the ρ0 peak, as well as the contribution
of φ mesons.
On the right top panel of the figure the peak at Emiss ≈ 0 is the signal of exclusive
ρ0 production. The width of the peak, σ ≈ 1.1 GeV, is due to the spectrometer resolution.
Non-exclusive events, where in addition to the recoil nucleon other undetected hadrons
are produced, appear at Emiss > 0. Due to the finite resolution, however, they are not
resolved from the exclusive peak. This background consists of two components: the double-
diffractive events where additionally to ρ0 an excited nucleon state is produced in the
nucleon vertex of reaction (2), and events with semi-inclusive ρ0 production, in which
other hadrons are produced but escape detection.
The p2t distribution shown on the bottom panel of the figure indicates a contribution
from coherent production on target nuclei at small p2t values. A three-exponential fit
to this distribution was performed, which indicates also a contribution of non-exclusive
background increasing with p2t . Therefore to select the sample of exclusive incoherent ρ
 [GeV/cππm
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
 [GeV]missE
-4 -2 0 2 4 6 8 10 12 14
10000
 [(GeV/c)2tp
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure 1: Distributions of mππ (top left), Emiss (top right) and p
t (bottom) for the exclu-
sive sample. The arrows show cuts imposed on each variable to define the final sample.
production, the aforementioned p2t cuts, indicated by arrows, were applied.
After all selections the final sample consists of about 2.44 million events. The dis-
tributions of Q2, x and W are shown in Fig. 2. The data cover a wide range in Q2 and
x which extends towards the small values by almost two orders of magnitude compared
to the similar studies reported in Ref. [17]. The sharp edge of the W distribution at the
low W values is a consequence of the cut applied on ν. For this sample 〈W 〉 is equal to
10.2 GeV and 〈p2t 〉 = 0.27(GeV/c)2.
4 Extraction of asymmetry A
The cross section asymmetry ALL = (σ↑↓ − σ↑↑)/(σ↑↓ + σ↑↑) for reaction (1) , for
antiparallel (↑↓) and parallel (↑↑) spins of the incoming muon and the target nucleon, is
related to the virtual-photon nucleon asymmetry A
ALL = D (A
1 + ηA
2) , (5)
where the factors D and η depend on the event kinematics and A
2 is related to the
interference cross section for exclusive production by longitudinal and transverse virtual
photons. As the presented results extend into the range of very small Q2, the exact
formulae for the depolarisation factor D and kinematical factor η [20] are used without
neglecting terms proportional to the lepton mass squared m2. The depolarisation factor
is given by
D(y,Q2) =
y [(1 + γ2y/2)(2 − y) − 2y2m2/Q2]
y2(1 − 2m2/Q2)(1 + γ2) + 2(1 + R)(1 − y − γ2y2/4)
, (6)
 [(GeV/c)2Q
-410 -310 -210 -110 1 10 210
 [(GeV/c)2Q
-410 -310 -210 -110 1 10 210
-610 -510 -410 -310 -210 -110 1
W [GeV]
0 5 10 15 20 25
Figure 2: Distributions of the kinematical variables for the final sample: Q2 with linear
and logarithmic vertical axis scale (top left and right panels respectively), x (bottom left),
and the energy W (bottom right).
where R = σL/σT , σL(T ) is the cross section for reaction (2) initiated by longitudinally
(transversely) polarised virtual photons, the fraction of the muon energy lost y = ν/Eµ
and γ2 = Q2/ν2. The kinematical factor η(y,Q2) is the same as for the inclusive asym-
metry.
The asymmetry A
2 obeys the positivity limit A
R, analogous to the one for
the inclusive case. For Q2 ≤ 0.1 (GeV/c)2 the ratio R for the reaction (2) is small, cf.
Fig. 3, and the positivity limit constrains A
2 to small values. Although for larger Q
2 the
ratio R for the process (2) increases with Q2, because of small values of η the product
R is small in the whole Q2 range of our sample. Therefore the second term in Eq. 5
can be neglected, so that
ALL, (7)
and the effect of this approximation is included in the systematic uncertainty of A
The number of events Ni collected from a given target cell in a given time interval
is related to the spin-independent cross section σ̄ for reaction (2) and to the asymmetry
Ni = aiφiniσ̄(1 + PBPTfDA
1), (8)
where PB and PT are the beam and target polarisations, φi is the incoming muon flux, ai
the acceptance for the target cell, ni corresponding number of target nucleons, and f the
target dilution factor. The asymmetry is extracted from the data sets taken before and
after a reversal of the target spin directions. The four relations of Eq. 8, corresponding
to the two cells (u and d) and the two spin orientations (1 and 2) lead to a second-
 [(GeV/c)2Q
-210 -110 1 10
Figure 3: The ratio R = σL/σT as a function of Q
2 measured in the E665 experiment.
The curve is a fit to the data described in the text.
order equation in A
1 for the ratio (Nu,1Nd,2/Nd,1Nu,2). Here fluxes cancel out as well as
acceptances, if the ratio of acceptances for the two cells is the same before and after
the reversal [21]. In order to minimise the statistical error all quantities used in the
asymmetry calculation are evaluated event by event with the weight factor w = PBfD.
The polarisation of the beam muon, PB, is obtained from a simulation of the beam line
and parameterised as a function of the beam momentum. The target polarisation is not
included in the event weight w because it may vary in time and generate false asymmetries.
An average PT is used for each target cell and each spin orientation.
The ratio R, which enters the formula for D and strongly depends on Q2 for reaction
(2), was calculated on an event-by-event basis using the parameterisation
R(Q2) = a0(Q
2)a1 , (9)
with a0 = 0.66 ± 0.05, and a1 = 0.61 ± 0.09. The parameterisation was obtained by the
Fermilab E665 experiment from a fit to their R measurements for exclusive ρ0 muopro-
duction on protons [3]. These are shown in Fig. 3 together with the fitted Q2-dependence.
The preliminary COMPASS results on R for the incoherent exclusive ρ0 production on
the nucleon [7], which cover a broader kinematic region in Q2 , agree reasonably well with
this parameterisation. The uncertainty of a0 and a1 is included in the systematic error of
The dilution factor f gives the fraction of events of reaction (2) originating from
nucleons in polarised deuterons inside the target material. It is calculated event-by-event
using the formula
f = C1 · f0 = C1 ·
nD + ΣAnA(σ̃A/σ̃D)
. (10)
Here nD and nA denote numbers of nucleons in deuteron and nucleus of atomic mass A
in the target, and σ̃D and σ̃A are the cross sections per nucleon for reaction (2) occurring
on the deuteron and on the nucleus of atomic mass A, respectively. The sum runs over all
nuclei present in the COMPASS target. The factor C1 takes into account that there are
two polarised deuterons in the 6LiD molecule, as the 6Li nucleus is in a first approximation
composed of a deuteron and an α particle.
The measurements of the σ̃A/σ̃D for incoherent exclusive ρ
0 production come from
the NMC [2], E665 [22] and early experiments on ρ0 photoproduction [23]. They were
 [(GeV/c)2Q
0 2 4 6 8 10 12 14
photoproduction
 [(GeV/c)2Q
-310 -210 -110 1 10
Figure 4: (Left) Parameter α of Eq. 11 as a function of Q2 (from Ref. [24]). The exper-
imental points and the fitted curve are shown. See text for details. (Right) The dilution
factor f as a function of Q2.
fitted in Ref. [24] with the formula:
σ̃A = σp ·Aα(Q
2)−1, with α(Q2) − 1 = −
exp{−Q2/Q20}, (11)
where σp is the cross section for reaction (2) on the free proton. The value of the fitted
parameter Q20 is equal to 9 ± 3 (GeV/c)2. The measured values of the parameter α and
the fitted curve α(Q2) are shown on the left panel of Fig. 4 taken from Ref. [24]. On the
right panel of the figure the average value of f is plotted for the various Q2 bins used in
the present analysis. The values of f are equal to about 0.36 in most of the Q2 range,
rising to about 0.38 at the highest Q2.
The radiative corrections (RC) have been neglected in the present analysis, in par-
ticular in the calculation of f , because they are expected to be small for reaction (1).
They were evaluated [25] to be of the order of 6% for the NMC exclusive ρ0 production
analysis. The small values of RC are mainly due to the requirement of event exclusivity
via cuts on Emiss and p
t , which largely suppress the dominant external photon radiation.
The internal (infrared and virtual) RC were estimated in Ref. [25] to be of the order of
5 Systematic errors
The main systematic uncertainty of A
1 comes from an estimate of possible false
asymmetries. In order to improve the accuracy of this estimate, in addition to the standard
sample of incoherent events, a second sample was selected by changing the p2t cuts to
0 < p2t < 0.5 (GeV/c)
2, (12)
and keeping all the remaining selections and cuts the same as for the ‘incoherent sample’.
In the following it will be referred to as the ‘extended p2t sample’. Such an extension of the
p2t range allows one to obtain a sample which is about five times larger than the incoherent
sample. However, in addition to incoherent events such a sample contains a large fraction of
events originating from coherent ρ0 production. Therefore, for the estimate of the dilution
factor f a different nuclear dependence of the exclusive cross section was used, applicable
for the sum of coherent and incoherent cross sections [2]. The physics asymmetries A
1 for
both samples are consistent within statistical errors.
Possible, false experimental asymmetries were searched for by modifying the se-
lection of data sets used for the asymmetry calculation. The grouping of the data into
configurations with opposite target-polarisation was varied from large samples, covering
at most two weeks of data taking, into about 100 small samples, taken in time intervals of
the order of 16 hours. A statistical test was performed on the distributions of asymmetries
obtained from these small samples. In each of the Q2 and x bins the dispersion of the
values of A
1 around their mean agrees with the statistical error. Time-dependent effects
which would lead to a broadening of these distributions were thus not observed. Allowing
the dispersion of A
1 to vary within its two standard deviations we obtain for each bin an
upper bound for the systematic error arising from time-dependent effects
σfalseA,tdep < 0.56 σstat. (13)
Here σstat is the statistical error on A
1 for the extended p
t sample. The uncertainty on the
estimates of possible false asymmetries due to the time-dependent effects is the dominant
contribution to the total systematic error in most of the kinematical region.
Asymmetries for configurations where spin effects cancel out were calculated to
check the cancellation of effects due to fluxes and acceptances. They were found compatible
with zero within the statistical errors. Asymmetries obtained with different settings of the
microwave (MW) frequency, used for DNP, were compared in order to test possible effects
related to the orientation of the target magnetic field. The results for the extended p2t
sample tend to show that there is a small difference between asymmetries for the two
MW configurations. However, because the numbers of events of the data samples taken
with each MW setting are approximately balanced, the effect of this difference on A
negligible for the total sample.
The systematic error on A
1 also contains an overall scale uncertainty of 6.5% due to
uncertainties on PB and PT . The uncertainty of the parameterisation of R(Q
2) affects the
depolarisation factor D. The uncertainty of the dilution factor f is mostly due to uncer-
tainty of the parameter α(Q2) which takes into account nuclear effects in the incoherent
ρ0 production. The neglect of the A
2 term mainly affects the highest bins of Q
2 and x.
Another source of systematic errors is due to the contribution of the non-exclusive
background to our sample. This background originates from two sources. First one is
due to the production of ρ0 accompanied by the dissociation of the target nucleon, the
second one is the production of ρ0 in inclusive scattering. In order to evaluate the amount
of background in the sample of exclusive events it is necessary to determine the Emiss
dependence for the non-exclusive background in the region under the exclusive peak (cf.
Fig. 1 ). For this purpose complete Monte Carlo simulations of the experiment were used,
with events generated by either the PYTHIA 6.2 or LEPTO 6.5.1 generators. Events
generated with LEPTO come only from deep inelastic scattering and cover the range of
Q2 > 0.5 (GeV/c)2. Those generated with PYTHIA cover the whole kinematical range
of the experiment and include exclusive production of vector mesons and processes with
diffractive excitation of the target nucleon or the vector meson, in addition to inelastic
production.
The generated MC events were reconstructed and selected for the analysis using the
same procedure as for the data. In each bin of Q2 the Emiss distribution for the MC was
normalised to the corresponding one for the data in the range of large Emiss > 7.5 GeV.
Then the normalised MC distribution was used to estimate the number of background
events under the exclusive peak in the data. The fraction of background events in the
sample of incoherent exclusive ρ0 production was estimated to be about 0.12±0.06 in most
of the kinematical range, except in the largest Q2 region, where it is about 0.24±0.12. The
large uncertainties of these fractions reflect the differences between estimates from LEPTO
and PYTHIA in the region where they overlap. In the case of PYTHIA the uncertainties
on the cross sections for diffractive photo- and electroproduction of vector mesons also
contribute. For events generated with PYTHIA the Emiss distributions for various physics
processes could be studied separately. It was found that events of ρ0 production with an
excitation of the target nucleon into N∗ resonances of small mass, M < 2 GeV/c2, cannot
be resolved from the exclusive peak and therefore were not included in the estimates of
number of background events.
An estimate of the asymmetry A
1 for the background was obtained using a non-
exclusive sample, which was selected with the standard cuts used in this analysis, except
the cut on Emiss which was modified to Emiss > 2.5 GeV. In different high-Emiss bins A
for this sample was found compatible with zero.
Because no indication of a non-zero A
1 for the background was found, and also due
to a large uncertainty of the estimated amount of background in the exclusive sample,
no background corrections were made. Instead, the effect of background was treated as a
source of systematic error. Its contribution to the total systematic error was not significant
in most of the kinematical range, except for the highest Q2 and x.
The total systematic error on A
1 was obtained as a quadratic sum of the errors
from all discussed sources. Its values for each Q2 and x bin are given in Tables 1 and 2.
The total systematic error amounts to about 40% of the statistical error for most of the
kinematical range. Both errors become comparable in the highest bin of Q2.
6 Results
The COMPASS results on A
1 are shown as a function of Q
2 and x in Fig. 5 and
listed in Tables 1 and 2. The statistical errors are represented by vertical bars and the
total systematic errors by shaded bands.
 [(GeV/c)2Q
-310 -210 -110 1 10
-410 -310 -210 -110
Figure 5: A
1 as a function of Q
2 (left) and x (right) from the present analysis. Error bars
correspond to statistical errors, while bands at the bottom represent the systematical
errors.
The wide range in Q2 covers four orders of magnitude from 3 · 10−3 to 7 (GeV/c)2.
The domain in x which is strongly correlated with Q2, varies from 5 · 10−5 to about
0.05 (see Tables for more details). For the whole kinematical range the A
1 asymmetry
measured by COMPASS is consistent with zero. As discussed in the introduction, this
indicates that the role of unnatural parity exchanges, like π- or A1-Reggeon exchange, is
Table 1: Asymmetry A
1 as a function of Q
2. Both the statistical errors (first) and the
total systematic errors (second) are listed.
Q2 range 〈Q2〉 [(GeV/c)2] 〈x〉 〈ν〉 [GeV] Aρ1
0.0004 − 0.005 0.0031 4.0 · 10−5 42.8 −0.030 ± 0.045 ± 0.014
0.005 − 0.010 0.0074 8.4 · 10−5 49.9 0.048 ± 0.038 ± 0.013
0.010 − 0.025 0.017 1.8 · 10−4 55.6 0.063 ± 0.026 ± 0.014
0.025 − 0.050 0.036 3.7 · 10−4 59.9 −0.035 ± 0.027 ± 0.009
0.05 − 0.10 0.072 7.1 · 10−4 62.0 −0.010 ± 0.028 ± 0.008
0.10 − 0.25 0.16 0.0016 62.3 −0.019 ± 0.029 ± 0.009
0.25 − 0.50 0.35 0.0036 60.3 0.016 ± 0.045 ± 0.014
0.5 − 1 0.69 0.0074 58.6 0.141 ± 0.069 ± 0.030
1 − 4 1.7 0.018 59.7 0.000 ± 0.098 ± 0.035
4 − 50 6.8 0.075 55.9 −0.85 ± 0.50 ± 0.39
small in that kinematical domain, which is to be expected if diffraction is the dominant
process for reaction (2).
In Fig. 6 the COMPASS results are compared to the HERMES results on A
1 ob-
tained on a deuteron target [17]. Note that the lowest Q2 and x HERMES points, re-
ferred to as ‘quasi-photoproduction’, come from measurements where the kinematics of
the small-angle scattered electron was not measured but estimated from a MC simulation.
This is in contrast to COMPASS, where scattered muon kinematics is measured even at
the smallest Q2.
 [(GeV/c)2Q
-310 -210 -110 1 10
COMPASS  
HERMES quasi-photoprod. (d)
HERMES electroprod. (d)
-410 -310 -210 -110
COMPASS 
HERMES quasi-photoprod. (d)
HERMES electroprod. (d)
Figure 6: A
1 as a function of Q
2 (left) and x (right) from the present analysis (circles)
compared to HERMES results on the deuteron target (triangles). For the COMPASS
results inner bars represent statistical errors, while the outer bars correspond to the total
error. For the HERMES results vertical bars represent the quadratic sum of statistical
and systematic errors. The curve represents the prediction explained in the text.
The results from both experiments are consistent within errors. The kinematical
range covered by the present analysis extends further towards small values of x and Q2
by almost two orders of magnitude. In each of the two experiments A
1 is measured at
different average W , which is equal to about 10 GeV for COMPASS and 5 GeV for
Table 2: Asymmetry A
1 as a function of x. Both the statistical errors (first) and the total
systematic errors (second) are listed.
x range 〈x〉 〈Q2〉 [(GeV/c)2] 〈ν〉 [GeV] Aρ1
8 · 10−6 − 1 · 10−4 5.8 · 10−5 0.0058 51.7 0.035 ± 0.026 ± 0.011
1 · 10−4 − 2.5 · 10−4 1.7 · 10−4 0.019 59.7 0.036 ± 0.024 ± 0.010
2.5 · 10−4 − 5 · 10−4 3.6 · 10−4 0.041 61.3 −0.039 ± 0.027 ± 0.012
5 · 10−4 − 0.001 7.1 · 10−4 0.082 60.8 −0.010 ± 0.030 ± 0.010
0.001 − 0.002 0.0014 0.16 58.6 −0.005 ± 0.036 ± 0.013
0.002 − 0.004 0.0028 0.29 54.8 0.032 ± 0.050 ± 0.019
0.004 − 0.01 0.0062 0.59 50.7 0.019 ± 0.069 ± 0.026
0.01 − 0.025 0.015 1.3 47.5 −0.03 ± 0.14 ± 0.06
0.025 − 0.8 0.049 3.9 43.8 −0.27 ± 0.38 ± 0.19
HERMES. Thus, no significant W dependence is observed for A
1 on an isoscalar nucleon
target.
The x dependence of the measured A
1 is compared in Fig. 6 to the prediction
given by Eq. 4, which relates A
1 to the asymmetry A1 for the inclusive inelastic lepton-
nucleon scattering. To produce the curve the inclusive asymmetry A1 was parameterised
as A1(x) = (x
α − γα) · (1 − e−βx) , where α = 1.158 ± 0.024, β = 125.1 ± 115.7 and
γ = 0.0180 ± 0.0038. The values of the parameters have been obtained from a fit of
A1(x) to the world data from polarised deuteron targets [26–31] including COMPASS
measurements at very low Q2 and x [32]. Within the present accuracy the results on A
are consistent with this prediction.
In the highest Q2 bin, 〈Q2〉 = 6.8 (GeV/c)2, in the kinematical domain of applica-
bility of pQCD-inspired models which relate the asymmetry to the spin-dependent GPDs
for gluons and quarks (cf. Introduction), one can observe a hint of a possible nonzero
asymmetry, although with a large error. It should be noted that in Ref. [18] a nega-
tive value of ALL different from zero by about 2 standard deviations was reported at
〈Q2〉 = 7.7 (GeV/c)2. At COMPASS, including the data taken with the longitudinally
polarised deuteron target in 2004 and 2006 will result in an increase of statistics by a
factor of about three compared to the present paper, and thus may help to clarify the
issue.
For the whole Q2 range future COMPASS data, to be taken with the polarised
proton target, would be very valuable for checking if the role of the flavour-blind exchanges
is indeed dominant, as expected for the Pomeron-mediated process.
7 Summary
The longitudinal double spin asymmetry A
1 for the diffractive muoproduction of ρ
meson, µ + N → µ + N + ρ, has been measured by scattering longitudinally polarised
muons off longitudinally polarised deuterons from the 6LiD target and selecting incoherent
exclusive ρ0 production. The presented results for the COMPASS 2002 and 2003 data cover
a range of energy W from about 7 to 15 GeV.
The Q2 and x dependence of A
1 is presented in a wide kinematical range 3 · 10−3 ≤
Q2 ≤ 7 (GeV/c)2 and 5 · 10−5 ≤ x ≤ 0.05. These results extend the range in Q2 and x by
two orders of magnitude down with respect to the existing data from HERMES.
The asymmetry A
1 is compatible with zero in the whole x and Q
2 range. This may
indicate that the role of unnatural parity exchanges like π- or A1-Reggeon exchange is
small in that kinematical domain.
The x dependence of measured A
1 is consistent with the prediction of Ref. [11] which
relates A
1 to the asymmetry A1 for the inclusive inelastic lepton–nucleon scattering.
8 Acknowledgements
We gratefully acknowledge the support of the CERN management and staff and the
skill and effort of the technicians of our collaborating institutes. Special thanks are due
to V. Anosov and V. Pesaro for their support during the installation and the running
of the experiment. This work was made possible by the financial support of our funding
agencies.
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http://arxiv.org/abs/hep-ph/0303053
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	 Introduction
	 The experimental set-up
	 Event sample
	 Extraction of asymmetry A1
	 Systematic errors
	 Results
	 Summary
	 Acknowledgements

  The longitudinal double spin asymmetry A_1^rho for exclusive leptoproduction
of rho^0 mesons, mu + N -> mu + N + rho, is studied using the COMPASS 2002 and
2003 data. The measured reaction is incoherent exclusive rho^0 production on
polarised deuterons. The Q^2 and x dependence of A_1^rho is presented in a wide
kinematical range: 3x10^-3 < Q^2 < 7 (GeV/c)^2 and 5x10^-5 < x < 0.05. The
presented results are the first measurements of A_1^rho at small Q2 (Q2 < 0.1
(GeV/c)^2) and small x (x < 3x10^-3). The asymmetry is in general compatible
with zero in the whole kinematical range.

Introduction
In this paper we present results on the longitudinal double spin asymmetry A
1 for
exclusive incoherent ρ0 production in the scattering of high energy muons on nucleons.
The experiment was carried out at CERN by the COMPASS collaboration using the
160 GeV muon beam and the large 6LiD polarised target.
The studied reaction is
µ + N → µ′ + ρ0 + N ′, (1)
where N is a quasi-free nucleon from the polarised deuterons. The reaction (1) can be
described in terms of the virtual photoproduction process
γ∗ + N → ρ0 + N ′. (2)
The reaction (2) can be regarded as a fluctuation of the virtual photon into a quark-
antiquark pair (in partonic language), or an off-shell vector meson (in Vector Meson
Dominance model), which then scatters off the target nucleon resulting in the production
of an on-shell vector meson. At high energies this is predominantly a diffractive process and
plays an important role in the investigation of Pomeron exchange and its interpretation
in terms of multiple gluon exchange.
Most of the presently available information on the spin structure of reaction (2)
stems from the ρ0 spin density matrix elements, which are obtained from the analysis
of angular distributions of ρ0 production and decay [1]. Experimental results on ρ0 spin
density matrix elements come from various experiments [2–6] including the preliminary
results from COMPASS [7].
The emerging picture of the spin structure of the considered process is the following.
At low photon virtuality Q2 the cross section by transverse virtual photons σT dominates,
while the relative contribution of the cross section by longitudinal photons σL rapidly
increases with Q2. At Q2 of about 2 (GeV/c)2 both components become comparable and
at a larger Q2 the contribution of σL becomes dominant and continues to grow, although
at lower rate than at low Q2. Approximately, the so called s-channel helicity conservation
(SCHC) is valid, i.e. the helicity of the vector meson is the same as the helicity of the
parent virtual photon. The data indicate that the process can be described approximately
by the exchange in the t-channel of an object with natural parity P . Small deviations from
SCHC are observed, also at the highest energies, whose origin is still to be understood. An
interesting suggestion was made in Ref. [8] that at high energies the magnitudes of various
helicity amplitudes for the reaction (2) may shed a light on the spin-orbital momentum
structure of the vector meson.
A complementary information can be obtained from measurements of the double
spin cross section asymmetry, when the information on both the beam and target polari-
sation is used. The asymmetry is defined as
σ1/2 − σ3/2
σ1/2 + σ3/2
, (3)
where σ1/2(3/2) stands for the cross sections of the reaction (2) and the subscripts denote
the total virtual photon–nucleon angular momentum component along the virtual photon
direction. In the following we will also use the asymmetry ALL which is defined for reaction
(1) as the asymmetry of muon–nucleon cross sections for antiparallel and parallel beam
and target longitudinal spin orientations.
In the Regge approach [9] the longitudinal double spin asymmetry A
1 can arise due
to the interference of amplitudes for exchange in the t-channel of Reggeons with natural
parity (Pomeron, ρ, ω, f , A2 ) with amplitudes for Reggeons with unnatural parity (π,A1).
No significant asymmetry is expected when only a non-perturbative Pomeron is exchanged
because it has small spin-dependent couplings as found from hadron-nucleon data for cross
sections and polarisations.
Similarly, in the approach of Fraas [10], assuming approximate validity of SCHC, the
spin asymmetry A
1 arises from the interference between parts of the helicity amplitudes
for transverse photons corresponding to the natural and unnatural parity exchanges in
the t channel. While a measurable asymmetry can arise even from a small contribution of
the unnatural parity exchange, the latter may remain unmeasurable in the cross sections.
A significant unnatural-parity contribution may indicate an exchange of certain Reggeons
like π, A1 or in partonic terms an exchange of qq̄ pairs.
In the same reference a theoretical prediction for A
1 was presented, which is based
on the description of forward exclusive ρ0 leptoproduction and inclusive inelastic lepton-
nucleon scattering by the off-diagonal Generalised Vector Meson Dominance (GVMD)
model, applied to the case of polarised lepton–nucleon scattering. At the values of Bjorken
variable x < 0.2, with additional assumptions [11], A
1 can be related to the A1 asymmetry
for inclusive inelastic lepton scattering at the same x as
1 + (A1)2
. (4)
This prediction is consistent with the HERMES results for both the proton and deuteron
targets, although with rather large errors.
In perturbative QCD, there exists a general proof of factorisation [12] for exclu-
sive vector meson production by longitudinal photons. It allows a decomposition of the
full amplitude for reaction (2) into three components: a hard scattering amplitude for
the exchange of quarks or gluons, a distribution amplitude for the meson and the non-
perturbative description of the target nucleon in terms of the generalised parton distri-
butions (GPDs), which are related to the internal structure of the nucleon. No similar
proof of factorisation exists for transverse virtual photons, and as a consequence the in-
terpretation of A
1 in perturbative QCD is not possible at leading twist. However, a model
including higher twist effects proposed by Martin et al. [13] describes the behaviour of
both σL as well as of σT reasonably well. An extension of this model by Ryskin [14] for
the spin dependent cross sections allows to relate A
1 to the spin dependent GPDs of
gluons and quarks in the nucleon. The applicability of this model is limited to the range
Q2 ≥ 4 (GeV/c)2. More recently another pQCD-inspired model involving GPDs has been
proposed by Goloskokov and Kroll [15,16]. The non-leading twist asymmetry ALL results
from the interference between the dominant GPD Hg and the helicity-dependent GPD H̃g.
The asymmetry is estimated to be of the order k2T H̃g/(Q
2Hg), where kT is the transverse
momentum of the quark and the antiquark.
Up to now little experimental information has been available on the double spin
asymmetries for exclusive leptoproduction of vector mesons. The first observation of a non-
zero asymmetry A
1 in polarised electron–proton deep-inelastic scattering was reported by
the HERMES experiment [11]. In the deep inelastic region (0.8 < Q2 < 3 (GeV/c)2)
the measured asymmetry is equal to 0.23 ± 0.14 (stat) ± 0.02 (syst) [17], with little
dependence on the kinematical variables. In contrast, for the ‘quasi-real photoproduction’
data, with 〈Q2〉 = 0.13 (GeV/c)2, the asymmetry for the proton target is consistent with
zero. On the other hand the measured asymmetry A
1 for the polarised deuteron target
and the asymmetry A
1 for exclusive production of φ meson either on polarised protons
or deuterons are consistent with zero both in the deep inelastic and in the quasi-real
photoproduction regions [17].
The HERMES result indicating a non-zero A
1 for the proton target differs from the
unpublished result of similar measurements by the SMC experiment [18] at comparable
values of Q2 but at about three times higher values of the photon-nucleon centre of mass
energy W , i.e. at smaller x. The SMC measurements of ALL in several bins of Q
2 are
consistent with zero for both proton and deuteron targets.
2 The experimental set-up
The experiment [19] was performed with the high intensity positive muon beam from
the CERN M2 beam line. The µ+ beam intensity is 2·108 per spill of 4.8 s with a cycle time
of 16.8 s. The average beam energy is 160 GeV and the momentum spread is σp/p = 0.05.
The momentum of each beam muon is measured upstream of the experimental area in a
beam momentum station consisting of several planes of scintillator strips or scintillating
fibres with a dipole magnet in between. The precision of the momentum determination
is typically ∆p/p ≤ 0.003. The µ+ beam is naturally polarised by the weak decays of
the parent hadrons. The polarisation of the muon varies with its energy and the average
polarisation is −0.76.
The beam traverses the two cells of the polarised target, each 60 cm long, 3 cm in
diameter and separated by 10 cm, which are placed one after the other. The target cells are
filled with 6LiD which is used as polarised deuteron target material and is longitudinally
polarised by dynamic nuclear polarisation (DNP). The two cells are polarised in opposite
directions so that data from both spin directions are recorded at the same time. The
typical values of polarisation are about 0.50. A mixture of liquid 3He and 4He, used to
refrigerate the target, and a small amount of heavier nuclei are also present in the target.
The spin directions in the two target cells are reversed every 8 hours by rotating the
direction of the magnetic field in the target. In this way fluxes and acceptances cancel
in the calculation of spin asymmetries, provided that the ratio of acceptances of the two
cells remains unchanged after the reversal.
The COMPASS spectrometer is designed to reconstruct the scattered muons and
the produced hadrons in wide momentum and angular ranges. It is divided in two stages
with two dipole magnets, SM1 and SM2. The first magnet, SM1, accepts charged particles
of momenta larger than 0.4 GeV/c, and the second one, SM2, those larger than 4 GeV/c.
The angular acceptance of the spectrometer is limited by the aperture of the polarised
target magnet. For the upstream end of the target it is ±70 mrad.
To match the expected particle flux at various locations in the spectrometer, COM-
PASS uses various tracking detectors. Small-angle tracking is provided by stations of
scintillating fibres, silicon detectors, micromesh gaseous chambers and gas electron mul-
tiplier chambers. Large-angle tracking devices are multiwire proportional chambers, drift
chambers and straw detectors. Muons are identified in large-area mini drift tubes and
drift tubes placed downstream of hadron absorbers. Hadrons are detected by two large
iron-scintillator sampling calorimeters installed in front of the absorbers and shielded to
avoid electromagnetic contamination. The identification of charged particles is possible
with a RICH detector, although in this paper we have not utilised the information from
the RICH.
The data recording system is activated by various triggers indicating the presence of
a scattered muon and/or an energy deposited by hadrons in the calorimeters. In addition
to the inclusive trigger, in which the scattered muon is identified by coincidence signals
in the trigger hodoscopes, several semi-inclusive triggers were used. They select events
fulfilling the requirement to detect the scattered muon together with the energy deposited
in the hadron calorimeters exceeding a given threshold. In 2003 the acceptance was further
extended towards high Q2 values by the addition of a standalone calorimetric trigger in
which no condition is set for the scattered muon. The COMPASS trigger system allows us
to cover a wide range of Q2, from quasi-real photoproduction to deep inelastic interactions.
A more detailed description of the COMPASS apparatus can be found in Ref. [19]
3 Event sample
For the present analysis the whole data sample taken in 2002 and 2003 with the
longitudinally polarised target is used. For an event to be accepted for further analysis it
is required to originate in the target, have a reconstructed beam track, a scattered muon
track, and only two additional tracks of oppositely charged hadrons associated to the
primary vertex. The fluxes of beam muons passing through each target cell are equalised
using appropriate cuts on the position and angle of the beam tracks.
The charged pion mass hypothesis is assigned to each hadron track and the invariant
mass of two pions, mππ, calculated. A cut on the invariant mass of two pions, 0.5 < mππ <
1 GeV/c2, is applied to select the ρ0. As slow recoil target particles are not detected, in
order to select exclusive events we use the cut on the missing energy, −2.5 < Emiss <
2.5 GeV, and on the transverse momentum of ρ0 with respect to the direction of virtual
photon, p2t < 0.5 (GeV/c)
2. Here Emiss = (M
X−M2p )/2Mp, where MX is the missing mass
of the unobserved recoiling system and Mp is the proton mass. Coherent interactions on
the target nuclei are removed by a cut p2t > 0.15 (GeV/c)
2. To avoid large corrections for
acceptance and misidentification of events, additional cuts ν > 30 GeV and Eµ′ > 20 GeV
are applied.
The distributions of mππ, Emiss and p
t are shown in Fig. 1. Each plot is obtained
applying all cuts except those corresponding to the displayed variable. On the left top
panel of Fig. 1 a clear peak of the ρ0 resonance, centred at 770 MeV/c2, is visible on the
top of the small contribution of background of the non-resonant π+π− pairs. Also the
skewing of the resonance peak towards smaller values of mππ, due to an interference with
the non-resonant background, is noticeable. A small bump below 0.4 GeV/c2 is due to
assignment of the charged pion mass to the kaons from decays of φ mesons. The mass cuts
eliminate the non-resonant background outside of the ρ0 peak, as well as the contribution
of φ mesons.
On the right top panel of the figure the peak at Emiss ≈ 0 is the signal of exclusive
ρ0 production. The width of the peak, σ ≈ 1.1 GeV, is due to the spectrometer resolution.
Non-exclusive events, where in addition to the recoil nucleon other undetected hadrons
are produced, appear at Emiss > 0. Due to the finite resolution, however, they are not
resolved from the exclusive peak. This background consists of two components: the double-
diffractive events where additionally to ρ0 an excited nucleon state is produced in the
nucleon vertex of reaction (2), and events with semi-inclusive ρ0 production, in which
other hadrons are produced but escape detection.
The p2t distribution shown on the bottom panel of the figure indicates a contribution
from coherent production on target nuclei at small p2t values. A three-exponential fit
to this distribution was performed, which indicates also a contribution of non-exclusive
background increasing with p2t . Therefore to select the sample of exclusive incoherent ρ
 [GeV/cππm
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
 [GeV]missE
-4 -2 0 2 4 6 8 10 12 14
10000
 [(GeV/c)2tp
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure 1: Distributions of mππ (top left), Emiss (top right) and p
t (bottom) for the exclu-
sive sample. The arrows show cuts imposed on each variable to define the final sample.
production, the aforementioned p2t cuts, indicated by arrows, were applied.
After all selections the final sample consists of about 2.44 million events. The dis-
tributions of Q2, x and W are shown in Fig. 2. The data cover a wide range in Q2 and
x which extends towards the small values by almost two orders of magnitude compared
to the similar studies reported in Ref. [17]. The sharp edge of the W distribution at the
low W values is a consequence of the cut applied on ν. For this sample 〈W 〉 is equal to
10.2 GeV and 〈p2t 〉 = 0.27(GeV/c)2.
4 Extraction of asymmetry A
The cross section asymmetry ALL = (σ↑↓ − σ↑↑)/(σ↑↓ + σ↑↑) for reaction (1) , for
antiparallel (↑↓) and parallel (↑↑) spins of the incoming muon and the target nucleon, is
related to the virtual-photon nucleon asymmetry A
ALL = D (A
1 + ηA
2) , (5)
where the factors D and η depend on the event kinematics and A
2 is related to the
interference cross section for exclusive production by longitudinal and transverse virtual
photons. As the presented results extend into the range of very small Q2, the exact
formulae for the depolarisation factor D and kinematical factor η [20] are used without
neglecting terms proportional to the lepton mass squared m2. The depolarisation factor
is given by
D(y,Q2) =
y [(1 + γ2y/2)(2 − y) − 2y2m2/Q2]
y2(1 − 2m2/Q2)(1 + γ2) + 2(1 + R)(1 − y − γ2y2/4)
, (6)
 [(GeV/c)2Q
-410 -310 -210 -110 1 10 210
 [(GeV/c)2Q
-410 -310 -210 -110 1 10 210
-610 -510 -410 -310 -210 -110 1
W [GeV]
0 5 10 15 20 25
Figure 2: Distributions of the kinematical variables for the final sample: Q2 with linear
and logarithmic vertical axis scale (top left and right panels respectively), x (bottom left),
and the energy W (bottom right).
where R = σL/σT , σL(T ) is the cross section for reaction (2) initiated by longitudinally
(transversely) polarised virtual photons, the fraction of the muon energy lost y = ν/Eµ
and γ2 = Q2/ν2. The kinematical factor η(y,Q2) is the same as for the inclusive asym-
metry.
The asymmetry A
2 obeys the positivity limit A
R, analogous to the one for
the inclusive case. For Q2 ≤ 0.1 (GeV/c)2 the ratio R for the reaction (2) is small, cf.
Fig. 3, and the positivity limit constrains A
2 to small values. Although for larger Q
2 the
ratio R for the process (2) increases with Q2, because of small values of η the product
R is small in the whole Q2 range of our sample. Therefore the second term in Eq. 5
can be neglected, so that
ALL, (7)
and the effect of this approximation is included in the systematic uncertainty of A
The number of events Ni collected from a given target cell in a given time interval
is related to the spin-independent cross section σ̄ for reaction (2) and to the asymmetry
Ni = aiφiniσ̄(1 + PBPTfDA
1), (8)
where PB and PT are the beam and target polarisations, φi is the incoming muon flux, ai
the acceptance for the target cell, ni corresponding number of target nucleons, and f the
target dilution factor. The asymmetry is extracted from the data sets taken before and
after a reversal of the target spin directions. The four relations of Eq. 8, corresponding
to the two cells (u and d) and the two spin orientations (1 and 2) lead to a second-
 [(GeV/c)2Q
-210 -110 1 10
Figure 3: The ratio R = σL/σT as a function of Q
2 measured in the E665 experiment.
The curve is a fit to the data described in the text.
order equation in A
1 for the ratio (Nu,1Nd,2/Nd,1Nu,2). Here fluxes cancel out as well as
acceptances, if the ratio of acceptances for the two cells is the same before and after
the reversal [21]. In order to minimise the statistical error all quantities used in the
asymmetry calculation are evaluated event by event with the weight factor w = PBfD.
The polarisation of the beam muon, PB, is obtained from a simulation of the beam line
and parameterised as a function of the beam momentum. The target polarisation is not
included in the event weight w because it may vary in time and generate false asymmetries.
An average PT is used for each target cell and each spin orientation.
The ratio R, which enters the formula for D and strongly depends on Q2 for reaction
(2), was calculated on an event-by-event basis using the parameterisation
R(Q2) = a0(Q
2)a1 , (9)
with a0 = 0.66 ± 0.05, and a1 = 0.61 ± 0.09. The parameterisation was obtained by the
Fermilab E665 experiment from a fit to their R measurements for exclusive ρ0 muopro-
duction on protons [3]. These are shown in Fig. 3 together with the fitted Q2-dependence.
The preliminary COMPASS results on R for the incoherent exclusive ρ0 production on
the nucleon [7], which cover a broader kinematic region in Q2 , agree reasonably well with
this parameterisation. The uncertainty of a0 and a1 is included in the systematic error of
The dilution factor f gives the fraction of events of reaction (2) originating from
nucleons in polarised deuterons inside the target material. It is calculated event-by-event
using the formula
f = C1 · f0 = C1 ·
nD + ΣAnA(σ̃A/σ̃D)
. (10)
Here nD and nA denote numbers of nucleons in deuteron and nucleus of atomic mass A
in the target, and σ̃D and σ̃A are the cross sections per nucleon for reaction (2) occurring
on the deuteron and on the nucleus of atomic mass A, respectively. The sum runs over all
nuclei present in the COMPASS target. The factor C1 takes into account that there are
two polarised deuterons in the 6LiD molecule, as the 6Li nucleus is in a first approximation
composed of a deuteron and an α particle.
The measurements of the σ̃A/σ̃D for incoherent exclusive ρ
0 production come from
the NMC [2], E665 [22] and early experiments on ρ0 photoproduction [23]. They were
 [(GeV/c)2Q
0 2 4 6 8 10 12 14
photoproduction
 [(GeV/c)2Q
-310 -210 -110 1 10
Figure 4: (Left) Parameter α of Eq. 11 as a function of Q2 (from Ref. [24]). The exper-
imental points and the fitted curve are shown. See text for details. (Right) The dilution
factor f as a function of Q2.
fitted in Ref. [24] with the formula:
σ̃A = σp ·Aα(Q
2)−1, with α(Q2) − 1 = −
exp{−Q2/Q20}, (11)
where σp is the cross section for reaction (2) on the free proton. The value of the fitted
parameter Q20 is equal to 9 ± 3 (GeV/c)2. The measured values of the parameter α and
the fitted curve α(Q2) are shown on the left panel of Fig. 4 taken from Ref. [24]. On the
right panel of the figure the average value of f is plotted for the various Q2 bins used in
the present analysis. The values of f are equal to about 0.36 in most of the Q2 range,
rising to about 0.38 at the highest Q2.
The radiative corrections (RC) have been neglected in the present analysis, in par-
ticular in the calculation of f , because they are expected to be small for reaction (1).
They were evaluated [25] to be of the order of 6% for the NMC exclusive ρ0 production
analysis. The small values of RC are mainly due to the requirement of event exclusivity
via cuts on Emiss and p
t , which largely suppress the dominant external photon radiation.
The internal (infrared and virtual) RC were estimated in Ref. [25] to be of the order of
5 Systematic errors
The main systematic uncertainty of A
1 comes from an estimate of possible false
asymmetries. In order to improve the accuracy of this estimate, in addition to the standard
sample of incoherent events, a second sample was selected by changing the p2t cuts to
0 < p2t < 0.5 (GeV/c)
2, (12)
and keeping all the remaining selections and cuts the same as for the ‘incoherent sample’.
In the following it will be referred to as the ‘extended p2t sample’. Such an extension of the
p2t range allows one to obtain a sample which is about five times larger than the incoherent
sample. However, in addition to incoherent events such a sample contains a large fraction of
events originating from coherent ρ0 production. Therefore, for the estimate of the dilution
factor f a different nuclear dependence of the exclusive cross section was used, applicable
for the sum of coherent and incoherent cross sections [2]. The physics asymmetries A
1 for
both samples are consistent within statistical errors.
Possible, false experimental asymmetries were searched for by modifying the se-
lection of data sets used for the asymmetry calculation. The grouping of the data into
configurations with opposite target-polarisation was varied from large samples, covering
at most two weeks of data taking, into about 100 small samples, taken in time intervals of
the order of 16 hours. A statistical test was performed on the distributions of asymmetries
obtained from these small samples. In each of the Q2 and x bins the dispersion of the
values of A
1 around their mean agrees with the statistical error. Time-dependent effects
which would lead to a broadening of these distributions were thus not observed. Allowing
the dispersion of A
1 to vary within its two standard deviations we obtain for each bin an
upper bound for the systematic error arising from time-dependent effects
σfalseA,tdep < 0.56 σstat. (13)
Here σstat is the statistical error on A
1 for the extended p
t sample. The uncertainty on the
estimates of possible false asymmetries due to the time-dependent effects is the dominant
contribution to the total systematic error in most of the kinematical region.
Asymmetries for configurations where spin effects cancel out were calculated to
check the cancellation of effects due to fluxes and acceptances. They were found compatible
with zero within the statistical errors. Asymmetries obtained with different settings of the
microwave (MW) frequency, used for DNP, were compared in order to test possible effects
related to the orientation of the target magnetic field. The results for the extended p2t
sample tend to show that there is a small difference between asymmetries for the two
MW configurations. However, because the numbers of events of the data samples taken
with each MW setting are approximately balanced, the effect of this difference on A
negligible for the total sample.
The systematic error on A
1 also contains an overall scale uncertainty of 6.5% due to
uncertainties on PB and PT . The uncertainty of the parameterisation of R(Q
2) affects the
depolarisation factor D. The uncertainty of the dilution factor f is mostly due to uncer-
tainty of the parameter α(Q2) which takes into account nuclear effects in the incoherent
ρ0 production. The neglect of the A
2 term mainly affects the highest bins of Q
2 and x.
Another source of systematic errors is due to the contribution of the non-exclusive
background to our sample. This background originates from two sources. First one is
due to the production of ρ0 accompanied by the dissociation of the target nucleon, the
second one is the production of ρ0 in inclusive scattering. In order to evaluate the amount
of background in the sample of exclusive events it is necessary to determine the Emiss
dependence for the non-exclusive background in the region under the exclusive peak (cf.
Fig. 1 ). For this purpose complete Monte Carlo simulations of the experiment were used,
with events generated by either the PYTHIA 6.2 or LEPTO 6.5.1 generators. Events
generated with LEPTO come only from deep inelastic scattering and cover the range of
Q2 > 0.5 (GeV/c)2. Those generated with PYTHIA cover the whole kinematical range
of the experiment and include exclusive production of vector mesons and processes with
diffractive excitation of the target nucleon or the vector meson, in addition to inelastic
production.
The generated MC events were reconstructed and selected for the analysis using the
same procedure as for the data. In each bin of Q2 the Emiss distribution for the MC was
normalised to the corresponding one for the data in the range of large Emiss > 7.5 GeV.
Then the normalised MC distribution was used to estimate the number of background
events under the exclusive peak in the data. The fraction of background events in the
sample of incoherent exclusive ρ0 production was estimated to be about 0.12±0.06 in most
of the kinematical range, except in the largest Q2 region, where it is about 0.24±0.12. The
large uncertainties of these fractions reflect the differences between estimates from LEPTO
and PYTHIA in the region where they overlap. In the case of PYTHIA the uncertainties
on the cross sections for diffractive photo- and electroproduction of vector mesons also
contribute. For events generated with PYTHIA the Emiss distributions for various physics
processes could be studied separately. It was found that events of ρ0 production with an
excitation of the target nucleon into N∗ resonances of small mass, M < 2 GeV/c2, cannot
be resolved from the exclusive peak and therefore were not included in the estimates of
number of background events.
An estimate of the asymmetry A
1 for the background was obtained using a non-
exclusive sample, which was selected with the standard cuts used in this analysis, except
the cut on Emiss which was modified to Emiss > 2.5 GeV. In different high-Emiss bins A
for this sample was found compatible with zero.
Because no indication of a non-zero A
1 for the background was found, and also due
to a large uncertainty of the estimated amount of background in the exclusive sample,
no background corrections were made. Instead, the effect of background was treated as a
source of systematic error. Its contribution to the total systematic error was not significant
in most of the kinematical range, except for the highest Q2 and x.
The total systematic error on A
1 was obtained as a quadratic sum of the errors
from all discussed sources. Its values for each Q2 and x bin are given in Tables 1 and 2.
The total systematic error amounts to about 40% of the statistical error for most of the
kinematical range. Both errors become comparable in the highest bin of Q2.
6 Results
The COMPASS results on A
1 are shown as a function of Q
2 and x in Fig. 5 and
listed in Tables 1 and 2. The statistical errors are represented by vertical bars and the
total systematic errors by shaded bands.
 [(GeV/c)2Q
-310 -210 -110 1 10
-410 -310 -210 -110
Figure 5: A
1 as a function of Q
2 (left) and x (right) from the present analysis. Error bars
correspond to statistical errors, while bands at the bottom represent the systematical
errors.
The wide range in Q2 covers four orders of magnitude from 3 · 10−3 to 7 (GeV/c)2.
The domain in x which is strongly correlated with Q2, varies from 5 · 10−5 to about
0.05 (see Tables for more details). For the whole kinematical range the A
1 asymmetry
measured by COMPASS is consistent with zero. As discussed in the introduction, this
indicates that the role of unnatural parity exchanges, like π- or A1-Reggeon exchange, is
Table 1: Asymmetry A
1 as a function of Q
2. Both the statistical errors (first) and the
total systematic errors (second) are listed.
Q2 range 〈Q2〉 [(GeV/c)2] 〈x〉 〈ν〉 [GeV] Aρ1
0.0004 − 0.005 0.0031 4.0 · 10−5 42.8 −0.030 ± 0.045 ± 0.014
0.005 − 0.010 0.0074 8.4 · 10−5 49.9 0.048 ± 0.038 ± 0.013
0.010 − 0.025 0.017 1.8 · 10−4 55.6 0.063 ± 0.026 ± 0.014
0.025 − 0.050 0.036 3.7 · 10−4 59.9 −0.035 ± 0.027 ± 0.009
0.05 − 0.10 0.072 7.1 · 10−4 62.0 −0.010 ± 0.028 ± 0.008
0.10 − 0.25 0.16 0.0016 62.3 −0.019 ± 0.029 ± 0.009
0.25 − 0.50 0.35 0.0036 60.3 0.016 ± 0.045 ± 0.014
0.5 − 1 0.69 0.0074 58.6 0.141 ± 0.069 ± 0.030
1 − 4 1.7 0.018 59.7 0.000 ± 0.098 ± 0.035
4 − 50 6.8 0.075 55.9 −0.85 ± 0.50 ± 0.39
small in that kinematical domain, which is to be expected if diffraction is the dominant
process for reaction (2).
In Fig. 6 the COMPASS results are compared to the HERMES results on A
1 ob-
tained on a deuteron target [17]. Note that the lowest Q2 and x HERMES points, re-
ferred to as ‘quasi-photoproduction’, come from measurements where the kinematics of
the small-angle scattered electron was not measured but estimated from a MC simulation.
This is in contrast to COMPASS, where scattered muon kinematics is measured even at
the smallest Q2.
 [(GeV/c)2Q
-310 -210 -110 1 10
COMPASS  
HERMES quasi-photoprod. (d)
HERMES electroprod. (d)
-410 -310 -210 -110
COMPASS 
HERMES quasi-photoprod. (d)
HERMES electroprod. (d)
Figure 6: A
1 as a function of Q
2 (left) and x (right) from the present analysis (circles)
compared to HERMES results on the deuteron target (triangles). For the COMPASS
results inner bars represent statistical errors, while the outer bars correspond to the total
error. For the HERMES results vertical bars represent the quadratic sum of statistical
and systematic errors. The curve represents the prediction explained in the text.
The results from both experiments are consistent within errors. The kinematical
range covered by the present analysis extends further towards small values of x and Q2
by almost two orders of magnitude. In each of the two experiments A
1 is measured at
different average W , which is equal to about 10 GeV for COMPASS and 5 GeV for
Table 2: Asymmetry A
1 as a function of x. Both the statistical errors (first) and the total
systematic errors (second) are listed.
x range 〈x〉 〈Q2〉 [(GeV/c)2] 〈ν〉 [GeV] Aρ1
8 · 10−6 − 1 · 10−4 5.8 · 10−5 0.0058 51.7 0.035 ± 0.026 ± 0.011
1 · 10−4 − 2.5 · 10−4 1.7 · 10−4 0.019 59.7 0.036 ± 0.024 ± 0.010
2.5 · 10−4 − 5 · 10−4 3.6 · 10−4 0.041 61.3 −0.039 ± 0.027 ± 0.012
5 · 10−4 − 0.001 7.1 · 10−4 0.082 60.8 −0.010 ± 0.030 ± 0.010
0.001 − 0.002 0.0014 0.16 58.6 −0.005 ± 0.036 ± 0.013
0.002 − 0.004 0.0028 0.29 54.8 0.032 ± 0.050 ± 0.019
0.004 − 0.01 0.0062 0.59 50.7 0.019 ± 0.069 ± 0.026
0.01 − 0.025 0.015 1.3 47.5 −0.03 ± 0.14 ± 0.06
0.025 − 0.8 0.049 3.9 43.8 −0.27 ± 0.38 ± 0.19
HERMES. Thus, no significant W dependence is observed for A
1 on an isoscalar nucleon
target.
The x dependence of the measured A
1 is compared in Fig. 6 to the prediction
given by Eq. 4, which relates A
1 to the asymmetry A1 for the inclusive inelastic lepton-
nucleon scattering. To produce the curve the inclusive asymmetry A1 was parameterised
as A1(x) = (x
α − γα) · (1 − e−βx) , where α = 1.158 ± 0.024, β = 125.1 ± 115.7 and
γ = 0.0180 ± 0.0038. The values of the parameters have been obtained from a fit of
A1(x) to the world data from polarised deuteron targets [26–31] including COMPASS
measurements at very low Q2 and x [32]. Within the present accuracy the results on A
are consistent with this prediction.
In the highest Q2 bin, 〈Q2〉 = 6.8 (GeV/c)2, in the kinematical domain of applica-
bility of pQCD-inspired models which relate the asymmetry to the spin-dependent GPDs
for gluons and quarks (cf. Introduction), one can observe a hint of a possible nonzero
asymmetry, although with a large error. It should be noted that in Ref. [18] a nega-
tive value of ALL different from zero by about 2 standard deviations was reported at
〈Q2〉 = 7.7 (GeV/c)2. At COMPASS, including the data taken with the longitudinally
polarised deuteron target in 2004 and 2006 will result in an increase of statistics by a
factor of about three compared to the present paper, and thus may help to clarify the
issue.
For the whole Q2 range future COMPASS data, to be taken with the polarised
proton target, would be very valuable for checking if the role of the flavour-blind exchanges
is indeed dominant, as expected for the Pomeron-mediated process.
7 Summary
The longitudinal double spin asymmetry A
1 for the diffractive muoproduction of ρ
meson, µ + N → µ + N + ρ, has been measured by scattering longitudinally polarised
muons off longitudinally polarised deuterons from the 6LiD target and selecting incoherent
exclusive ρ0 production. The presented results for the COMPASS 2002 and 2003 data cover
a range of energy W from about 7 to 15 GeV.
The Q2 and x dependence of A
1 is presented in a wide kinematical range 3 · 10−3 ≤
Q2 ≤ 7 (GeV/c)2 and 5 · 10−5 ≤ x ≤ 0.05. These results extend the range in Q2 and x by
two orders of magnitude down with respect to the existing data from HERMES.
The asymmetry A
1 is compatible with zero in the whole x and Q
2 range. This may
indicate that the role of unnatural parity exchanges like π- or A1-Reggeon exchange is
small in that kinematical domain.
The x dependence of measured A
1 is consistent with the prediction of Ref. [11] which
relates A
1 to the asymmetry A1 for the inclusive inelastic lepton–nucleon scattering.
8 Acknowledgements
We gratefully acknowledge the support of the CERN management and staff and the
skill and effort of the technicians of our collaborating institutes. Special thanks are due
to V. Anosov and V. Pesaro for their support during the installation and the running
of the experiment. This work was made possible by the financial support of our funding
agencies.
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	 Introduction
	 The experimental set-up
	 Event sample
	 Extraction of asymmetry A1
	 Systematic errors
	 Results
	 Summary
	 Acknowledgements
