Exclusive ϱ0 production in deep inelastic electron-proton scattering at HERA

Abstract

The exclusive production of ϱ0 mesons in deep inelastic electron-proton scattering has been studied using the ZEUS detector. Cross sections have been measured in the range 7 < Q2 < 25 GeV2 for λ∗p centre of mass (c.m.) energies 40 to 130 GeV. The λ∗p → ϱ0p cross section exhibits a Q−(4.2±0.8−0.5+1.4) dependence and both longitudinally and transversely polarised ϱ0's are observed. The λ∗p → ϱ0p cross section rises strongly with increasing c.m. energy, when compared with NMC data at lower energy, which cannot be explained by production through soft pomeron exchange. The data are compared with perturbative QCD calculations where the rise in the cross section reflects the increase in the gluon density at low x.

Full text

arXiv:hep-ex/9507001v1 5 Jul 1995
Exclusive ρ0production in deep inelastic
electron-proton scattering at HERA
ZEUS Collaboration
Abstract
The exclusive production of ρ0mesons in deep inelastic electron-proton scattering has
been studied using the ZEUS detector. Cross sections have been measured in the range
7< Q2<25 GeV2for γ∗pcentre of mass (c.m.) energies from 40 to 130 GeV. The
γ∗p→ρ0pcross section exhibits a Q−(4.2±0.8+1.4
−0.5)dependence and both longitudinally and
transversely polarised ρ0’s are observed. The γ∗p→ρ0pcross section rises strongly with
increasing c.m. energy, when compared with NMC data at lower energy, which cannot be
explained by production through soft pomeron exchange. The data are compared with
perturbative QCD calculations where the rise in the cross section reflects the increase in
the gluon density at low x. the gluon density at low x.
DESY 95-133
July 1995

The ZEUS Collaboration
M. Derrick, D. Krakauer, S. Magill, D. Mikunas, B. Musgrave, J. Repond, R. Stanek, R.L. Talaga, H. Zhang
Argonne National Laboratory, Argonne, IL, USA p
R. Ayad1, G. Bari, M. Basile, L. Bellagamba, D. Boscherini, A. Bruni, G. Bruni, P. Bruni, G. Cara Romeo,
G. Castellini2, M. Chiarini, L. Cifarelli3, F. Cindolo, A. Contin, M. Corradi, I. Gialas4, P. Giusti, G. Iacobucci,
G. Laurenti, G. Levi, A. Margotti, T. Massam, R. Nania, C. Nemoz,
F. Palmonari, A. Polini, G. Sartorelli, R. Timellini, Y. Zamora Garcia1, A. Zichichi
University and INFN Bologna, Bologna, Italy f
A. Bargende5, J. Crittenden, K. Desch, B. Diekmann6, T. Doeker, M. Eckert, L. Feld, A. Frey, M. Geerts,
M. Grothe, H. Hartmann, K. Heinloth, E. Hilger, H.-P. Jakob, U.F. Katz, S.M. Mari4, S. Mengel, J. Mollen,
E. Paul, M. Pfeiffer, Ch. Rembser, D. Schramm, J. Stamm, R. Wedemeyer
Physikalisches Institut der Universit¨at Bonn, Bonn, Federal Republic of Germany c
S. Campbell-Robson, A. Cassidy, N. Dyce, B. Foster, S. George, R. Gilmore, G.P. Heath, H.F. Heath, T.J. Llewellyn,
C.J.S. Morgado, D.J.P. Norman, J.A. O’Mara, R.J. Tapper, S.S. Wilson, R. Yoshida
H.H. Wills Physics Laboratory, University of Bristol, Bristol, U.K. o
R.R. Rau
Brookhaven National Laboratory, Upton, L.I., USA p
M. Arneodo7, M. Capua, A. Garfagnini, L. Iannotti, M. Schioppa, G. Susinno
Calabria University, Physics Dept.and INFN, Cosenza, Italy f
A. Bernstein, A. Caldwell, N. Cartiglia, J.A. Parsons, S. Ritz8, F. Sciulli, P.B. Straub, L. Wai, S. Yang, Q. Zhu
Columbia University, Nevis Labs., Irvington on Hudson, N.Y., USA q
P. Borzemski, J. Chwastowski, A. Eskreys, K. Piotrzkowski, M. Zachara, L. Zawiejski
Inst. of Nuclear Physics, Cracow, Poland j
L. Adamczyk, B. Bednarek, K. Jele´n, D. Kisielewska, T. Kowalski, E. Rulikowska-Zar¸ebska,
L. Suszycki, J. Zaj¸ac
Faculty of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Cracow, Poland j
A. Kota´nski, M. Przybycie´n
Jagellonian Univ., Dept. of Physics, Cracow, Poland k
L.A.T. Bauerdick, U. Behrens, H. Beier9, J.K. Bienlein, C. Coldewey, O. Deppe, K. Desler, G. Drews,
M. Flasi´nski10, D.J. Gilkinson, C. Glasman, P. G¨ottlicher, J. Große-Knetter, B. Gutjahr11, T. Haas, W. Hain,
D. Hasell, H. Heßling, Y. Iga, K. Johnson12 , P. Joos, M. Kasemann, R. Klanner, W. Koch, L. K¨opke13, U. K¨otz,
H. Kowalski, J. Labs, A. Ladage, B. L¨ohr, M. L¨owe, D. L¨uke, J. Mainusch, O. Ma´nczak, T. Monteiro14 ,
J.S.T. Ng, S. Nickel15, D. Notz, K. Ohrenberg, M. Roco, M. Rohde, J. Rold´an, U. Schneekloth, W. Schulz,
F. Selonke, E. Stiliaris16, B. Surrow, T. Voß, D. Westphal, G. Wolf, C. Youngman, W. Zeuner, J.F. Zhou17
Deutsches Elektronen-Synchrotron DESY, Hamburg, Federal Republic of Germany
H.J. Grabosch, A. Kharchilava, A. Leich, M.C.K. Mattingly, A. Meyer, S. Schlenstedt, N. Wulff
DESY-Zeuthen, Inst. f¨ur Hochenergiephysik, Zeuthen, Federal Republic of Germany
G. Barbagli, P. Pelfer
University and INFN, Florence, Italy f
G. Anzivino, G. Maccarrone, S. De Pasquale, L. Votano
INFN, Laboratori Nazionali di Frascati, Frascati, Italy f
A. Bamberger, S. Eisenhardt, A. Freidhof, S. S¨oldner-Rembold18 , J. Schroeder19, T. Trefzger
Fakult¨at f¨ur Physik der Universit¨at Freiburg i.Br., Freiburg i.Br., Federal Republic of Germany c
I

N.H. Brook, P.J. Bussey, A.T. Doyle20, J.I. Fleck4, D.H. Saxon, M.L. Utley, A.S. Wilson
Dept. of Physics and Astronomy, University of Glasgow, Glasgow, U.K. o
A. Dannemann, U. Holm, D. Horstmann, T. Neumann, R. Sinkus, K. Wick
Hamburg University, I. Institute of Exp. Physics, Hamburg, Federal Republic of Germany c
E. Badura21, B.D. Burow22 , L. Hagge, E. Lohrmann, J. Milewski, M. Nakahata23, N. Pavel, G. Poelz, W. Schott,
F. Zetsche
Hamburg University, II. Institute of Exp. Physics, Hamburg, Federal Republic of Germany c
T.C. Bacon, N. Bruemmer, I. Butterworth, E. Gallo, V.L. Harris, B.Y.H. Hung, K.R. Long, D.B. Miller,
P.P.O. Morawitz, A. Prinias, J.K. Sedgbeer, A.F. Whitfield
Imperial College London, High Energy Nuclear Physics Group, London, U.K. o
U. Mallik, E. McCliment, M.Z. Wang, S.M. Wang, J.T. Wu
University of Iowa, Physics and Astronomy Dept., Iowa City, USA p
P. Cloth, D. Filges
Forschungszentrum J¨ulich, Institut f¨ur Kernphysik, J¨ulich, Federal Republic of Germany
S.H. An, S.M. Hong, S.W. Nam, S.K. Park, M.H. Suh, S.H. Yon
Korea University, Seoul, Korea h
R. Imlay, S. Kartik, H.-J. Kim, R.R. McNeil, W. Metcalf, V.K. Nadendla
Louisiana State University, Dept. of Physics and Astronomy, Baton Rouge, LA, USA p
F. Barreiro24, G. Cases, J.P. Fernandez, R. Graciani, J.M. Hern´andez, L. Herv´as24, L. Labarga24 , M. Martinez,
J. del Peso, J. Puga, J. Terron, J.F. de Troc´oniz
Univer. Aut´onoma Madrid, Depto de F´ısica Te´or´ıca, Madrid, Spain n
G.R. Smith
University of Manitoba, Dept. of Physics, Winnipeg, Manitoba, Canada a
F. Corriveau, D.S. Hanna, J. Hartmann, L.W. Hung, J.N. Lim, C.G. Matthews, P.M. Patel,
L.E. Sinclair, D.G. Stairs, M. St.Laurent, R. Ullmann, G. Zacek
McGill University, Dept. of Physics, Montr´eal, Qu´ebec, Canada a, b
V. Bashkirov, B.A. Dolgoshein, A. Stifutkin
Moscow Engineering Physics Institute, Mosocw, Russia l
G.L. Bashindzhagyan, P.F. Ermolov, L.K. Gladilin, Yu.A. Golubkov, V.D. Kobrin, I.A. Korzhavina, V.A. Kuzmin,
O.Yu. Lukina, A.S. Proskuryakov, A.A. Savin, L.M. Shcheglova, A.N. Solomin,
N.P. Zotov
Moscow State University, Institute of Nuclear Physics, Moscow, Russia m
M. Botje, F. Chlebana, A. Dake, J. Engelen, M. de Kamps, P. Kooijman, A. Kruse, H. Tiecke, W. Verkerke,
M. Vreeswijk, L. Wiggers, E. de Wolf, R. van Woudenberg
NIKHEF and University of Amsterdam, Netherlands i
D. Acosta, B. Bylsma, L.S. Durkin, K. Honscheid, C. Li, T.Y. Ling, K.W. McLean25, W.N. Murray, I.H. Park,
T.A. Romanowski26, R. Seidlein27
Ohio State University, Physics Department, Columbus, Ohio, USA p
D.S. Bailey, A. Byrne28, R.J. Cashmore, A.M. Cooper-Sarkar, R.C.E. Devenish, N. Harnew,
M. Lancaster, L. Lindemann4, J.D. McFall, C. Nath, V.A. Noyes, A. Quadt, J.R. Tickner,
H. Uijterwaal, R. Walczak, D.S. Waters, F.F. Wilson, T. Yip
Department of Physics, University of Oxford, Oxford, U.K. o
G. Abbiendi, A. Bertolin, R. Brugnera, R. Carlin, F. Dal Corso, M. De Giorgi, U. Dosselli,
S. Limentani, M. Morandin, M. Posocco, L. Stanco, R. Stroili, C. Voci
Dipartimento di Fisica dell’ Universita and INFN, Padova, Italy f
II

J. Bulmahn, J.M. Butterworth, R.G. Feild, B.Y. Oh, J.J. Whitmore29
Pennsylvania State University, Dept. of Physics, University Park, PA, USA q
G. D’Agostini, G. Marini, A. Nigro, E. Tassi
Dipartimento di Fisica, Univ. ’La Sapienza’ and INFN, Rome, Italy f
J.C. Hart, N.A. McCubbin, K. Prytz, T.P. Shah, T.L. Short
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, U.K. o
E. Barberis, T. Dubbs, C. Heusch, M. Van Hook, W. Lockman, J.T. Rahn, H.F.-W. Sadrozinski, A. Seiden,
D.C. Williams
University of California, Santa Cruz, CA, USA p
J. Biltzinger, R.J. Seifert, O. Schwarzer, A.H. Walenta, G. Zech
Fachbereich Physik der Universit¨at-Gesamthochschule Siegen, Federal Republic of Germany c
H. Abramowicz, G. Briskin, S. Dagan30, A. Levy31
School of Physics,Tel-Aviv University, Tel Aviv, Israel e
T. Hasegawa, M. Hazumi, T. Ishii, M. Kuze, S. Mine, Y. Nagasawa, M. Nakao, I. Suzuki, K. Tokushuku, S. Ya-
mada, Y. Yamazaki
Institute for Nuclear Study, University of Tokyo, Tokyo, Japan g
M. Chiba, R. Hamatsu, T. Hirose, K. Homma, S. Kitamura, Y. Nakamitsu, K. Yamauchi
Tokyo Metropolitan University, Dept. of Physics, Tokyo, Japan g
R. Cirio, M. Costa, M.I. Ferrero, L. Lamberti, S. Maselli, C. Peroni, R. Sacchi, A. Solano, A. Staiano
Universita di Torino, Dipartimento di Fisica Sperimentale and INFN, Torino, Italy f
M. Dardo
II Faculty of Sciences, Torino University and INFN - Alessandria, Italy f
D.C. Bailey, D. Bandyopadhyay, F. Benard, M. Brkic, D.M. Gingrich32, G.F. Hartner, K.K. Joo, G.M. Levman,
J.F. Martin, R.S. Orr, S. Polenz, C.R. Sampson, R.J. Teuscher
University of Toronto, Dept. of Physics, Toronto, Ont., Canada a
C.D. Catterall, T.W. Jones, P.B. Kaziewicz, J.B. Lane, R.L. Saunders, J. Shulman
University College London, Physics and Astronomy Dept., London, U.K. o
K. Blankenship, B. Lu, L.W. Mo
Virginia Polytechnic Inst. and State University, Physics Dept., Blacksburg, VA, USA q
W. Bogusz, K. Charchu la, J. Ciborowski, J. Ga jewski, G. Grzelak, M. Kasprzak, M. Krzy˙zanowski,
K. Muchorowski, R.J. Nowak, J.M. Pawlak, T. Tymieniecka, A.K. Wr´oblewski, J.A. Zakrzewski, A.F. ˙
Zarnecki
Warsaw University, Institute of Experimental Physics, Warsaw, Poland j
M. Adamus
Institute for Nuclear Studies, Warsaw, Poland j
Y. Eisenberg30, U. Karshon30 , D. Revel30, D. Zer-Zion
Weizmann Institute, Nuclear Physics Dept., Rehovot, Israel d
I. Ali, W.F. Badgett, B. Behrens, S. Dasu, C. Fordham, C. Foudas, A. Goussiou, R.J. Loveless, D.D. Reeder,
S. Silverstein, W.H. Smith, A. Vaiciulis, M. Wodarczyk
University of Wisconsin, Dept. of Physics, Madison, WI, USA p
T. Tsurugai
Meiji Gakuin University, Faculty of General Education, Yokohama, Japan
S. Bhadra, M.L. Cardy, C.-P. Fagerstroem, W.R. Frisken, K.M. Furutani, M. Khakzad, W.B. Schmidke
York University, Dept. of Physics, North York, Ont., Canada a
III

1supported by Worldlab, Lausanne, Switzerland
2also at IROE Florence, Italy
3now at Univ. of Salerno and INFN Napoli, Italy
4supported by EU HCM contract ERB-CHRX-CT93-0376
5now at M¨obelhaus Kramm, Essen
6now a self-employed consultant
7now also at University of Torino
8Alfred P. Sloan Foundation Fellow
9presently at Columbia Univ., supported by DAAD/HSPII-AUFE
10 now at Inst. of Computer Science, Jagellonian Univ., Cracow
11 now at Comma-Soft, Bonn
12 visitor from Florida State University
13 now at Univ. of Mainz
14 supported by DAAD and European Community Program PRAXIS XXI
15 now at Dr. Seidel Informationssysteme, Frankfurt/M.
16 now at Inst. of Accelerating Systems & Applications (IASA), Athens
17 now at Mercer Management Consulting, Munich
18 now with OPAL Collaboration, Faculty of Physics at Univ. of Freiburg
19 now at SAS-Institut GmbH, Heidelberg
20 also supported by DESY
21 now at GSI Darmstadt
22 also supported by NSERC
23 now at Institute for Cosmic Ray Research, University of Tokyo
24 partially supported by CAM
25 now at Carleton University, Ottawa, Canada
26 now at Department of Energy, Washington
27 now at HEP Div., Argonne National Lab., Argonne, IL, USA
28 now at Oxford Magnet Technology, Eynsham, Oxon
29 on leave and partially supported by DESY 1993-95
30 supported by a MINERVA Fellowship
31 partially supported by DESY
32 now at Centre for Subatomic Research, Univ.of Alberta, Canada and TRIUMF, Vancouver, Canada
asupported by the Natural Sciences and Engineering Research Council of Canada (NSERC)
bsupported by the FCAR of Qu´ebec, Canada
csupported by the German Federal Ministry for Research and Technology (BMFT)
dsupported by the MINERVA Gesellschaft f¨ur Forschung GmbH, and by the Israel Academy of
Science
esupported by the German Israeli Foundation, and by the Israel Academy of Science
fsupported by the Italian National Institute for Nuclear Physics (INFN)
gsupported by the Japanese Ministry of Education, Science and Culture (the Monbusho) and its
grants for Scientific Research
hsupported by the Korean Ministry of Education and Korea Science and Engineering Foundation
isupported by the Netherlands Foundation for Research on Matter (FOM)
jsupported by the Polish State Committee for Scientific Research (grant No. SPB/P3/202/93) and
the Foundation for Polish- German Collaboration (proj. No. 506/92)
ksupported by the Polish State Committee for Scientific Research (grant No. PB 861/2/91 and No.
2 2372 9102, grant No. PB 2 2376 9102 and No. PB 2 0092 9101)
lpartially supported by the German Federal Ministry for Research and Technology (BMFT)
msupported by the German Federal Ministry for Research and Technology (BMFT), the Volkswagen
Foundation, and the Deutsche Forschungsgemeinschaft
nsupported by the Spanish Ministry of Education and Science through funds provided by CICYT
osupported by the Particle Physics and Astronomy Research Council
psupported by the US Department of Energy
qsupported by the US National Science Foundation
IV

1 Introduction
With the high energy electron-proton collider HERA, it has become possible to study deep
inelastic scattering (DIS) processes at large values of Q2, the negative of the four-momentum
transfer squared of the exchanged virtual photon, and large values of W, the virtual photon-
proton centre of mass (c.m.) energy. The exclusive production of vector mesons in DIS is of
particular interest. While numerous data exist at low Q2[1-5] on the exclusive reaction
e(or µ) + p→e(or µ) + ρ0+p, (1)
only two experiments have reported DIS measurements for Q2>5 GeV2[6, 7]. These latter
measurements have been restricted to W < 20 GeV.
Previous studies of exclusive leptoproduction (γ∗N→ρ0N) and real photoproduction
(γN →ρ0N) off a nucleon Nhave shown that for ρ0production at low Q2(typically <2
GeV2):
•the Q2dependence of the cross section can be described by the Vector Dominance Model
(VDM) [1] in which it is assumed that the photon fluctuates into a ρ0meson yielding:
dσ(Q2)
dt =dσ(0)
dt M2
ρ
M2
ρ+Q2!2 1 + ǫξ2Q2
M2
ρ!ebt,(2)
where ξis the ratio of the longitudinal to transverse forward amplitudes, ǫis the relative
longitudinal polarisation of the virtual photon and Mρis the ρ0mass; the distribution of
t, the square of the four-momentum transfer between the photon and the ρ0, is described
by a single exponential dependence, in the range from t= 0 to t=−0.5 GeV2, with a
slope parameter, b≈7−12 GeV−2;
•in real photoproduction (Q2= 0), the process is ‘quasi-elastic’ and the helicity of the
ρ0is similar to that of the incident photon, i.e. s-channel helicity is largely conserved
(SCHC) [8]. The ρ0decay distribution exhibits an approximate sin2θhdependence, where
θhis the polar angle of the π+in the ρ0c.m. system and the quantisation axis is the ρ0
direction in the γp c.m. system;
•the real photoproduction ρ0total cross section increases slowly as a function of Wfor
W > 15 GeV [9, 10]. This is expected for an elastic reaction dominated by the exchange
of a ‘soft’ pomeron with an intercept of the Regge trajectory of α(0) = 1 + ǫ′= 1.08. The
intercept is determined from fits [11] to hadron-hadron total cross sections: for a γp total
cross section σtot ∼W2(α(0)−1) ∼W2ǫ′, the optical theorem yields dσel
dt t=0 ∼W4ǫ′∼W0.32.
At larger Q2(2 < Q2<25 GeV2), leptoproduction results from the EMC [6] and NMC [7]
experiments indicate that:
•the γ∗p→ρ0pcross section is consistent with a 1/Q4behaviour;
•at larger Q2(>6 GeV2), the distribution of the square of the transverse momentum of
the ρ0with respect to the virtual photon (p2
T) is exponentially falling with a slope of
b= 4.6±0.8 GeV−2[7], about a factor of two smaller than that of the photoproduction
elastic process;
1

•as Q2increases, the fraction of zero-helicity, longitudinally polarised ρ0s increases above
50%; assuming SCHC [1], this implies that the longitudinal virtual photon cross section
dominates;
•for 2 < W < 4 GeV the cross section falls with Wat small Q2<4 GeV2[4]. No
significant dependence on Wis observed for 9 < W < 19 GeV [7].
The reaction γ∗p→ρ0phas also been the focus of theoretical investigations. Early studies
based on VDM are described elsewhere [1]. A study of diffractive leptoproduction by Donnachie
and Landshoff based on a zeroth order perturbative QCD (pQCD) calculation for pomeron ex-
change at small values of Bjorken x∼Q2/W 2[11] reproduced many of the features seen
experimentally, including the Q2dependence of the data at low W. In more recent presenta-
tions, the pomeron is treated as a non-perturbative two-gluon exchange [12]. This approach
has also been studied by Cudell [13]. Calculations in pQCD have been performed in the leading
logarithm approximation for J/ψ electroproduction by Ryskin [14]. Ginzburg et al. [15] and
Nemchik et al. [16] have also performed a calculation in pQCD for vector meson production.
These more recent calculations predict a Q−6dependence of the longitudinal cross section at
high Q2, in contrast to the Q−4VDM expectation. Brodsky et al. [17] have studied the forward
scattering cross section for this reaction by applying pQCD in the double leading logarithm
approximation (DLLA). They predict that at high Q2the vector mesons should be produced
dominantly by longitudinally polarised virtual photons with a dependence for the longitudinal
cross section:
dσL
dt t=0
(γ∗N→ρ0N) = A
Q6α2
s(Q2)·"1 + i(π/2)( d
d ln x)#xg(x, Q2)
2
,(3)
where Ais a constant, which can be calculated, and xg(x, Q2) is the momentum density of the
gluon in the proton. Using the x-dependence of xg(x, Q2) measured at HERA and the relation
W2∼Q2/x for small x, at fixed Q2one expects that dσel
dt t=0 ∼W1.4[18], in contrast to the
W0.32 dependence expected for the ‘soft’ pomeron.
This letter presents a measurement with the ZEUS detector of the exclusive cross section for
ρ0mesons produced at large Q2by the virtual photoproduction process γ∗p→ρ0pat HERA.
The data come from neutral current, deep inelastic electron-proton scattering in the Q2range
of 7 - 25 GeV2, similar to that of the earlier fixed target experiments [6, 7]; however, they cover
a lower xregion (4 ·10−4< x < 1·10−2) and, consequently, a higher Wregion (40-130 GeV).
2 Experimental conditions
The experiment was performed at the electron-proton collider HERA using the ZEUS detector.
During 1993 HERA operated with bunches of electrons of energy Ee= 26.7 GeV colliding with
bunches of protons of energy Ep= 820 GeV, with a time interval between bunch crossings of
96 ns. For this data-taking period 84 bunches were filled for each beam (paired bunches) and
in addition 10 electron and 6 proton bunches were left unpaired for background studies. The
electron and proton beam currents were typically 10 mA. The ep c.m. energy is √s= 296 GeV
and the integrated luminosity was 0.55 pb−1.
ZEUS is a multipurpose magnetic detector whose 1993 configuration has been described
elsewhere [19]. This brief description concentrates on those parts of the detector relevant to
the present analysis.
2

Charged particles are tracked by the inner tracking detectors which operate in a magnetic
field of 1.43 T. Immediately surrounding the beampipe is the vertex detector (VXD) [20] which
consists of 120 radial cells, each with 12 sense wires. Surrounding the VXD is the central
tracking detector (CTD) [21] which consists of 72 cylindrical drift chamber layers, organised
into 9 ‘superlayers’. In events with charged particle tracks, using the combined data from both
chambers, resolutions of 0.4 cm in Zand 0.1 cm in radius in the XY plane1are obtained for
the primary vertex reconstruction. These detectors provide a momentum resolution given by
σpT/pT=q(0.005pT)2+ (0.016)2(with pTin GeV).
The superconducting solenoid is surrounded by a high resolution uranium/scintillator calor-
imeter which is divided into three parts: forward (FCAL), barrel (BCAL), and rear (RCAL)
covering the angular region 2.2o< θ < 176.5o, where θ= 0ois defined as the proton beam
direction. Holes of 20 ×20 cm2in the centre of FCAL and RCAL are required to accommodate
the HERA beam pipe. The calorimeter parts are subdivided into towers which in turn are sub-
divided longitudinally into electromagnetic (EMC) and hadronic (HAC) sections. The sections
are subdivided into cells, each of which is viewed by two photomultiplier tubes which provide
the energy and the time of the energy deposit with a resolution of better than 1 ns. An addi-
tional hadron-electron separator (RHES)[22], located at the electromagnetic shower maximum
in the RCAL and consisting of a layer of 3 ×3 cm2silicon diodes, was used to provide more
accurate position information for electrons scattered at low angles than was available from the
calorimeter alone.
The luminosity is measured from the rate observed in the luminosity photon detector of hard
bremsstrahlung photons from the Bethe-Heitler process ep →epγ. The luminosity detector
consists of photon and electron lead-scintillator calorimeters [23]. Bremsstrahlung photons
emerging from the electron-proton interaction point at angles below 0.5 mrad with respect to
the electron beam axis hit the photon calorimeter placed 107 m along the electron beam line.
Electrons emitted at scattering angles less than 5 mrad and with energies 0.2Ee< E′
e<0.9Ee
are deflected by beam magnets and hit the electron calorimeter placed 35 m from the interaction
point.
The data were collected with a three-level-trigger. The first-level-trigger (FLT) for DIS
events required a logical OR of three conditions on sums of energy in the EMC calorimeter
cells. Details are given elsewhere [19, 24]. For events with the scattered electron detected in
the calorimeter, the FLT was essentially independent of the DIS hadronic final state. The FLT
acceptance was greater than 97% for Q2>7 GeV2. The second-level-trigger used information
from a subset of detector components to reject proton beam-gas events, thereby reducing the
FLT DIS triggers by an order of magnitude, but without loss of DIS events.
The third-level-trigger (TLT) had available the full event information on which to apply
physics-based filters. The TLT applied stricter cuts on the event times and also rejected beam-
halo muons and cosmic ray muons. Events remaining after the above veto cuts were selected
for output by the TLT if δ≡ΣiEi(1 −cos θi)>20 GeV −2Eγ, where Ei, θiare the energy
and polar angle (with respect to the nominal beam interaction point) of the geometric centre
of a calorimeter cell and Eγis the energy measured in the photon calorimeter of the luminosity
monitor. For fully contained events δ∼2Ee= 53.4 GeV. For events from photoproduction,
the scattered electrons remain in the rear beam pipe and δpeaks at low values.
1The ZEUS coordinate system is defined as right-handed with the Zaxis pointing in the proton beam
direction, hereafter referred to as forward, and the Xaxis horizontal, pointing towards the centre of HERA.
3

3 Kinematics of exclusive ρ0production
The kinematic variables used to describe ρ0production in the reaction:
e+p→e+ρ0+X, (4)
where Xrepresents either a proton or a diffractively dissociated proton remnant of mass MX,
are the following: the negative of the squared four-momentum transfer carried by the virtual
photon2Q2=−q2=−(k−k′)2, where k(k′) is the four-momentum of the incident (scattered)
electron; the Bjorken variable x=Q2
2P·q, where Pis the four-momentum of the incident proton;
the variable which describes the energy transfer to the hadronic final state y=q·P
k·P; the c.m.
energy, √s, of the ep system, where s= (k+P)2;W, the c.m. energy of the γ∗psystem:
W2= (q+P)2=Q2(1−x)
x+M2
p≈ys, where Mpis the proton mass; and t′=|t−tmin |, where
tis the four-momentum transfer squared, t= (q−v)2= (P−P′)2, from the photon to the
ρ0(with four-momentum v), tmin is the minimum kinematically allowed value of tand P′is
the four-momentum of the outgoing proton. The squared transverse momentum p2
Tof the ρ0
with respect to the photon direction is a good approximation to t′since t′is, in general, small
(<< 1 GeV2). For the present data3tmin ranges from −0.0006 to −0.08 GeV2.
In this analysis, the ρ0was observed in the decay ρ0→π+π−. The momentum vector
of the ρ0was reconstructed from the pion momentum vectors determined with the tracking
system. The production angles (θρand φρ) and momentum (pρ) of the ρ0and the angles of the
scattered electron (θe
′and φe
′), as determined with RCAL and RHES, were used to reconstruct
the kinematic variables x, Q2, etc. The energy of the scattered electron was determined from
the relation:
Ec
e=(s+M2
ππ −M2
X)/2−(Ee+Ep)(Eρ− |pρ|cosθρ)
(Ee+Ep)(1 −βcosθ′
e)−(Eρ− |pρ|cosθeρ),(5)
where Eρis the energy of the ππ pair, θeρ is the angle between the ππ three vector and the
scattered electron and β= (Ep−Ee)/(Ep+Ee). For the case of reaction (1), MX=Mpand Ec
e
is a good estimator of the energy of the scattered electron, E′
e; for events in which the proton
diffractively dissociates into the system X,MX> Mpand Ec
eis only slightly different from E′
e.
The above expression simplifies to
Ec
e≈[2Ee−(Eρ− |pρ|cosθρ)]/(1 −cosθ′
e) (6)
when MX=Mpand the transverse momentum of the proton is negligible compared to its
longitudinal component. This last relation provides an accurate way to calculate the kinematic
variables and is a simple expression used to evaluate the radiative corrections for this process.
The variable yis calculated from the expression y= (Eρ− |pρ|cosθρ)/2Ee. The calculation of
p2
Talso uses the ρ0and electron momenta: p2
T= (pex +pρx)2+ (pey +pρy )2.
4 Monte Carlo simulations
The reaction ep →eρ0pwas modelled using two different Monte Carlo generators. The first,
DIPSI [25], describes elastic ρ0production in terms of pomeron exchange with the pomeron
treated as a colourless two-gluon system [14]. The model assumes that the exchanged photon
2In the Q2range covered by this data sample, effects due to Z0exchange can be neglected.
3The −0.08 GeV2value corresponds to MX= 8 GeV and Q2= 25 GeV2.
4

fluctuates into a quark-antiquark pair which then interacts with the two-gluon system. The
cross section is proportional to the square of the gluon momentum density in the proton.
Samples of φand ωevents were generated in a similar way.
A second sample of ρ0events was generated with a Q−6dependence for the ep reaction, a
flat helicity angular distribution, and an exponentially falling p2
Tdistribution with a slope of
b= 5 GeV−2. The Monte Carlo generator used the HERWIG framework [26] and the events
were weighted according to the measured helicity, p2
Tand ydistributions.
A third ρ0Monte Carlo generator (RHODI), based on the model of Forshaw and Ryskin [27],
was used to model the proton dissociative processes with a dσ(γ∗p)/dM2
X∝1/M2.5
Xdependence.
Different MXdependences were obtained by weighting the events. Events were generated for
M2
Xvalues between 1.2 and 4000 GeV2. All Monte Carlo events were passed through the
standard ZEUS detector and trigger simulation programs and through the event reconstruction
software.
The radiative corrections were calculated to be (10-15)% for the selection cuts used in the
analysis and for the Q2and Wdependences found in the data. They are taken into account in
the cross sections given below.
5 Analysis and cross sections
5.1 Data selection
For the selection of exclusive ρ0candidates, the off-line analysis required:
•a scattered electron energy, as measured in the calorimeter, greater than 5 GeV. The elec-
tron identification algorithms used in this analysis were optimised to have high efficiency
(>97%);
•δ=PiEi(1 −cosθi)>35 GeV, where the sum runs over all calorimeter cells; this cut
reduces the radiative corrections and photoproduction background;
•two tracks with opposite charge, both associated with the reconstructed vertex; if there
was a third track at the vertex, it should be from the scattered electron. Each of the
two tracks was required to have a transverse momentum above 0.16 GeV and a polar
angle between 25oand 155o; this corresponds to the region where the CTD response and
systematics are well understood;
•a measured vertex (Zvtx), as reconstructed from VXD and CTD tracks, to be in the range
−50 < Zvtx <40 cm;
•events with a scattered electron whose impact point in the RCAL was outside the square
of 32 ×32 cm2centered on the beam axis or events with an RHES impact point outside
the square of 26 ×26 cm2; this requirement controls the determination of the electron
scattering angle; and
•the residual calorimeter energy not associated with the electron to be compatible with
the ρ0momentum measured in the tracking system, Eρ
CAL /Pρ<1.5 (see Fig. 1a), where
Eρ
CAL is the calorimeter energy excluding that due to the scattered electron and Pρis the
sum of the absolute values of the momenta of the two oppositely charged tracks. This
cut suppresses backgrounds with additional calorimeter energy unmatched to the tracks
5

and events with proton dissociation depositing energy in the calorimeter towers around
the FCAL beampipe. Also shown in Fig. 1a is the distribution from the ρ0DIPSI Monte
Carlo events, indicating that only a small fraction of the exclusive ρ0events are removed
by this cut. Fig. 1b shows the same distribution after the final selection indicating good
agreement with the expected distribution.
A total of 352 events passed these selection requirements.
Possible backgrounds to the exclusive reaction (1) are from ρ0events with additional unde-
tected particles, from φand ωproduction and from proton dissociation events where MXis
small and therefore does not deposit energy in the calorimeter. To reduce these backgrounds,
two additional cuts were imposed:
•0.6< Mπ+π−<1.0 GeV; this selection reduces the contamination from φand ωproduc-
tion in the low π+π−mass region as well as higher mass resonant states and non-exclusive
events in the high mass region; and
•p2
T<0.6 GeV2; this cut reduces non-exclusive background and proton dissociation events.
Fig. 1c shows the measured, uncorrected p2
Tdistribution for the selected ρ0events, indi-
cating a clear excess of events above a single exponential for p2
T>0.6 GeV2, consistent
with the presence of proton dissociation events which, in hadron-hadron scattering, have
a less steep p2
Tdistribution [28]. (The acceptance is relatively flat, rising by about 5%
from p2
T= 0 to 0.6 GeV2.)
Fig. 1d shows a scatter plot of Q2versus xfor the 140 events which pass the above criteria.
The efficiency drops sharply at small Q2(due to the cut on the electron impact point in
RCAL) and at small and large y(due to the requirements on the π+, π−tracks). To remove
poorly reconstructed events and to select a region of phase space where the acceptance is well
determined and relatively constant as a function of the kinematic variables, two additional
kinematic cuts were applied to the data:
•7< Q2<25 GeV2and 0.02 < y < 0.20.
The final ρ0sample contains 82 events.
5.2 Background estimates and acceptance corrections
The DIPSI ρ0Monte Carlo simulated events were used to correct the data for acceptance and
detector resolution. The acceptance (which includes the geometric acceptance, reconstruction
efficiencies, detector efficiency and resolution, corrections for the offline analysis cuts and a
correction for the Mπ+π−cut) in this region of Q2varies between 40% and 55%. The acceptance
is constant at about 47% as a function of y,p2
Tor Mπ+π−in the above kinematic region. The
resolutions in the measured kinematic variables, as determined from the Monte Carlo events,
are 6% for Q2and 2% for y.
Fig. 2a, which shows the uncorrected π+π−mass distribution for the events passing all of
the final cuts (except for the Mπ+π−cut, but with a MK+K−>1.05 GeV cut, when the tracks
are assigned a kaon mass, to remove φevents), indicates a pure sample of ρ0events. A ρ0
non-relativistic Breit-Wigner form, with a constant background, is fit to the mass spectrum
between 0.6 and 2.0 GeV. The resulting parameters for the ρ0mass and width are 774 ±9 MeV
and 134 ±20 MeV, respectively, to be compared with the values 769.9 MeV and 151.2 MeV
from the Particle Data Group [29]. The fit also includes a flat background estimate of (4 ±4)%
6

for Mπ+π−masses between 0.6 and 1.0 GeV, as determined from comparing the Monte Carlo
ρ0events with the data for Mπ+π−masses between 1.0 and 1.5 GeV. Background contributions
from exclusive φand ωevents were estimated to be at the 1% level and are included in the
above background estimate.
Since the proton was not detected, the proton dissociation background contribution had to
be subtracted. This was done using the RHODI event generator combined with the detector
simulation. The normalisation was obtained by requiring that the Monte Carlo generated
sample have the same number of events with energy between 1 and 20 GeV in the FCAL
as for the data (7 events) when the constraint that Eρ
CAL /Pρ<1.5 was relaxed to (Eρ
CAL −
EF CAL )/Pρ<1.5 and the additional constraint θπ±>50owas imposed. Assuming an MX
dependence of the form 1/M2.25
X, as measured by the CDF experiment [30] for pp →p+ X,
yielded a contribution of (22 ±8±15)% where the systematic error was obtained from varying
the exponent of 1/MXbetween 2 and 3. This is consistent with an estimate from the excess
above the exponential in the p2
Tdistribution mentioned above. In the exclusive ρ0sample
under study here, there are no events with an electron energy in the range 5 < E′
e<14 GeV
and so the photoproduction background is negligible. No events were found from the unpaired
bunches demonstrating that the beam-gas background is also negligible. The overall background
contamination was estimated to be ∆ = (26 ±18)%. Unless explicitly stated otherwise, this
background was subtracted as a constant fraction for the cross sections given below.
5.3 The ep cross section
The cross section, measured in the kinematic region defined above, is obtained from σ(ep →
eρ0p) = N(1 −∆)C1/(C2·A·Lint), where N(= 82) is the observed number of events after
all cuts with 0.6 < Mππ <1.0 GeV, ∆ is the background estimation, Ais the acceptance as
discussed above, Lint is the integrated luminosity of 0.55 pb−1and C2is the correction for QED
radiative effects. These radiative corrections were calculated for the exclusive reaction using
the xand Q2dependences found in this experiment (see section 6.1) and vary between 1.10 (at
low Q2and low y) and 1.14 (at high Q2and high y). A systematic uncertainty of ±0.10 was
included on this correction to account for the uncertainties in the cross section dependences
on xand Q2. To compare later with results from the NMC experiment, which has determined
exclusive ρ0cross sections integrated over all p2
T[7], C1is a 4.5% correction for the cross section
in the p2
Trange between 0.6 and 1.0 GeV2based on the slope of the distribution measured in
the present analysis. The corrected ep cross section for exclusive ρ0production at √s= 296
GeV is
σ(ep →eρ0p) = 0.21 ±0.03(stat.)±0.06(syst.) nb,
integrated over the ranges 7 < Q2<25 GeV2, 0.02 < y < 0.20 and p2
T<1.0 GeV2, with
acceptance corrected < Q2>and < W > of 11.0 GeV2and 78.9 GeV, respectively.
The quoted systematic uncertainty is derived from the following (the systematic uncertainty
for each item is indicated in parentheses):
•the cuts used to remove non-exclusive backgrounds were varied and independent analyses
using differing selection cuts and background estimates were compared to the previously
described analysis: tracks were matched to the calorimeter energy deposits and events
containing an energy in excess of that of the ρ0of more than 0.4, 1 or 2 GeV were
discarded; events were selected based on the position of the electron measured by the
calorimeter rather than by the RHES and the cut on the impact position of the electron
in RCAL was varied (10%);
7

•using different trigger configurations (8%),
•the cuts on the tracks were varied. The lower cut on the transverse momentum was varied
between 0.1 and 0.2 GeV and different polar angle selections were made. The maximum
variation occurred for pT>0.2 GeV (9%); and
•events from different Monte Carlo generators were used to calculate the acceptance and
efficiency (7%).
Adding these in quadrature to those from the uncertainties due to background subtraction
(24%), luminosity (3.3%) and radiative corrections (10%) yields 31% as the overall systematic
uncertainty.
5.4 The γ∗pcross sections
The ep cross section was converted to a γ∗pcross section as follows. The differential ep cross
section for one photon exchange can be expressed in terms of the transverse and longitudinal
virtual photoproduction cross sections (see [2]) as:
d2σ(ep)
dxdQ2=α
2πxQ2h1 + (1 −y)2·σγ∗p
T(y, Q2) + 2(1 −y)·σγ∗p
L(y, Q2)i.
The virtual photon-proton cross section can then be written in terms of the electron-proton
differential cross section:
σ(γ∗p→ρ0p) = (σγ∗p
T+ǫσγ∗p
L) = 1
ΓT
d2σ(ep →eρop)
dxdQ2(7)
where ΓT, the flux of transverse virtual photons, and ǫ, the ratio of the longitudinal to transverse
virtual photon flux, are given by
ΓT=α(1 + (1 −y)2)
2πxQ2and ǫ=2(1 −y)
(1 + (1 −y)2).
Throughout the kinematic range studied here, ǫis in the range 0.97 < ǫ < 1.0.
Using Eq. (7), σ(γ∗p→ρ0p) was determined with the flux calculated from the Q2,xand y
values on an event-by-event basis. The 31% overall systematic uncertainty on σ(ep) applies to
every value for σ(γ∗p→ρ0p) and thus becomes an overall normalisation uncertainty.
6 Results
6.1 Q2and p2
Tdistributions
After correcting for detector acceptance and backgrounds, the cross sections were obtained
as a function of Q2. Fig. 2b displays the Q2dependence of the γ∗p→ρopcross section for
events in the xrange between 0.0014 and 0.004. Also displayed in Fig. 2b are data from the
NMC experiment [7]. The ZEUS values of the cross sections are larger than those of the NMC
experiment. However, it should be noted that for this figure as well as for Figs. 2d, 3 and 4
the different experiments have different mixtures of longitudinal and transverse photon fluxes
(ǫvaries from 0.5-0.8 for the NMC results). More importantly, the region of γ∗pc.m. energy
of the NMC experiment (8-19 GeV) is lower than that in this experiment (40-130 GeV).
8

A fit of the form Q−2αto the distribution of the ZEUS data in Fig. 2b yields the power
of the Q2dependence. To study the systematic uncertainty on the value of α, a maximum
likelihood analysis was performed with the cross section factorised as:
σ(γ∗p→ρ0p)∼(Q2)−α·x−β·e−bp2
T.(8)
This study, applied to the 82 events in the final data sample in the region 0.02 < y < 0.20,
p2
T<0.6 GeV2and 7 < Q2<25 GeV2, yields results similar to those obtained from fitting
Fig. 2b. The best estimate of the Q2dependence is 2α= 4.2±0.8(stat.)+1.4
−0.5(syst.), where
the systematic uncertainty comes from the variation in the value of αobtained from the two
different fitting methods as well as from the variation obtained from the systematic studies
described in section 5.3.
The uncorrected p2
Tdistribution was presented in Fig. 1c and showed an exponentially falling
behaviour, with an excess of events for p2
T>0.6 GeV2, as discussed previously. After correcting
for detector acceptance and resolution, a fit in the range 0 < p2
T<1.0 GeV2of the form:
dσ
dp2
T
=Ae(−bp2
T)+Be(−b
2p2
T),(9)
was performed. In Eq. (9) the contribution from the second term, which was constrained to be
22% of the number of events for p2
T<0.6 GeV2, represents the proton dissociative background
contribution which was assumed to have a slope half that of the exclusive reaction [28]. The fit
yields a slope parameter of b= 5.1+1.2
−0.9(stat.)±1.0(syst.) GeV−2, which is consistent with that
found in the maximum likelihood fit. The systematic uncertainty comes from the variation in
the value of bobtained from fits without the second term in Eq. (9), the maximum likelihood
fit and from the systematic studies described in section 5.3. This value of bis about half that
found in elastic ρ0photoproduction [10] and is in agreement with the result from the NMC
experiment [7].
6.2 ρ0decay distribution
The ρ0s-channel helicity decay angular distribution H(cosθh, φh,Φh) can be used to determine
the ρ0spin state [31], where θhand φhare the polar and azimuthal angles, respectively, of the
π+in the ρ0c.m. system and Φhis the azimuthal angle of the ρ0production plane with respect
to the electron scattering plane. The quantisation axis is defined as the ρ0direction in the γ∗p
c.m. system. Only the cosθhdependence is presented here. After integrating over φhand Φh,
the decay angular distribution can be written as:
1
N
dN
dcosθh
=3
4[1 −r04
00 + (3r04
00 −1)cos2θh],(10)
where the density matrix element r04
00 represents the probability that the ρ0was produced
longitudinally polarised by either transversely or longitudinally polarised virtual photons.
The helicity cosθhdistribution (uncorrected for background, since the dominant contribution
to the background is from proton dissociation which is expected to have the same helicity as
the ρ0pfinal state) is shown in Fig. 2c. The curve shown in the figure is from a maximum
likelihood fit to the form of Eq. (10) yielding r04
00 = 0.6±0.1+0.2
−0.1at < Q2>= 11.0 GeV2and
< W > = 78.9 GeV, where the first uncertainty is statistical, and the second is derived from
the variations of the result when different ranges in cosθhwere used in the fit and when the
9

systematic studies of section 5.3 were used. In Fig. 2d this measurement of r04
00 is compared to
other published data at various values of Q2. These data show the presence of both transversely
and longitudinally polarised ρ0’s at high Q2(above 2 GeV2). If SCHC is assumed, an estimate
of R, the ratio of longitudinal to transverse cross sections, for ρ0production is obtained [2]:
R=σL
σT
=1
ǫ·r04
00
1−r04
00
= 1.5+2.8
−0.6
(where the statistical and systematic uncertainties in r04
00 have been added in quadrature). This
may be compared with the value of R= 2.0±0.3 at < Q2>= 6 GeV2and < W >∼14 GeV
from the NMC experiment [7].
6.3 The Wand xdependences of the γ∗p→ρ0pcross section
Fig. 3 shows a compilation [2,4,5,7-9] of photoproduction and selected leptoproduction exclusive
ρ0cross sections as a function of both Q2and W. In this figure the cross sections obtained
in this analysis are shown as a function of Wat Q2= 8.8 and 16.9 GeV2. The cross sections
at different Wvalues (and slightly different < Q2>) were scaled to Q2= 8.8 and 16.9 GeV2
using the measured Q−4.2dependence in order to compare with the NMC cross sections4from
deuterium at the same values of Q2. At high energies, W > 50 GeV, data exist only at Q2=
0, 8.8 and 16.9 GeV2. The real (Q2= 0) γp ‘elastic’ cross section [10] shows only a slow rise,
consistent with that seen in the photon-proton total cross section. At small Q2(<2.6 GeV2),
the data first decrease with increasing Wfollowed by a slow increase. No high energy data are
yet available to see how the increase develops. At higher Q2, the cross sections rise strongly
with increasing W. At Q2= 8.8 GeV2and W∼100 GeV, the cross section is about a factor
of six larger than at W= 12.9 GeV [7]. This strong increase in the γ∗p→ρ0pcross section is
in contrast to that expected from the Donnachie and Landshoff model [11, 12].
To compare with the QCD calculations of Brodsky et al. and Donnachie and Landshoff, the
ZEUS and NMC cross sections are shown as a function of xat Q2= 8.8 and 16.9 GeV2in Figs.
4a, b. The total cross sections are predicted from the pQCD calculations of Brodsky et al. [17]
using the longitudinal contribution to the differential cross section at t= 0, (see Eq. (3)):
σ(x, Q2) = Z1
0
dσ(x, Q2, p2
T)
dp2
T
dp2
T=(1 −e−b)
b·d(σT+σL)
dt t=0
=(1 −e−b)
b·(1
R+ǫ)·dσL
dt t=0
(11)
where bis the slope of the p2
Tdistribution. The measured values of ǫ= 0.98, R= 1.5 and
b= 5.1 GeV−2were used to calculate σ(x, Q2). For the gluon momentum density, xg(x, Q2),
the form xg ∼xδ·(1 −x)ηwas assumed. The values of δand ηwere allowed to vary within
the ranges (−0.25 to −0.39) and (6.44 to 4.81) respectively. These ranges were determined
from the leading order gluon density extracted [18] from the scaling violations of the ZEUS
F2measurements [19]. The uncertainty in Eq. (11) arising from the 1σrange in the gluon
density[18] is shown as the light shaded region in Fig. 4. The uncertainty in the prediction
arising from measurement uncertainties of Rand bwhen added in quadrature to that of the
gluon distribution yields the larger dark shaded area. The shaded areas in Fig. 4 are restricted
to x < 0.01 where Eq. (3) is valid. The range in the predicted cross sections at a given x
is dominated by the uncertainty on δ. Since the calculation is made in DLLA, the value of
4Since the EMC and NMC data cover approximately the same kinematic region, the more recent NMC
data[7] have been chosen to make comparisons.
10

Q2at which the gluon density and αsare evaluated is not defined to better than a factor of
two. Varying the Q2scale for αs(Q2)·xg(x, Q2) from Q2/2 to 2Q2changes the prediction by
about 50%. The xscale in the calculation can also range from x/2 to 2xso that the curves
can be shifted left or right to reflect this uncertainty. At the present level of precision of the
measurement and theory, the data are consistent with the pQCD calculation of Brodsky et al.
The hatched region shows the range of the predictions of Donnachie and Landshoff based on
soft pomeron exchange [11] with σ=1
b
dσ
dt t=0. The range of the hatched area comes from the
uncertainty in the measured value of b. The data do not agree with these expectations, being
typically a factor of three above the predictions.
7 Conclusions
Exclusive ρ0production has been studied in deep inelastic electron-proton scattering at large Q2
(7 - 25 GeV2) in the γ∗pcentre of mass energy (W) range from 40 to 130 GeV. Cross sections
are given for both the ep and γ∗pprocesses. The cross section for the γ∗pprocess exhibits
aQ−(4.2±0.8+1.4
−0.5)dependence. The γ∗p→ρ0pcross section at these large Q2values shows a
strong increase with Wat HERA energies over the lower energy NMC data, in contrast to the
behaviour of the elastic photoproduction cross section. Both longitudinally and transversely
polarised ρ0’s are produced. The Q2dependence, the polarisation and the slope of the p2
T
distribution are consistent with those observed at lower energies. However, the cross sections
are significantly larger. The Donnachie and Landshoff prediction for soft pomeron exchange
underestimates the measured cross sections while the data are consistent with the perturbative
QCD calculation of Brodsky et al. given the present knowledge of the gluon momentum density
in the proton.
Acknowledgements
The strong support and encouragement of the DESY Directorate is greatly appreciated.
The experiment was made possible by the inventiveness and the diligent efforts of the HERA
machine group who continued to run HERA most efficiently during 1993. We also acknowledge
the many informative discussions we have had with S. Brodsky, J. Cudell, J. Forshaw, L.
Frankfurt, J. Gunion, P. Landshoff, A. Mueller, M. Ryskin, A. Sandacz and M. Strikman.
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[28] K. Goulianos, Phys. Rep. 101 (1983) 169.
12

[29] Review of Particle Properties, Particle Data Group, Phys. Rev. D50 (1994) 1664.
[30] CDF Collab., F. Abe et al., Phys. Rev. D50 (1994) 5535.
[31] K. Schilling, P. Seyboth and G. Wolf, Nucl. Phys. B15 (1970) 397;
K. Schilling and G. Wolf, Nucl. Phys. B61 (1973) 381.
13

Figure 1: (a) The distribution of Eρ
CAL /Pρfor the candidate events; (b) the same distribution
for the final sample of 82 events; (c) the p2
Tdistribution; and (d) a scatter plot of Q2versus
xfor the selected ρ0events. These plots are not corrected for detector and trigger efficiencies
and acceptances. The histograms in (a-c) are obtained from the DIPSI ρ0Monte Carlo sample
after detector and trigger simulation. In (d) the lines correspond to the region in Q2and y
selected for this analysis.
14

Figure 2: (a) The π+π−invariant mass distribution for the final sample of events; the curve
is a maximum likelihood fit with a non-relativistic Breit-Wigner distribution plus a flat (4%)
background (see text for details); (b) the cross section for γ∗p→ρ0pas a function of Q2for
0.0014 < x < 0.004. Also shown are data from the NMC experiment [7]; the errors shown are
just the statistical errors. The ZEUS (NMC) data have an additional 31% (20%) normalisation
uncertainty (not shown); (c) the cosθhdistribution for the decay π+, in the s-channel helicity
system, corrected for acceptance, for π+π−pairs in the mass range 0.6-1.0 GeV. The curve is a
fit to the form of Eq. (10); (d) the ρ0density matrix element, r04
00, compared with results from
fixed target experiments [2,3,7] as a function of Q2. The thick error is the statistical error and
the thin error is the systematic error added in quadrature.
15

10 -3
10 -2
10 -1
1
10
50
1 5 10 50 100 500
Figure 3: The γ∗p→ρ0pcross section as a function of W, the γ∗pcentre of mass energy, for
several values of Q2. The low energy data (W < 20 GeV) come from fixed target experiments
[2,4,5,7,8]. The high energy data (W > 50 GeV) come from the ZEUS experiment [10] and the
present analysis. The ZEUS data at Q2= 8.8 and 16.9 GeV2have an additional 31% systematic
normalisation uncertainty (not shown); the data from Refs. [2], [4] and [7] have additional 10%,
25%, and 20% normalisation uncertainties, respectively.
16

Figure 4: (a) The cross section, σ(γ∗p→ρ0p), as a function of xat a value of Q2= 8.8
GeV2. (b) A similar plot for data at Q2= 16.9 GeV2. The errors shown are only the statistical
errors. In addition, there is a 31% systematic uncertainty which is not shown but applies
to the overall normalisation. Also shown is the NMC result (which has an additional 20%
normalisation uncertainty [7]). The shaded area corresponds to the predictions of Eqs. (3)
and (11) for x < 0.01. The range of the predictions shown by the light shaded area is a result
of the experimental uncertainty of the gluon distribution [18]. The dark shaded area includes
the uncertainties on band Radded in quadrature to that of the gluon. In addition, there is a
50% uncertainty in the predicted cross section from the choice of the Q2scale; furthermore, the
value of xin Eq. (3) is only defined to within a factor of 2. The hatched area displays the cross
section expected from the soft pomeron model [11]. The range comes from the uncertainty in
the measured value of b.
17