# Double spin asymmetry in exclusive ρ0 muoproduction at COMPASS

**ABSTRACT** The longitudinal double spin asymmetry A1

ρ for exclusive leptoproduction of ρ0 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 A1

ρ is presented in a wide kinematical range, 3×10-3<Q2< 7(GeV/c)2 and 5×10-5<x<0.05. The results presented are the first measurements of A1

ρ at small Q2 (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.

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**ABSTRACT:**Zugl.: Bonn, Univ., Diss., 2002.01/2003; - SourceAvailable from: nuclear.ucdavis.edu[Show abstract] [Hide abstract]

**ABSTRACT:**The kinematics of the process ℓN → ℓNV, is studied in the one-photon approximation for unpolarized as well as polarized leptons ℓ. The vector-meson spin density matrix is expressed in terms of the s-channel helicity amplitudes in the hadron c.m.s. and the vector-meson decay angular distribution is discussed. The use of longitudinally polarized lepton beams is found to increase considerably the amount of information that can be deduced from the decay distribution. With longitudinal beam polarization it is possible to separate all 26 observable independent density matrix elements into contributions from natural and unnatural parity exchange in the t-channel, respectively.Nuclear Physics B 01/1973; · 4.33 Impact Factor - SourceAvailable from: lss.fnal.gov[Show abstract] [Hide abstract]

**ABSTRACT:**The diffractive production of r0 (770)\rho^0 (770) mesons in muon-proton interactions is studied in the kinematic region 0.15 GeV2 < Q2 < 20^2 < Q^2 < 20 GeV2^2 and 20 GeV < n << \nuZeitschrift für Physik C 03/1997; 74(2):237-261.

Page 1

arXiv:0704.1863v2 [hep-ex] 10 Jul 2007

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 Aρ

mesons, µ + N → µ + N + ρ, is studied using the COMPASS 2002 and 2003

data. The measured reaction is incoherent exclusive ρ0production on polarised

deuterons. The Q2and x dependence of Aρ

range 3 · 10−3< Q2< 7 (GeV/c)2and 5 · 10−5< x < 0.05. The presented results

are the first measurements of Aρ

(x < 3 · 10−3). The asymmetry is in general compatible with zero in the whole

kinematical range.

1for exclusive leptoproduction of ρ0

1is presented in a wide kinematical

1at small Q2(Q2< 0.1 (GeV/c)2) and small x

(to be submitted to Eur. Phys. J. C)

Page 2

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. D¨ unnweber19), 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. Grabm¨ uller20),

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. K¨ onigsmann10), 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. N¨ ahle3), 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. Sch¨ onmeier9), W. Schr¨ oder9), 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. Wi´ slicki30),

K. Zaremba31), M. Zavertyaev18), E. Zemlyanichkina8), J. Zhao16), R. Ziegler3), and

A. Zvyagin19)

Page 3

1)Universit¨ at Bielefeld, Fakult¨ at f¨ ur Physik, 33501 Bielefeld, Germanye)

2)Universit¨ at Bochum, Institut f¨ ur Experimentalphysik, 44780 Bochum, Germanye)

3)Universit¨ at Bonn, Helmholtz-Institut f¨ ur Strahlen- und Kernphysik, 53115 Bonn, Germanye)

4)Universit¨ at 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)Universit¨ at Erlangen–N¨ urnberg, Physikalisches Institut, 91054 Erlangen, Germanye)

10)Universit¨ at Freiburg, Physikalisches Institut, 79104 Freiburg, Germanye)

11)CERN, 1211 Geneva 23, Switzerland

12)Universit¨ at 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)Universit¨ at Mainz, Institut f¨ ur Kernphysik, 55099 Mainz, Germanye)

17)University of Miyazaki, Miyazaki 889-2192, Japanj)

18)Lebedev Physical Institute, 119991 Moscow, Russia

19)Ludwig-Maximilians-Universit¨ at M¨ unchen, Department f¨ ur Physik, 80799 Munich, Germanye)

20)Technische Universit¨ at M¨ unchen, 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 T´ ecnica 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 f¨ ur Bildung und Forschung

f)Suppported by Czech Republic MEYS grants ME492 and LA242

g)SupportedbythePortuguese FCT-Funda¸ c˜ ao

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)SupportedbyKBNgrantnr621/E-78/SPUB-M/CERN/P-03/DZ

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

paraaCiˆ enciae Tecnologiagrants

298 2000,nr 621/E-

1

Page 4

1Introduction

In this paper we present results on the longitudinal double spin asymmetry Aρ

exclusive incoherent ρ0production 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 large6LiD polarised target.

The studied reaction is

1for

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 ρ0spin density matrix elements, which are obtained from the analysis

of angular distributions of ρ0production and decay [1]. Experimental results on ρ0spin

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 Q2the cross section by transverse virtual photons σTdominates,

while the relative contribution of the cross section by longitudinal photons σL rapidly

increases with Q2. At Q2of about 2 (GeV/c)2both components become comparable and

at a larger Q2the contribution of σLbecomes 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

Aρ

1=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 ALLwhich is defined for reaction

(1) as the asymmetry of muon–nucleon cross sections for antiparallel and parallel beam

and target longitudinal spin orientations.

2

Page 5

In the Regge approach [9] the longitudinal double spin asymmetry Aρ

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 Aρ

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, A1or in partonic terms an exchange of q¯ q pairs.

In the same reference a theoretical prediction for Aρ

on the description of forward exclusive ρ0leptoproduction 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], Aρ

for inclusive inelastic lepton scattering at the same x as

1can arise due

1arises from the interference between parts of the helicity amplitudes

1was presented, which is based

1can be related to the A1asymmetry

Aρ

1=

2A1

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 Aρ

including higher twist effects proposed by Martin et al. [13] describes the behaviour of

both σLas well as of σT reasonably well. An extension of this model by Ryskin [14] for

the spin dependent cross sections allows to relate Aρ

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 ALLresults

from the interference between the dominant GPD Hgand the helicity-dependent GPD˜Hg.

The asymmetry is estimated to be of the order k2

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 Aρ

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

1in perturbative QCD is not possible at leading twist. However, a model

1to the spin dependent GPDs of

T˜Hg/(Q2Hg), where kTis the transverse

1in polarised electron–proton deep-inelastic scattering was reported by

3

Page 6

zero. On the other hand the measured asymmetry Aρ

and the asymmetry Aφ

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 Aρ

unpublished result of similar measurements by the SMC experiment [18] at comparable

values of Q2but 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 Q2are

consistent with zero for both proton and deuteron targets.

1for the polarised deuteron target

1for exclusive production of φ meson either on polarised protons

1for the proton target differs from the

2The 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 2·108per 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 with6LiD 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 liquid3He and4He, 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

4

Page 7

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 Q2values 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]

3Event 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 ρ0with respect to the direction of virtual

photon, p2

of the unobserved recoiling system and Mpis the proton mass. Coherent interactions on

the target nuclei are removed by a cut p2

acceptance and misidentification of events, additional cuts ν > 30 GeV and Eµ′ > 20 GeV

are applied.

The distributions of mππ, Emissand p2

applying all cuts except those corresponding to the displayed variable. On the left top

panel of Fig. 1 a clear peak of the ρ0resonance, 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/c2is 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 ρ0peak, 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

ρ0production. 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 ρ0an excited nucleon state is produced in the

nucleon vertex of reaction (2), and events with semi-inclusive ρ0production, in which

other hadrons are produced but escape detection.

The p2

from coherent production on target nuclei at small p2

to this distribution was performed, which indicates also a contribution of non-exclusive

background increasing with p2

t< 0.5 (GeV/c)2. Here Emiss= (M2

X−M2

p)/2Mp, where MXis the missing mass

t> 0.15 (GeV/c)2. To avoid large corrections for

tare shown in Fig. 1. Each plot is obtained

tdistribution shown on the bottom panel of the figure indicates a contribution

tvalues. A three-exponential fit

t. Therefore to select the sample of exclusive incoherent ρ0

5

Page 8

]

2

[GeV/c

ππ

m

0.3 0.4 0.5 0.6 0.7 0.8 0.911.1 1.2

Number of events

0

200

400

600

800

1000

1200

2

10

×

[GeV]

miss

E

-4 -20246810 12 14

Number of events

0

2000

4000

6000

8000

10000

1

10

×

]

2

[(GeV/c)

2

tp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91

Number of events

3

10

4

10

5

10

6

10

Figure 1: Distributions of mππ(top left), Emiss(top right) and p2

sive sample. The arrows show cuts imposed on each variable to define the final sample.

t(bottom) for the exclu-

production, the aforementioned p2

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 Q2and

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 ?p2

tcuts, indicated by arrows, were applied.

t? = 0.27(GeV/c)2.

4 Extraction of asymmetry Aρ

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 Aρ

1

1by

ALL= D(Aρ

1+ ηAρ

2), (5)

where the factors D and η depend on the event kinematics and Aρ

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

2is related to the

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)

6

Page 9

]

2

[(GeV/c)

2

Q

-4

10

-3

10

-2

10

-1

101 10

2

10

Number of events

0

200

400

600

800

1000

1200

2

10

×

]

2

[(GeV/c)

2

Q

-4

10

-3

10

-2

10

-1

10 1 10

2

10

Number of events

1

10

2

10

3

10

4

10

5

10

x

-6

10

-5

10

-4

10

-3

10

-2

10

-1

101

Number of events

0

200

400

600

800

1000

1200

1400

2

10

×

W [GeV]

05 10 152025

Number of events

0

200

400

600

800

1000

1200

1400

2

10

×

Figure 2: Distributions of the kinematical variables for the final sample: Q2with 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 Aρ

the inclusive case. For Q2≤ 0.1 (GeV/c)2the ratio R for the reaction (2) is small, cf.

Fig. 3, and the positivity limit constrains Aρ

ratio R for the process (2) increases with Q2, because of small values of η the product

η√R is small in the whole Q2range of our sample. Therefore the second term in Eq. 5

can be neglected, so that

Aρ

DALL,

and the effect of this approximation is included in the systematic uncertainty of Aρ

The number of events Nicollected from a given target cell in a given time interval

is related to the spin-independent cross section ¯ σ for reaction (2) and to the asymmetry

Aρ

Ni= aiφini¯ σ(1 + PBPTfDAρ

2obeys the positivity limit Aρ

2<

√R, analogous to the one for

2to small values. Although for larger Q2the

1≃1

(7)

1.

1by

1), (8)

where PBand PTare the beam and target polarisations, φiis the incoming muon flux, ai

the acceptance for the target cell, nicorresponding 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-

7

Page 10

]

2

[(GeV/c)

2

Q

-2

10

-1

10

110

R

0

0.5

1

1.5

2

2.5

Figure 3: The ratio R = σL/σT as a function of Q2measured in the E665 experiment.

The curve is a fit to the data described in the text.

order equation in Aρ

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 Q2for reaction

(2), was calculated on an event-by-event basis using the parameterisation

1for the ratio (Nu,1Nd,2/Nd,1Nu,2). Here fluxes cancel out as well as

R(Q2) = a0(Q2)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 ρ0muopro-

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 ρ0production on

the nucleon [7], which cover a broader kinematic region in Q2, agree reasonably well with

this parameterisation. The uncertainty of a0and a1is included in the systematic error of

Aρ

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

1.

f = C1· f0= C1·

nD

nD+ ΣAnA(˜ σA/˜ σD). (10)

Here nDand nAdenote numbers of nucleons in deuteron and nucleus of atomic mass A

in the target, and ˜ σDand ˜ σAare 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 C1takes into account that there are

two polarised deuterons in the6LiD molecule, as the6Li nucleus is in a first approximation

composed of a deuteron and an α particle.

The measurements of the ˜ σA/˜ σDfor incoherent exclusive ρ0production come from

the NMC [2], E665 [22] and early experiments on ρ0photoproduction [23]. They were

8

Page 11

]

2

[(GeV/c)

2

Q

0246810 12 14

)

2

(Q

α

0.5

0.6

0.7

0.8

0.9

1

1.1

photoproduction

E665

NMC

]

2

[(GeV/c)

2

Q

-3

10

-2

10

-1

10

1 10

〉

f

〈

0.3

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

0.4

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:

˜ σA= σp· Aα(Q2)−1,with α(Q2) − 1 = −1

3exp{−Q2/Q2

0}, (11)

where σpis the cross section for reaction (2) on the free proton. The value of the fitted

parameter Q2

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 Q2bins used in

the present analysis. The values of f are equal to about 0.36 in most of the Q2range,

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 ρ0production

analysis. The small values of RC are mainly due to the requirement of event exclusivity

via cuts on Emissand p2

The internal (infrared and virtual) RC were estimated in Ref. [25] to be of the order of

2%.

0is equal to 9 ± 3 (GeV/c)2. The measured values of the parameter α and

t, which largely suppress the dominant external photon radiation.

5Systematic errors

The main systematic uncertainty of Aρ

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 p2

1comes from an estimate of possible false

tcuts to

0 < p2

t< 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 p2

p2

sample. However, in addition to incoherent events such a sample contains a large fraction of

events originating from coherent ρ0production. 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 Aρ

both samples are consistent within statistical errors.

tsample’. Such an extension of the

trange allows one to obtain a sample which is about five times larger than the incoherent

1for

9

Page 12

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 Q2and x bins the dispersion of the

values of Aρ

which would lead to a broadening of these distributions were thus not observed. Allowing

the dispersion of Aρ

upper bound for the systematic error arising from time-dependent effects

1around their mean agrees with the statistical error. Time-dependent effects

1to vary within its two standard deviations we obtain for each bin an

σfalseA,tdep< 0.56 σstat.(13)

Here σstatis the statistical error on Aρ

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 p2

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 Aρ

negligible for the total sample.

The systematic error on Aρ

uncertainties on PBand PT. The uncertainty of the parameterisation of R(Q2) 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

ρ0production. The neglect of the Aρ

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 ρ0accompanied by the dissociation of the target nucleon, the

second one is the production of ρ0in 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 Q2the Emissdistribution 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 ρ0production was estimated to be about 0.12±0.06 in most

1for the extended p2

tsample. The uncertainty on the

t

1is

1also contains an overall scale uncertainty of 6.5% due to

2term mainly affects the highest bins of Q2and x.

10

Page 13

of the kinematical range, except in the largest Q2region, 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 Emissdistributions for various physics

processes could be studied separately. It was found that events of ρ0production 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 Aρ

exclusive sample, which was selected with the standard cuts used in this analysis, except

the cut on Emisswhich was modified to Emiss> 2.5 GeV. In different high-Emissbins Aρ

for this sample was found compatible with zero.

Because no indication of a non-zero Aρ

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 Q2and x.

The total systematic error on Aρ

from all discussed sources. Its values for each Q2and 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.

1for the background was obtained using a non-

1

1for the background was found, and also due

1was obtained as a quadratic sum of the errors

6 Results

The COMPASS results on Aρ

listed in Tables 1 and 2. The statistical errors are represented by vertical bars and the

total systematic errors by shaded bands.

1are shown as a function of Q2and x in Fig. 5 and

]

2

[(GeV/c)

2

Q

-3

10

-2

10

-1

101 10

ρ

A

1

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

x

-4

10

-3

10

-2

10

-1

10

ρ

A

1

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

Figure 5: Aρ

correspond to statistical errors, while bands at the bottom represent the systematical

errors.

1as a function of Q2(left) and x (right) from the present analysis. Error bars

The wide range in Q2covers four orders of magnitude from 3 · 10−3to 7 (GeV/c)2.

The domain in x which is strongly correlated with Q2, varies from 5 · 10−5to about

0.05 (see Tables for more details). For the whole kinematical range the Aρ

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

1asymmetry

11

Page 14

Table 1: Asymmetry Aρ

total systematic errors (second) are listed.

1as a function of Q2. Both the statistical errors (first) and the

Q2range?Q2? [(GeV/c)2]

0.0031

?x??ν? [GeV]

42.8

Aρ

1

0.0004 − 0.005

0.005 − 0.010

0.010 − 0.025

0.025 − 0.050

0.05 − 0.10

0.10 − 0.25

0.25 − 0.50

0.5 − 1

1 − 4

4 − 50

4.0 · 10−5

8.4 · 10−5

1.8 · 10−4

3.7 · 10−4

7.1 · 10−4

0.0016

−0.030 ± 0.045 ± 0.014

0.048 ± 0.038 ± 0.013

0.063 ± 0.026 ± 0.014

−0.035 ± 0.027 ± 0.009

−0.010 ± 0.028 ± 0.008

−0.019 ± 0.029 ± 0.009

0.016 ± 0.045 ± 0.014

0.141 ± 0.069 ± 0.030

0.000 ± 0.098 ± 0.035

−0.85 ± 0.50 ± 0.39

0.0074 49.9

0.01755.6

0.03659.9

0.07262.0

0.1662.3

0.350.0036 60.3

0.690.007458.6

1.70.01859.7

6.80.07555.9

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 Aρ

tained on a deuteron target [17]. Note that the lowest Q2and 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.

1ob-

]

2

[(GeV/c)

2

Q

-3

10

-2

10

-1

10110

ρ

A

1

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

COMPASS

HERMES quasi-photoprod. (d)

HERMES electroprod. (d)

x

-4

10

-3

10

-2

10

-1

10

ρ

A

1

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

COMPASS

HERMES quasi-photoprod. (d)

HERMES electroprod. (d)

Figure 6: Aρ

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.

1as a function of Q2(left) and x (right) from the present analysis (circles)

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 Aρ

different average W, which is equal to about 10 GeV for COMPASS and 5 GeV for

1is measured at

12

Page 15

Table 2: Asymmetry Aρ

systematic errors (second) are listed.

1as a function of x. Both the statistical errors (first) and the total

x range?x??Q2? [(GeV/c)2]

0.0058

?ν? [GeV]

51.7

Aρ

1

8 · 10−6− 1 · 10−4

1 · 10−4− 2.5 · 10−4

2.5 · 10−4− 5 · 10−4

5 · 10−4− 0.001

0.001 − 0.002

0.002 − 0.004

0.004 − 0.01

0.01 − 0.025

0.025 − 0.8

5.8 · 10−5

1.7 · 10−4

3.6 · 10−4

7.1 · 10−4

0.0014

0.035 ± 0.026 ± 0.011

0.036 ± 0.024 ± 0.010

−0.039 ± 0.027 ± 0.012

−0.010 ± 0.030 ± 0.010

−0.005 ± 0.036 ± 0.013

0.032 ± 0.050 ± 0.019

0.019 ± 0.069 ± 0.026

−0.03 ± 0.14 ± 0.06

−0.27 ± 0.38 ± 0.19

0.019 59.7

0.04161.3

0.08260.8

0.16 58.6

0.0028 0.2954.8

0.0062 0.5950.7

0.015 1.347.5

0.0493.943.8

HERMES. Thus, no significant W dependence is observed for Aρ

target.

The x dependence of the measured Aρ

given by Eq. 4, which relates Aρ

nucleon scattering. To produce the curve the inclusive asymmetry A1was parameterised

as A1(x) = (xα− 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 Q2and x [32]. Within the present accuracy the results on Aρ

are consistent with this prediction.

In the highest Q2bin, ?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 Q2range 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.

1on an isoscalar nucleon

1is compared in Fig. 6 to the prediction

1to the asymmetry A1for the inclusive inelastic lepton-

1

7Summary

The longitudinal double spin asymmetry Aρ

meson, µ + N → µ + N + ρ, has been measured by scattering longitudinally polarised

muons off longitudinally polarised deuterons from the6LiD target and selecting incoherent

exclusive ρ0production. The presented results for the COMPASS 2002 and 2003 data cover

a range of energy W from about 7 to 15 GeV.

The Q2and x dependence of Aρ

Q2≤ 7 (GeV/c)2and 5·10−5≤ x ≤ 0.05. These results extend the range in Q2and x by

1for the diffractive muoproduction of ρ0

1is presented in a wide kinematical range 3·10−3≤

13