Content uploaded by Irina Korzhavina
Author content
All content in this area was uploaded by Irina Korzhavina on Dec 23, 2013
Content may be subject to copyright.
arXiv:hep-ex/9505010v1 17 May 1995
Measurement of the diffractive structure
function in deep inelastic scattering at HERA
ZEUS Collaboration
Abstract
This paper presents an analysis of the inclusive properties of diffractive deep inelastic
scattering events produced in ep interactions at HERA. The events are characterised by
a rapidity gap between the outgoing proton system and the remaining hadronic system.
Inclusive distributions are presented and compared with Monte Carlo models for diffractive
processes. The data are consistent with models where the pomeron structure function has
a hard and a soft contribution. The diffractive structure function is measured as a function
of xIP , the momentum fraction lost by the proton, of β, the momentum fraction of the
struck quark with respect to xIP , and of Q2. The xIP dependence is consistent with
the form (1/xIP )awhere a= 1.30 ±0.08 (stat)+ 0.08
−0.14 (sys) in all bins of βand Q2.
In the measured Q2range, the diffractive structure function approximately scales with
Q2at fixed β. In an Ingelman-Schlein type model, where commonly used pomeron flux
factor normalisations are assumed, it is found that the quarks within the pomeron do not
saturate the momentum sum rule.
DESY 95-093
May 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,
G. Geitz7, M. Grothe, H. Hartmann, K. Heinloth, E. Hilger, H.-P. Jakob, U.F. Katz,
S.M. Mari4, A. Mass8, S. Mengel, J. Mollen, E. Paul, 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. Arneodo9, 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. Ritz10, 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. Beier11, J.K. Bienlein, C. Coldewey, O. Deppe, K. Desler, G. Drews,
M. Flasi´nski12, D.J. Gilkinson, C. Glasman, P. G¨ottlicher, J. Große-Knetter, B. Gutjahr13, T. Haas, W. Hain,
D. Hasell, H. Heßling, Y. Iga, P. Joos, M. Kasemann, R. Klanner, W. Koch, L. K¨opke14, U. K¨otz, H. Kowalski,
J. Labs, A. Ladage, B. L¨ohr, M. L¨owe, D. L¨uke, J. Mainusch, O. Ma´nczak, T. Monteiro15 , J.S.T. Ng, S. Nickel16,
D. Notz, K. Ohrenberg, M. Roco, M. Rohde, J. Rold´an, U. Schneekloth, W. Schulz, F. Selonke, E. Stiliaris17,
B. Surrow, T. Voß, D. Westphal, G. Wolf, C. Youngman, J.F. Zhou
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, 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, Y. Zhang
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, B. Hubbard, W. Lockman, J.T. Rahn,
H.F.-W. Sadrozinski, A. Seiden
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, M.B. Crombie, D.M. Gingrich32 , G.F. Hartner, K.K. Joo,
G.M. Levman, J.F. Martin, R.S. Orr, 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. Gajewski, 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
7on leave of absence
8now at Institut f¨ur Hochenergiephysik, Univ. Heidelberg
9now also at University of Torino
10 Alfred P. Sloan Foundation Fellow
11 presently at Columbia Univ., supported by DAAD/HSPII-AUFE
12 now at Inst. of Computer Science, Jagellonian Univ., Cracow
13 now at Comma-Soft, Bonn
14 now at Univ. of Mainz
15 supported by DAAD and European Community Program PRAXIS XXI
16 now at Dr. Seidel Informationssysteme, Frankfurt/M.
17 supported by the European Community
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
We present an analysis of deep inelastic scattering (DIS) events with a large rapidity gap
between the outgoing proton system and the remaining hadronic final state. The general
properties of these events indicate that the underlying production mechanism is leading twist
and diffractive [1, 2]. Diffractive processes are generally understood to proceed through the
exchange of a colourless object with the quantum numbers of the vacuum, generically called
the pomeron [3]. The true nature of this exchanged “object” remains unclear.
The analysis of soft hadron-hadron collisions implies that pomeron-exchange can be described
by a pomeron-hadron coupling constant and a pomeron-propagator [4]. This led to the propo-
sition of Ingelman and Schlein [5] to treat the pomeron as a quasi-real particle which is emitted
by a hadron, described in terms of a parton density and characterised by a structure function
FIP
2which can be studied in deep inelastic scattering. The assumption of factorisation implies
that the pomeron structure is independent of the process of emission. Evidence for a partonic
structure of the pomeron was observed by the UA8 collaboration [6] and later by the HERA
experiments [2, 7, 8, 9]. These data also gave a first insight into the structure function of the
pomeron. The UA8 data show a predominantly hard structure, where on average the par-
tons carry a large fraction of the momentum of the pomeron. However, these data could not
distinguish between the quark and the gluon content of the pomeron.
This paper presents a study of the structure of the pomeron in DIS at HERA. We discuss
first the variables and cuts which are used to isolate diffractive DIS events. The observed
kinematic distributions of the data are compared to Monte Carlo models of diffractive processes
in a region where the diffractive contribution dominates. A measurement of the diffractive
structure function is presented, integrated over t, the square of the momentum transfer at
the proton vertex, as a function of xIP , the momentum fraction lost by the proton, of β,
the momentum fraction of the struck quark with respect to xIP , and of Q2. The data are
used to determine the xIP dependence at fixed βin order to test factorisation; extract the β
dependence of the diffractive structure function at fixed Q2; investigate the Q2dependence of
the diffractive structure function at fixed β, in order to test scale invariance; and, examine the
general dependence on xIP ,βand Q2by comparing the data with different models for diffractive
dissociation.
2 Experimental setup
2.1 HERA
This analysis is based on data collected with the ZEUS detector at the electron-proton collider
HERA. During 1993, HERA was operated at a proton energy, Ep, of 820 GeV and an electron
energy, Ee, of 26.7 GeV. HERA is designed to run with 210 bunches in each of the electron and
proton rings, with an interbunch spacing of 96 ns. For the 1993 data-taking 84 paired bunches
were filled for each beam and in addition 10 electron and 6 proton bunches were left unpaired
for background studies. Typical total currents were 10 mA for both beams.
1
2.2 The ZEUS detector
Details of the ZEUS detector can be found in [10, 11]. The following is hence restricted to a
short description of the components relevant to the present analysis.
Charged particles are tracked by the inner tracking detectors which operate in a magnetic field
of 1.43 T provided by a thin superconducting coil. Immediately surrounding the beampipe is
the vertex detector (VXD) which consists of 120 radial cells, each with 12 sense wires [12].
Surrounding the VXD is the cylindrical central tracking detector (CTD) which consists of 72
cylindrical drift chamber layers, organised into 9 superlayers [13] (5 axial and 4 small angle
stereo layers). In events with charged 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.
The high resolution uranium-scintillator calorimeter (CAL) [14, 15, 16] consists of three parts,
forward (FCAL) covering the pseudorapidity2region 4.3≥η≥1.1, barrel (BCAL) covering
the central region 1.1≥η≥ −0.75 and rear (RCAL) covering the backward region −0.75 ≥
η≥ −3.8. Holes of 20 ×20 cm2in the centre of FCAL and RCAL are required to accommodate
the HERA beam pipe. The resulting solid angle coverage is 99.7% of 4π. The calorimeter
is subdivided longitudinally into one electromagnetic (EMC) section and one (RCAL) or two
(FCAL and BCAL) hadronic (HAC) sections. The sections are subdivided into cells, each of
which is read out by two photomultiplier tubes. The CAL also provides a time resolution
of better than 1 ns for energy deposits greater than 4.5 GeV, which is used for background
rejection.
The C5 beam monitor, a small lead-scintillator counter assembly around the beam pipe located
at Z=−3.2 m, has been used to measure the timing and longitudinal structure of the proton
and electron bunches, and to reject events from upstream proton-gas interactions. The vetowall
detector, consisting of two layers of orthogonal scintillator strips on either side of an 87 cm thick
iron wall centred at Z=−7.3 m, was also used to tag upstream background events.
The luminosity is measured from the rate observed in the luminosity photon detector of hard
bremsstrahlung photons from the Bethe-Heitler process ep →e′pγ. The luminosity detector
[17] consists of a photon and an electron lead-scintillator calorimeter. 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 at 107 m distance along the electron
beam line. Electrons emitted at scattering angles less than 5 mrad and with energies 0.2Ee<
E′
e<0.9Eeare deflected by beam magnets and hit the electron calorimeter placed 35 m from
the interaction point.
2.3 Trigger conditions
Data were collected with a three level trigger [10]; details of the first (FLT) and second (SLT)
level decision for DIS events can be found in previous publications [18].
1The ZEUS coordinate system is defined as right handed with the Zaxis pointing in the proton beam
direction, hereafter referred to as forward, the Xaxis pointing towards the centre of HERA and the Yaxis
pointing upwards.
2The pseudorapidity ηis defined as −ln(tan θ
2), where the polar angle θis taken with respect to the proton
beam direction and, in this case, refers to the nominal interaction point.
2
The third level trigger (TLT) rejects beam-gas events using timing and cosmic-ray events by
a combination of timing and topology. Finally it passes the accepted events through a set of
filters in order to categorise the events. The category of DIS neutral current events is defined
by the requirement of an electron candidate in the RCAL or BCAL. A cut was performed on
δ≡ΣiEi(1 −cos θi)>20GeV −2Eγ,where Eiand θiare the energies and polar angles (in this
case, with respect to the nominal interaction point) of calorimeter cells and Eγis the energy
measured in the photon calorimeter of the luminosity monitor. For events fully contained in the
main detector δ≃2Ee= 53.4 GeV, whereas for low-Q2events the scattered electron escapes
through the rear beam pipe and δpeaks at low values.
3 Kinematic variables
The kinematic variables used to describe DIS events
e(k) + p(P)→e′(k′) + anything
are the following: the negative of the squared four-momentum transfer carried by the virtual
photon3:
Q2=−q2=−(k−k′)2;
the Bjorken variable:
x=Q2
2P·q;
the variable which describes the energy transfer to the hadronic final state:
y=P·q
P·k;
and the centre-of-mass energy Wof the virtual-photon proton (γ∗p) system, where:
W2= (q+P)2=Q2(1 −x)
x+M2
p
with Mpdenoting the proton mass.
These variables, only two of which are independent at fixed ep centre-of-mass energy squared
s= (k+P)2, can be reconstructed in a variety of ways using combinations of electron and
hadronic system energies and angles [19]. The variable y, calculated from the electron variables,
is given by:
ye= 1 −E′
e
Ee
1−cos θ′
e
2
where E′
e,θ′
edenote the energy and angle of the scattered electron. Alternatively, ycan be
estimated from the hadronic system, using the Jacquet-Blondel technique [20]:
yJB =PiEi(1 −cosθi)
2·Ee
3In the Q2range used for this analysis, ep interactions are described to sufficient accuracy by the exchange
of a virtual photon.
3
where Eiand θiare the energies and polar angles of calorimeter cells which are associated with
the hadronic system.
Studies of the kinematic variables have shown that for this analysis it is advantageous to use
the so-called double angle (DA) method, in which the angles of the scattered electron and the
hadron system are used to determine xand Q2. Quantities determined in this way will be
denoted by the subscript DA. Formulae to calculate Q2
DA,WDA,xDA and yDA are given in [19].
In the diffractive DIS process shown in Fig. 1:
e(k) + p(P)→e′(k′) + p′(P′) + X,
the hadronic system X(exclusive of the proton) and the scattered electron e′are detected in
the main detector. The proton remnant p′remains undetected. When the system Xis fully
contained its invariant mass, MX, can be determined from the calorimeter cell information as
follows [1]. Denoting the energy, momentum and polar angle of the final hadronic system as
EH,pHand θH, respectively; and ~pias the vector constructed from the energy Ei, polar angle
θiand azimuthal angle φiof cell i; then:
cos θH=Pipzi
|Pi~pi|(1)
p2
H=Q2
DA(1 −yDA)
sin2θH
EH=pHcos θH+ 2EeyDA
from which MXis determined by the definition MX=qE2
H−p2
H.
The squared four-momentum transfer at the proton vertex is given by:
t= (P−P′)2,
whose absolute magnitude is expected to be small compared to Q2+M2
Xin diffractive processes
for the kinematic region studied here. To describe diffractive deep inelastic scattering, in
addition to xand Q2, the following variables are used:
xIP =(P−P′)·q
P·q=M2
X+Q2−t
W2+Q2−M2
p
≃M2
X+Q2
W2+Q2,
β=Q2
2(P−P′)·q=x
xIP
=Q2
M2
X+Q2−t≃Q2
M2
X+Q2.
In models where diffraction is described by the exchange of a particle-like pomeron, xIP is the
momentum fraction of the pomeron in the proton and βis the momentum fraction of the struck
quark within the pomeron. For the structure of the pomeron in DIS, the variable βplays a role
analogous to that of Bjorken-xfor the structure of the proton.
4
4 Diffractive structure function
For unpolarised beams, the differential cross section for single diffractive dissociation can be
described in terms of the diffractive structure function, FD(4)
2(β, Q2, xIP , t):
d4σdiff
dβdQ2dxIP dt =2πα2
βQ4[(1 + (1 −y)2)FD(4)
2−y2FD(4)
L] (1 + δZ)(1 + δr)
where αis the electromagnetic coupling constant and the δidenote corrections due to Z0
exchange and due to radiative corrections which are small in the measured range. The contri-
bution of FLto the diffractive cross section is not known. If such a term were included, the F2
values would become larger at large yvalues (corresponding to small xIP values). The effect of
this uncertainty is considered in section 8.1. Note that the function FD(4)
2(β, Q2, xIP , t) can be
related to that of FD(4)
2(x, Q2, xIP , t). Integrating FD(4)
2over xIP and tone can directly compare
it to the inclusive proton structure function F2(x, Q2) [21].
In this analysis, an integral is performed over t, corresponding to the (undetected) momentum
transfer to the proton system. For this initial measurement we neglect the effect of FLand
the additional contributions noted above, yielding the following expression for FD(3)
2, where the
cross section is evaluated as a function of β, Q2and xIP :
d3σdiff
dβdQ2dxIP
=2πα2
βQ4(1 + (1 −y)2)FD(3)
2(β, Q2, xIP ),
following the procedure of [22], where the relation x=βxIP has been used.
5 Diffractive models and Monte Carlo simulation
Different approaches exist to model diffractive processes such as that depicted in Fig. 1. In
this paper we compare the data with the predictions of the factorisable models of Ingelman
and Schlein [5], Donnachie and Landshoff [23] and Capella et al. [24], as well as the non-
factorisable model of Nikolaev and Zakharov [25, 26]. We have earlier found that the Monte
Carlo implementations [27, 28] of the models described above provide reasonable descriptions of
the shape of the energy flow and of the observed fraction of events with one or more jets [2, 45].
In the model of Ingelman and Schlein [5] the proton emits a pomeron which is treated as a
(virtual) hadron whose structure is probed by the virtual photon. The pomeron is described by
a structure function FIP
2(β, Q2) which is independent of the process of emission. In this sense
factorisation is predicted in the model:
FD(4)
2(β, Q2, xIP , t) = fIP (xIP , t)·FIP
2(β, Q2).
The flux factor f(xIP , t), describing the flux of pomerons in the proton, can be extracted from
hadron-hadron scattering with an accuracy of approximately 30%, assuming universality of the
pomeron flux. A comparison of different flux factors can be found in [29].
5
For this analysis we used the POMPYT Monte Carlo implementation [27] of the Ingelman-
Schlein model. Two samples of events were generated, corresponding to a hard quarkonic
structure function,
FIP
2(β, Q2) = X
qi
e2
iβfq(β , Q2) = 5
3·β(1 −β),
and to a soft quarkonic structure function,
FIP
2(β, Q2) = X
qi
e2
iβfq(β , Q2) = 5
3·(1 −β)5.
The two samples are denoted by “Hard Pomeron” (HP) and “Soft Pomeron” (SP) respectively.
The normalisation constant 5/3 is based on the assumption that the momentum sum rule
(MSR) is satisfied for two light quark flavours (u,d). If s quarks would have to be included the
normalisation factor would be reduced from 5/3 to 4/3 [31]. The Q2dependence is expected
to be weak and is neglected. The Ingelman-Schlein form of the flux is parametrised by a fit to
UA4 data [27, 30]:
fIP (xIP , t) = 1
2
1
2.3·xIP
·(6.38 e8t+ 0.424 e3t).
In the Donnachie-Landshoff (DL) model diffraction in DIS is described through pomeron ex-
change between the virtual photon and the proton, with the pomeron coupling predominantly
to quarks [32]. The authors calculate the cross section in the framework of Regge theory. The
result can be interpreted in terms of a pomeron structure function with the resulting βde-
pendence similar to HP but with a normalisation which is calculated to be approximately a
factor of 6.2 smaller. The authors also predict an additional soft contribution to the pomeron
structure function which is expected to become important only for β < 0.1. The flux factor,
fIP (xIP , t) = 9β2
0
4π2F1(t)2xIP
1−2α(t),
is related to the elastic form factor of the proton, F1(t) = 4M2−2.8t
4M2−t(1
1−t/0.7)2, and to the pomeron-
quark coupling, β0≃1.8 GeV−1, extracted from hadron-hadron data. The xIP term represents
the pomeron propagator with the pomeron trajectory, α(t) = 1.085 + 0.25 ·t. Therefore the xIP
dependence of FD(4)
2is controlled by the pomeron trajectory (FD(4)
2∝xIP
1−2α(t)). Integrated
over t, the predicted effective xIP -dependence at fixed βis approximately (1/xIP )1.09 in the
measured range of xIP .
In a recent publication [33] Goulianos proposed to use a modified flux factor, which is renor-
malised to unity for fixed centre-of-mass energy W. Also a modification of the t-dependence
and the pomeron trajectory according to recent CDF data [34] is proposed:
fIP (xIP , t) = 1
N0
·0.73 ·e4.6t·xIP
1−2α(t),
where α(t) = 1.115 + 0.26 ·tand N0is a normalisation factor which can be approximated by
(W2
400 )0.23. Integrated over t, the effective xIP -dependence of this flux factor is approximately
(1/xIP )0.93.
Capella et al. calculate the diffractive structure function in the framework of conventional
Regge theory [24]. Using Regge factorisation, they relate the pomeron structure function to
6
the deuteron structure function using parameters which are determined from soft hadronic
diffraction data with an appropriate change for the disappearance of screening corrections with
increasing Q2. For Q2= 10 GeV2they obtain:
FIP
2(β, Q2) = a·β0.6·(1 −β)0.6+ 0.015 ·β−0.22 ·(1 −β)4.6,
where ais estimated to be in the range 0.04 to 0.06. We chose a= 0.06 for comparison with
the data.
In the model of Nikolaev and Zakharov diffractive dissociation is described as a fluctuation
of the photon into a q¯qor q¯qg Fock state [25, 26]. The interaction with the proton proceeds
via the exchange of a BFKL [35] type pomeron, starting in lowest-order from the exchange of
a Low-Nussinov [4] pomeron which corresponds to two gluons in a colour-singlet state. The
result for the cross section can be approximated by a two-component structure function of the
pomeron, each component having its own flux factor. This corresponds to factorisation breaking
which is caused by BFKL evolution effects. The result for the “hard” component reflects the
case where the photon fluctuates into a q¯qpair and leads to a βdependence similar to that of
the HP and the DL models with a normalisation closer to the latter (but with very different
predictions for the contribution of heavy flavours). The “soft” contribution, which reflects the
case where the photon fluctuates into q¯qg, is assumed to be proportional to (1 −β)2and the
normalisation is fixed by the triple pomeron coupling. The relative size of these contributions
and the overall normalisation are predicted with an uncertainty of about 30%. Q2evolution
effects have been calculated for this model, and have been found to be rather weak for β > 0.1.
We used a Monte Carlo implementation of this model [28] which is based on the cross section
given in [25] and is interfaced to the Lund fragmentation scheme. We refer to this model as
NZ. In this implementation the mass spectrum contains both components but the q¯qg states
are fragmented into hadrons as if they were a q¯qsystem with the same MX.
Both Monte Carlo generators have limitations in the generation of small masses MX
(MX<1.7 GeV for NZ and MX′<5 GeV for POMPYT, where MX′includes the final
state electron). We exclude these regions for the measurement of the diffractive structure func-
tion by an upper cut on β. To study acceptance and migration effects for these small masses
we have generated an additional sample of exclusively produced ρ0’s [36].
The cuts given below to select diffractive events limit the acceptance for double-dissociative
events, where the proton also dissociates. The PYTHIA Monte Carlo [37] has been used to
study the detector response for the nucleon system MNin double dissociation γp events. The
nucleon system mass spectrum and the fraction of double-dissociative to single-dissociative
events was taken from hadron data.
Non-diffractive DIS processes were generated using the HERACLES 4.4 program [38] which
incorporates first order electroweak corrections. The Monte Carlo generator LEPTO 6.1 [39],
interfaced to HERACLES via the program DJANGO 6.0 [40], was used to simulate QCD
cascades and fragmentation. The parton cascade was modelled with the colour-dipole model
including the boson-gluon fusion process by the ARIADNE 4.03 [41] (CDMBGF) program.
The fragmentation into hadrons was performed with the Lund string hadronisation model [42]
as implemented in JETSET 7.2 [43]. For the proton parton densities the MRSD′
−set [44] was
chosen, which adequately represents our structure function results [18]. In previous studies [45]
it was shown that this model gives a good description of the energy flow between the current
jet and the remnant jet.
7
Combined sets of the Monte Carlo generators, described above, were used to simulate the
expected final states in our DIS sample: the first one to describe non-diffractive DIS processes
and the second one to model diffractive events.
QED radiative processes were not simulated for diffractive events; however, with the selection
cuts of section 6, radiative corrections to the DIS cross sections are below 10% [18] and are
expected to be of the same order for diffractive processes. All Monte Carlo events were passed
through the standard ZEUS detector and trigger simulations and the event reconstruction
package [10]. According to Monte Carlo studies, the efficiency of the trigger and of the final
selection cuts is the same for diffractive and non-diffractive DIS events. The overall trigger
acceptance is above 95%, independent of xand Q2in the range of interest for this analysis.
6 Event selection
The selection of DIS events was similar to that described in our earlier publications [1, 18].
The following offline cuts were applied:
•E′
e≥5 GeV, to ensure good electron identification;
•Q2
DA ≥8 GeV2;
•yJB ≥0.04, to give sufficient accuracy for DA reconstruction;
•δ≥35 GeV (with respect to the measured interaction point), to reduce radiative correc-
tions and photoproduction background;
•ye≤0.95, to reduce photoproduction background;
•the impact point of the electron on the face of the RCAL was required to lie outside a
square of side 32 cm centred on the beam axis (box cut), to ensure that the electron
shower was fully contained within the calorimater and its position could be reconstructed
with sufficient accuracy;
•a vertex, as reconstructed from VXD+CTD tracks, was required with |Zvtx| ≤ 40 cm.
In addition algorithms were used to reject cosmic-ray induced events and QED Compton events.
A total of 31k events was selected in this way corresponding to an integrated luminosity of
0.54 pb−1. Using the number of events produced by unpaired electron and proton bunches,
the contamination from beam-gas background and from cosmic-ray muons were estimated to
be less than 1% each. The background in the total DIS sample due to photoproduction was
estimated to be (2.5±1)% from a fit to the shape of the δdistribution before the above cut
on δwas applied [18].
7 Properties of diffractive events
In the following section, the observed data distributions are compared to distributions from
various Monte Carlo models. We discuss the criteria used to select the diffractive events, the
methods used to determine their relative contribution and the observed inclusive distributions
of the diffractive sample.
8
7.1 Selection criterion
A large fraction of diffractive processes at HERA exhibit a rapidity gap in the main detector
between the scattered proton system and the hadronic activity generated by the dissociation of
the photon, while large rapidity gaps are suppressed in non-diffractive DIS events. Therefore
the presence of a rapidity gap has been used as a selection criterion [1, 2]. An improved criterion
to separate diffractive from non-diffractive events is presented here, which uses the direction of
the total hadronic energy flow of the event, determined from all the detected particles in the
final state.
We define the maximum pseudorapidity of an event, ηmax, as the maximum value of the pseu-
dorapidity of all calorimeter condensates with energy greater than 400 MeV or tracks with
momentum of at least 400 MeV/c. A condensate is a contiguous energy deposit above a mini-
mum energy threshold. We studied the effect of varying the minimum energy Emin = 400 MeV
and found that above Emin = 200 MeV the ηmax distribution does not change significantly. We
chose Emin = 400 MeV as a conservative compromise between accepting diffractive events and
rejecting noise.
For values of ηmax up to 1–1.5 the non-diffractive DIS background is a negligible background
to the diffractive sample, which increases for values of ηmax above 1.5–2. In previous ZEUS
publications [1, 2] diffractive events were selected by ηmax <1.5. This cut selects a rather pure
sample of diffractive events, useful to establish a signal but it limits acceptance for events with
large MX.
The ηmax-cut is dependent on the most forward condensate but does not use the information
from the full energy flow. Larger acceptance can be achieved by including more information
from the hadronic energy flow. Since in diffractive scattering the proton remains intact or, in
the case of double-dissociative events, dissociates independently from the photon, the hadronic
activity in the detector in general will not follow the proton direction. The hadronic angle
θHdefined in eq. (1) represents the average direction of the hadronic activity. Non-diffractive
DIS events have mostly cosθHnear 1 because of the colour flow between the struck quark and
the outgoing proton system, while a substantial fraction of diffractive events is found at cosθH
less than 1. Figures 2a, b show scatter plots of ηmax versus θHfor the diffractive and non-
diffractive DIS Monte Carlo samples. A cut cosθH<0.75 combined with ηmax <2.5 allows a
larger acceptance of diffractive events than the ηmax <1.5 cut, at the price of a slightly higher
background which has to be subtracted. We call this combined cut, used to select the diffractive
sample, the ηmax-θHcut.
Note that the term “diffractive” is used to indicate single diffractive dissociation of the photon
together with that fraction of events where both the photon and the proton dissociate and the
proton system is not detected. From proton-proton measurements of the ratio of double- to
single-dissociative events, we estimate this ratio to be approximately 0.76 in the measured W
range. As shown in Fig. 3, we find that excited proton states with mass MN<
∼4 GeV would
pass the diffractive selection cuts. Beyond this range the energy deposition in the forward
calorimeter is typically above 400 MeV. The overall acceptance for double-dissociative events
is 23%. We therefore have an estimated double-dissociative contribution of ≃(15±10)% which
is expected to be independent of βand Q2and not vary significantly with xIP . This result
assumes factorisation in Regge theory, i.e. that the nucleon mass spectrum and the ratio of
double- to single-dissociative events is similar to that measured in proton-proton collisions at
similar energies.
9
7.2 Estimation of the diffractive component
In this section, only the shapes of the distributions and not the absolute normalisations of
the diffractive models are considered. The ηmax and θHdistributions are used to determine
the fraction of diffractive events passing the DIS selection criteria. A linear combination of
diffractive DIS (NZ or POMPYT) and non-diffractive DIS Monte Carlo events are fitted to the
data.
The ηmax and θHdistributions were first fitted separately to check consistency between the
results and then together to obtain a global result. Figure 4 shows the fits to these distributions.
The part of each distribution that corresponds to the forward region of the detector (high values
of ηmax and low values of θH) was put into one single bin to reduce problems associated with a
detailed description of the hadronisation of the proton remnant. For each distribution a variety
of different binnings was tried and the results were found to be stable.
Model ηmax θHηmax+θH
% of diffr. χ2
dof % of diffr. χ2
dof % of diffr. χ2
dof
NZ 14.2 ±2.5 4.7 15.3 ±2.5 4.0 14.8 ±3.0 4.3
SP 35.9 ±7.0 10.5 15.4 ±2.6 5.0 33.0 ±6.0 24
HP 10.3 ±2.0 2.2 10.8 ±2.0 4.1 10.5 ±2.7 3.0
HP+SP 15.6 ±1.3 3.7 13.4 ±1.3 5.4 14.6 ±1.4 4.6
Table 1: Fraction of diffractive events and χ2per degree of freedom (χ2
dof ) values obtained from fits
using NZ, SP, HP or HP+SP.
The results are summarised in Table 1, where the default parameters have been used for the
models. Since neither NZ nor POMPYT describes diffractive vector meson production a simu-
lation of exclusive ρoproduction was added in order to incorporate the effect of low-mass states.
This contribution was estimated to be typically ∼7% of the diffractive sample from a fit to the
observed MXspectrum in different Q2intervals. For each model, a reduction of χ2
dof by 1–2
was found when ρoproduction was included, with consistent results obtained for the fraction
of diffractive events.
The SP model was also extensively tested. In fits to the ηmax and θHdistributions, SP does
not reproduce the shapes correctly. Its very soft βdistribution tends to populate large ηmax
bins and, consequently, the fits do not describe the data. The inconsistency of the results
obtained by the fits to the ηmax and the θHdistributions shown in Table 1 indicate that a
pure soft βdistribution cannot describe the data. For these reasons the SP model alone is not
considered any further. Results obtained with the combined HP+SP model, discussed in the
following section, are also given in Table 1. The fractions obtained with the HP+SP model are
similar to those determined using the NZ model.
It is possible to explain the different predictions from NZ and HP models in terms of the
βdistribution used in these models: they both contain the hard component responsible for low
ηmax (high θH) events but the NZ model also contains a soft contribution which is predicted
to be ∼40% of the diffractive cross section. Most of the events originating from this soft
component are hidden under the large background from normal DIS events and so are not
accessible to the present study.
10
7.3 Inclusive distributions
In the following, the shapes of the observed distributions in W,Q2,x,MX,xIP and βare
considered. The relative normalisation of the models is obtained from the above fits. It should
be noted that the normalisation of the non-diffractive component, which is relevant for the
background subtraction, is independent of the diffractive model used to fit the data to within
5%.
In order to confine the analysis to regions of acceptance above ≃80%, the following (MX, y)
intervals were considered:
MX<10 GeV for 0.08 < y < 0.2
MX<16 GeV for 0.2< y < 0.3
MX<20 GeV for 0.3< y < 0.8
According to Monte Carlo studies, the ηmax-θHcut reduces the non-diffractive DIS component
by ≃60% and the diffractive component by ≃20%, giving a contamination from non-diffractive
DIS of less than 15% in these (MX,y) intervals. This background is subtracted from the data
before comparison with the diffractive Monte Carlo predictions.
Figure 5 shows the x,Q2, W, xIP ,MXand βdistributions after applying the ηmax-θHcut,
requiring the data to be in the accepted ranges of (MX,y) and subtracting the DIS back-
ground indicated in the figure. The errors on the data points are calculated by summing in
quadrature the statistical error (which is the dominant error) and 50% of the total subtracted
DIS background (which is taken as a conservative estimate of the uncertainty due to the DIS
background). In addition, the predictions from the two diffractive models (NZ and HP) are
shown.
In general, both models describe the data. Differences are observed in the MXand βdistribu-
tions, where the HP model underestimates the observed number of events at low βvalues and
does not reproduce the observed MXdistribution at large MX. The NZ model, incorporating
a soft component, describes the observed βand MXdistributions.
A pure “hard” βdistribution cannot account for the data, therefore, the observed βspectrum
was fitted as a sum of a “hard + soft” contribution from the POMPYT Monte Carlo. This
resulted in a contribution of ≃60% and ≃40% from HP and SP, respectively. This HP+SP
model is also shown in Fig. 5. Comparison with the data indicates that such a model also
describes the observed βbehaviour.
To investigate the βdistribution in more detail, each (MX, y) interval was divided into two Q2
bins:
Q2= 8 −20,20 −160 GeV2
The results, together with the predictions from the diffractive models are shown in Fig. 6. In
general, the Monte Carlo models reproduce the shape of the data reasonably well. However,
in the high-yand low-Q2intervals where the mass extends to larger values (Fig. 6a and c),
the soft contribution is important. The NZ model describes the data best in this region. The
HP+SP model reasonably describes the data and gives an improved description compared to
the HP model in each (MX, y) interval.
11
Using the NZ model, the combined fit to the ηmax and θHdistributions was performed in bins of
Wand xrespectively, separately for the two Q2intervals indicated above, to extract the fraction
of diffractive events as a function of these variables. Figure 7 shows the diffractive fraction as a
function of Wand xfor different values of Q2. The results extracted using the HP+SP model
agree within statistical errors. The results extracted using the HP model give a normalisation
which is ≃30% lower, but with the same dependence on x,Wand Q2. The fits are mainly
sensitive to the hard component: a large uncertainty on the diffractive contribution to the DIS
sample comes from the soft part in the pomeron structure function, which is suppressed by the
applied cuts, especially at small values of W. In all cases, no strong dependence of this ratio is
observed as a function of x,Wor Q2.
8 Measurement of the diffractive structure function
As described in section 4, the differential cross section can be expressed in terms of the diffractive
structure function FD(3)
2as a function of β,xIP and Q2. In this section, we discuss the resolution
of the measured quantities and describe the kinematic region chosen. We finally discuss the
systematic errors and present the results of the measurement of FD(3)
2.
8.1 Extraction of FD(3)
2
According to Monte Carlo studies (see section 5), the resolution of Q2is 25%, independent
of Q2. The resolution of xvaries smoothly with xfrom 20% at x= 10−2to 50% at 10−3,
almost independent of Q2. The resolution of MX, reconstructed with the method described in
section 3, is approximately 27%, independent of MX. The MXreconstruction is affected by
energy loss in inactive material in front of the calorimeter and the position determination of
hadrons. In order to reduce migrations at small masses, the cell energy thresholds for isolated
cells were increased. Monte Carlo studies show that, except for very small masses (<3 GeV)
where calorimeter noise becomes important, MXis systematically shifted by 10% to smaller
values, independent of yand Q2. In order to compensate for this shift, a correction factor of
1.10 was applied to the measured MXvalues for the determination of the diffractive structure
function. The resolution of xIP is approximately 25%. The resolution of βvaries smoothly with
βfrom 40% at β= 0.1 to 20% at β= 0.8.
Below Q2of 8 GeV2, the event acceptance drops below 50% due to the box cut requirement.
The statistics of the 1993 data allow four ranges in Q2to be selected above this lower limit.
The migration of events is large at small values of x: we therefore chose bins where the central
x-value is above 4 ·10−4. The acceptance of the diffractive component increases as a function
of y: we therefore select only bins with y > 0.08. The overall acceptance due to the DIS and
diffractive cuts in the selected bins given in Table 2 is always greater than 50% and typically
≃80%. The MXresolution determines the chosen bin size in the variables βand xIP . The
purity, defined as the fraction of simulated events generated in a bin and measured in the same
bin, is always greater than 25% and typically ≃40% in each of the selected bins.
In order to control the influence of photoproduction background, radiative corrections and FL
contributions, we restrict our analysis to y < 0.5. As a consequence the minimum scattered
electron energy requirement is raised to 10 GeV. We checked that our sensitivity to FLis smaller
12
than the quoted errors in all bins. Furthermore, the region β < 0.8 is selected to exclude the
region of low masses where vector meson production is dominant.
The level of photoproduction background is estimated in bins of xIP and Q2by fits to the δ
distributions (see [18] for details). Since it is typically ≃1% and always below 4% we do not
correct for this background.
We select bins with xIP <0.01 and β > 0.1 where the non-diffractive component can be safely
estimated. In each of the bins the number of events is then evaluated by subtraction of the
estimated number of DIS background events, based on the ARIADNE Monte Carlo program
with the normalisation described in section 6. The contribution of the DIS background is given
in Table 2.
To unfold the effects of acceptance and event migration we used the NZ Monte Carlo event
sample, which gives a good description of our data. For this initial study we used a one-step
matrix unfolding procedure and applied a bin-centring correction for the quoted FD(3)
2values.
8.2 Systematic errors
Several systematic checks were performed to estimate the uncertainties due to the selection
cuts, background estimate and the unfolding. Systematic errors due to the DIS event selection
were evaluated in the following way (see [18] for a detailed discussion):
•different algorithms were used to identify the scattered electron which differ in purity and
efficiency. The changes to FD(3)
2were below 10%;
•the cut on E′
ewas decreased from 10 to 5 GeV to study the effect of a possible mismatch
of the shower profiles of data and Monte Carlo at small energies. The change of FD(3)
2
was less than 5% in each bin;
•the box-cut was changed by 2 cm from the nominal values, to study the effects of electron
position reconstruction at small angles. This resulted in changes which were always less
than 15%;
•the δ-cut was raised from 35 GeV to 40 GeV, to study the effect of radiative corrections,
which were not included in the simulations. This resulted in a general shift of ≃10%
towards smaller FD(3)
2values;
•the yJB-cut was changed from 0.04 to 0.02 and to 0.06. This affected the region of large
xIP where FD(3)
2changes by about 10%.
Systematic errors due to the diffractive event selection were evaluated in the following way:
•the effect of a possible mismatch between the hadronic energy scale in the Monte Carlo
and the data was investigated by shifting the hadron energy scale by 7% in the Monte
Carlo simulation. The use of the DA variables resulted in changes on FD(3)
2which were
always smaller than 2%;
13
•the fraction of low-mass events was reduced by 50%. Due to migrations from β > 0.8,
this change influences the small Q2, high βbin, where the values were shifted upwards
by ≃10%;
•the HP model was used instead of the NZ simulation for unfolding the data. Some effect
was seen in the small β-region, where the pomeron structure functions differ. The changes
to FD(3)
2were typically ≃10%;
•as a systematic check for the estimate of the DIS background the ηmax-cut was reduced
from 2.5 to 2.0 resulting in changes of up to 20% in the highest xIP bins. The ηmax-cut
was also increased from 2.5 to 3.0 resulting in changes of up to 10%;
•similarly, the θHcut was removed, yielding changes below 5%;
•the cells with η > 2.5 were removed to check the dependence on the double-dissociative
contribution, resulting in changes which were up to 5%.
Overall most of these checks yielded results which agree with the standard method within
statistical errors. The differences of the DIS and diffractive systematic checks compared to the
standard method were combined in quadrature to yield the quoted systematic errors.
8.3 Results
Table 2 summarises the results for FD(3)
2, for the 0.54 pb−1(±3.5%) integrated luminosity. The
statistical errors include statistical uncertainties from the Monte Carlo models used for the
unfolding.
The FD(3)
2results are displayed in Fig. 8. The data are observed to fall rapidly as a function of
increasing xIP . In the measured bins the dependence of FD(3)
2on Q2at fixed βvalues is weak.
We have investigated whether the xIP -dependence of FD(3)
2is the same in each β, Q2interval,
as expected if factorisation holds. For this purpose we performed fits of the form:
bi·(1/xIP )a
where the normalisation constants biwere allowed to differ, while the exponent was the same
for each β, Q2interval. The result of the fit was:
a= 1.30 ±0.08 (stat)+ 0.08
−0.14 (sys).
The systematic errors are calculated by re-fitting the FD(3)
2values according to the variations
listed in section 8.2 and combining the positive or negative deviations from the central value
of ain quadrature. The overall statistical χ2values of these fits are in the range 8.2–14.0
for 23 degrees of freedom depending on the systematic check. The χ2values for each of the
β,Q2intervals are in the range 0.1–1.1 per degree of freedom. Within the present accuracy,
the data are therefore consistent with the assumption of factorisation in the measured kine-
matic range. The value of ais consistent with recent results from the H1 Collaboration of
a= 1.19 ±0.06 ±0.07 [9].
14
The observed dependence on xIP is steeper but still compatible with a Donnachie-Landshoff
type of flux factor which yields a≃1.09 and which is based on a phenomenological de-
scription of “soft hadronic” diffractive interactions. The modified flux of Goulianos yields
a (1/xIP )adependence with a≃0.93, a value which is disfavoured by the data.
In order to illustrate the βand Q2dependence of FD(3)
2(β, Q2, xIP ), we integrated FD(3)
2over the
measured range of xIP , 6.3·10−4< xIP <10−2, using the fitted xIP dependence. The resulting
values of ˜
FD
2(β, Q2) are shown in Fig. 9 as a function of βand Q2. It should be noted that these
results assume that a universal xIP dependence holds in all regions of βand Q2. In particular,
there is a contribution due to regions of xIP which are not measured and where the hypothesis
of a universal xIP dependence has not been tested experimentally.
The ˜
FD
2(β, Q2) values as a function of βfor fixed Q2are consistent with a flat βdependence
as expected from the aligned jet model [46] and the model of Buchm¨uller [47]. As a function
of Q2for fixed β, the ˜
FD
2(β, Q2) values are approximately independent of Q2for all βvalues,
which is consistent with a picture where the underlying interaction is the scattering of a virtual
photon with point-like quarks within the pomeron.
As a next step we determined a compact parametrisation for the FD(3)
2results, which is also
shown in Fig. 8 and Fig. 9, where the following form was adopted:
FD(3)
2= (1/xIP )a·b·(β(1 −β) + c
2·(1 −β)2),
with a= 1.30. This parametrisation assumes factorisation and no Q2-dependence. The soft
contribution to the structure function was considered by the inclusion of the (1 −β)2term.
The multiplicative factor of c
2was chosen such that the integral over βof the soft contribution
is equal to that of the hard contribution when c= 1. The power of 2 was adopted from the NZ
model; this assumption cannot be tested with the current measurement. The results of the fit
were:
b= 0.018 ±0.001 (stat)±0.005 (sys),
c= 0.57 ±0.12 (stat)±0.22 (sys),
with a statistical χ2in the range 15–23 for 33 degrees of freedom depending on the systematic
check. A fit without the (1 −β)2soft contribution resulted in χ2values in the range 56–81 for
34 degrees of freedom. This increased χ2value indicates that a soft component is required in
the pomeron structure function.
We now consider the cross section predictions of the models discussed in section 5. The FD(3)
2
results are displayed in Fig. 10 where the data are compared with the predictions of several
models of single-diffractive dissociation for which the momentum sum rule for quarks is not
satisfied. The estimated 15% fraction of double-dissociative events has been subtracted in order
to compare with these models.
At high β-values the predictions of Nikolaev-Zakharov, Donnachie-Landshoff and Capella et
al. underestimate the observed values slightly, but are generally in reasonable agreement. At
smaller β-values, the Donnachie-Landshoff parametrisation, which includes only a hard com-
ponent of the pomeron structure function, underestimates the observed FD(3)
2. The Capella
et al. and Nikolaev-Zakharov predictions, which also include a soft component, are able to
give a fair description at smaller β-values. The factorisation-breaking effects in the model
15
of Nikolaev-Zakharov, which occur at small βvalues, are too small to be observable in this
analysis.
In Fig. 11 the data are compared with a model for which the momentum sum rule for the
pomeron structure function is assumed for the light quark flavours (u,d) and the βdependence
is taken from the parametrisation, discussed above. Adopting the Donnachie-Landshoff flux
factor, the observed FD(3)
2is about a factor three to four below the expectation if the momentum
sum rule is assumed to be fulfilled only by quarks. An uncertainty arises from the choice of
the pomeron flux factor: if the Ingelman-Schlein form for the flux factor is adopted then the
prediction is reduced by approximately 30%. Even if the Goulianos prescription for the flux
is adopted, the observed FD(3)
2results are always below the predictions. These comparisons
indicate that in an Ingelman-Schlein type model the quarks alone inside the pomeron do not
satisfy the momentum sum rule.
9 Conclusions
The properties of diffractive DIS events with Q2>8 GeV2, selected by a large rapidity gap
requirement, have been investigated. Different Monte Carlo models, such as the POMPYT
model, with a soft plus a hard pomeron structure function, or the Nikolaev-Zakharov model
describe the shape of the observed kinematic distributions. Using these models, reliable ac-
ceptance corrections for the measured data can be obtained and corrected cross sections can
be determined. The relative contribution of diffractive events to the total DIS cross section is
found to have no strong dependence on x,Wor Q2.
The diffractive proton structure function FD(3)
2is presented, integrated over t, the square of the
momentum transfer at the proton vertex, as a function of xIP , the momentum fraction lost by
the proton, of β, the momentum fraction of the struck quark with respect to xIP , and of Q2. The
structure function is measured in the kinematic range of 0.08 < y < 0.5, 8 < Q2<100 GeV2,
6.3·10−4< xIP <10−2and 0.1< β < 0.8. Within the experimental errors, the measurement is
consistent with models where diffraction is described by the exchange of a particle-like pomeron
where the structure function factorises into a pomeron flux factor, which depends on xIP and
a pomeron structure function, which is independent of xIP . The diffractive structure function
is also well-described by the Nikolaev-Zakharov model, which does not require the concept of
a particle-like pomeron, in terms of overall normalisation and dependence on the kinematic
variables, xIP ,βand Q2. The xIP dependence is consistent with the form (1/xIP )awhere
a= 1.30 ±0.08 (stat)+ 0.08
−0.14 (sys) in all bins of βand Q2. The value of ais slightly higher but
compatible with that obtained from hadron-hadron interactions and in agreement with recent
results from the H1 collaboration. In the measured Q2range, the pomeron structure function
is approximately independent of Q2at fixed βconsistent with an underlying interaction where
the virtual photon scatters off point-like quarks within the pomeron. The β-dependence of the
pomeron structure function requires both a hard and a soft component. In an Ingelman-Schlein
type model, where commonly used pomeron flux factor normalisations are assumed, it is found
that the quarks within the pomeron do not saturate the momentum sum rule.
16
Acknowledgements
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.
The design, construction and installation of the ZEUS detector have been made possible by the
ingenuity and dedicated effort of many people from inside DESY and from the home institutes
who are not listed as authors. Their contributions are acknowledged with great appreciation.
The strong support and encouragement of the DESY Directorate has been invaluable.
We would like to thank A. Donnachie, L. Frankfurt, G. Ingelman and N. Nikolaev for valuable
discussions.
References
[1] ZEUS Collab., M. Derrick et al., Phys. Lett. B315 (1993) 481.
[2] ZEUS Collab., M. Derrick et al., Phys. Lett. B332 (1994) 228.
[3] K. Goulianos, Nucl. Phys. B (Proc. Suppl.) 12 (1990) 110.
[4] F. E. Low, Phys. Rev. D12 (1975) 163;
S. Nussinov, Phys. Rev. Lett. 34 (1975) 1286 and Phys. Rev. D14 (1976) 246.
[5] G. Ingelman and P. Schlein, Phys. Lett. 152B (1985) 256.
[6] UA8 Collab., R.Bonino et al., Phys. Lett. B211 (1988) 239;
UA8 Collab., A.Brandt et al., Phys. Lett. B297 (1992) 417.
[7] ZEUS Collab., M. Derrick et al., Phys. Lett. B346 (1995) 399.
[8] H1 Collab., T. Ahmed et al., Phys. Lett. B435 (1995) 3.
[9] H1 Collab., T. Ahmed et al., DESY 95-036.
[10] The ZEUS Detector, Status Report 1993, DESY 1993.
[11] ZEUS Collab., M. Derrick et al., Phys. Lett. B293 (1992) 465.
[12] C. Alvisi et al., Nucl. Instrum. Methods A305 (1991) 30.
[13] C.B. Brooks et al., Nucl. Instrum. Methods A283 (1989) 477;
N. Harnew et al., ibid. A279 (1989) 290;
B. Foster et al., ibid. A338 (1994) 254.
[14] A. Andresen et al., Nucl. Instrum. Methods A309 (1991) 101.
[15] A. Bernstein et al., Nucl. Instrum. Methods A336 (1993) 23.
[16] A. Caldwell et al., Nucl. Instrum. Methods A321 (1992) 356.
17
[17] J. Andruszk´ow et al., DESY 92-066.
[18] ZEUS Collab., M. Derrick et al., Z. Phys. C65 (1995) 379.
[19] S. Bentvelsen, J. Engelen and P. Kooijman, Proceedings of the Workshop on Physics at
HERA, DESY Vol. 1 (1992) 23.
[20] F. Jacquet and A. Blondel, Proceedings of the Study for an ep facility for Europe, DESY
79/48 (1979) 391.
[21] W. Buchm¨uller and A. Hebecker, DESY 95-077.
[22] G. Ingelman and K. Jansen-Prytz, Proceedings of the Workshop on Physics at HERA,
DESY Vol. 1 (1992) 233;
G. Ingelman and K. Jansen-Prytz, Z. Phys. C58 (1993) 285.
[23] A. Donnachie and P.V. Landshoff, Nucl. Phys. B244 (1984) 322.
[24] A. Capella et al., Phys. Lett. B343 (1995) 403.
[25] N.N. Nikolaev and B.G. Zakharov, Z. Phys. C53 (1992) 331.
[26] M. Genovese, N.N. Nikolaev and B.G. Zakharov, KFA-IKP(Th)-1994-37 and CERN–
TH.13/95.
[27] POMPYT 1.0: P. Bruni and G. Ingelman (unpublished);
DESY 93-187; Proceedings of the Europhysics Conference on HEP, Marseille 1993, 595.
[28] A. Solano, Ph.D. Thesis, University of Torino 1993 (unpublished);
A. Solano, Proceedings of the International Conference on Elastic and Diffractive Scatter-
ing, Nucl. Phys. B (Proc. Suppl.) 25 (1992) 274;
P. Bruni et al., Proceedings of the Workshop on Physics at HERA, DESY Vol. 1 (1991) 363.
[29] K. Prytz, Z. Phys. C64 (1994) 79.
[30] UA4 Collab., M. Bozzo et al., Phys. Lett. 136B (1984) 217.
[31] T. Gehrmann and W.J. Stirling, Durham preprint DTP/95/26.
[32] A. Donnachie and P.V. Landshoff, Phys. Lett. B191 (1987) 309;
A. Donnachie and P.V. Landshoff, Nucl. Phys. B303 (1988) 634.
[33] K. Goulianos, Rockefeller University preprint RU 95/E-06.
[34] CDF Collab., F. Abe et al., Phys. Rev. D50 (1994) 5518.
[35] L.N. Lipatov, Sov. J. Nucl. Phys. 23 (1976) 338;
Y.Y. Balitsky and L. N. Lipatov, Sov. J. Nucl. Phys. 28 (1978) 822;
E.A. Kuraev, L. N. Lipatov and V. S. Fadin, Sov. Phys. JETP 45 (1977) 199.
[36] ZEUS Collab., M. Derrick et al., in preparation.
[37] PYTHIA 5.6: H.-U. Bengtsson and T. Sj¨ostrand, Comp. Phys. Comm. 46 (1987) 43.
18
[38] A. Kwiatkowski, H. Spiesberger and H.-J. M¨ohring, Proceedings of the Workshop on
Physics at HERA, DESY Vol. 3 (1992) 1294.
[39] G. Ingelman, Proceedings of the Workshop on Physics at HERA, DESY Vol. 3 (1992) 1366.
[40] K. Charchu la, G. Schuler and H. Spiesberger, Comp. Phys. Comm. 81 (1994) 381.
[41] L. L¨onnblad, Comp. Phys. Comm. 71 (1992) 15.
[42] B. Andersson et al., Phys. Rep. 97 (1983) 31.
[43] T. Sj¨ostrand, Comp. Phys. Comm. 39 (1986) 347;
T. Sj¨ostrand and M. Bengtsson, Comp. Phys. Comm. 43 (1987) 367.
[44] A.D. Martin, W.J. Stirling and R.G. Roberts, Phys. Lett. B306 (1993) 145.
[45] ZEUS Collab., M. Derrick et al., Phys. Lett. B338 (1994) 483.
[46] J.D. Bjorken and J. Kogut, Phys. Rev. D8 (1973) 1341.
[47] W. Buchm¨uller, Phys. Lett. B335 (1994) 479;
W. Buchm¨uller, DESY 95-065.
19
Q2β xIP #events #non-diff. FD(3)
2±stat. ±sys.
(GeV2) background
10 0.175 0.0032 54 7.1 9.7 ±1.6 ±2.8
10 0.175 0.0050 32 5.2 5.0 ±1.1 ±2.3
10 0.375 0.0013 62 0.9 37.7 ±5.2 ±6.5
10 0.375 0.0020 43 2.8 22.0 ±3.7 ±3.7
10 0.375 0.0032 15 2.8 9.2 ±3.0 ±4.5
10 0.65 0.00079 56 0.9 47.7 ±8.7 ±29.9
10 0.65 0.0013 20 0.9 29.1 ±7.0 ±8.5
10 0.65 0.0020 23 0 10.9 ±2.3 ±6.9
16 0.175 0.0032 48 5.2 9.5 ±1.6 ±2.1
16 0.175 0.0050 50 4.7 6.5 ±1.1 ±1.8
16 0.175 0.0079 33 7.5 3.8 ±0.9 ±2.0
16 0.375 0.0013 54 2.8 38.2 ±5.9 ±5.3
16 0.375 0.0020 54 3.3 20.1 ±3.1 ±3.6
16 0.375 0.0032 52 3.3 13.3 ±2.0 ±3.6
16 0.375 0.0050 44 3.8 6.2 ±1.0 ±1.8
16 0.65 0.00079 49 0 39.8 ±11.6 ±13.8
16 0.65 0.0013 38 2.8 32.5 ±6.3 ±6.5
16 0.65 0.0020 43 1.4 13.3 ±2.5 ±3.7
16 0.65 0.0032 29 0 8.5 ±1.6 ±2.3
28 0.175 0.0050 35 3.3 6.4 ±1.3 ±1.4
28 0.175 0.0079 32 8.0 3.8 ±0.9 ±1.7
28 0.375 0.0020 26 1.4 23.4 ±5.0 ±3.3
28 0.375 0.0032 35 1.9 15.7 ±2.9 ±2.0
28 0.375 0.0050 41 3.3 7.5 ±1.3 ±1.5
28 0.375 0.0079 19 3.3 3.1 ±0.9 ±1.1
28 0.65 0.0013 30 0.5 26.5 ±6.4 ±9.4
28 0.65 0.0020 35 1.9 15.7 ±3.4 ±2.5
28 0.65 0.0032 25 1.4 9.2 ±2.1 ±2.5
28 0.65 0.0050 23 1.4 5.4 ±1.3 ±2.9
63 0.375 0.0050 17 2.4 6.8 ±2.0 ±1.7
63 0.375 0.0079 16 3.8 2.6 ±0.9 ±1.5
63 0.65 0.0032 22 0.5 10.8 ±2.9 ±0.8
63 0.65 0.0050 17 0.5 6.2 ±1.7 ±0.9
63 0.65 0.0079 11 2.4 3.0 ±1.2 ±0.7
Table 2: ZEUS 1993 FD(3)
2results. The overall normalisation uncertainty of 3.5% is not in-
cluded. The data contain an estimated 15±10% fraction of double-dissociative events.
20
Figure 1: Diagram of a diffractive event.
21
ηmax
θH
NZ
ηmax
θH
CDMBGF
ηmax
θH
Data
0
1
2
3
-2 0 2 4 0
1
2
3
-2 0 2 4
0
1
2
3
-2 0 2 4
Figure 2: θHversus ηmax distribution for diffractive (NZ) and non-diffractive (CDMBGF) Monte
Carlo events and for the selected DIS data. The full line indicates the ηmax -θHcut used to select
diffractive events. The dotted line corresponds to ηmax =1.5.
22
MN [GeV]
1/N dN/dMN [GeV-1]
Fraction of rejected events
0
0.02
0.04
0.06
0.08
0.1
0 2 4 6 8 10 12 14 16 18 20 0
0.2
0.4
0.6
0.8
1
1.2
Figure 3: Acceptance for double dissociative events. The mass of the nucleon system, MN, for double
dissociative events generated by the PYTHIA Monte Carlo is indicated by the full line histogram.
The shaded area indicates those events which are selected by the ηmax-θHcut. The fraction of double
dissociative events rejected by this cut, as a function of MN, is indicated by the line.
23
ZEUS 1993
a)
14.8%NZ+85.2%CDMBGF
Diff. MC
ηmax
%
c)
10.5%HP+89.5%CDMBGF
Diff. MC
ηmax
%
b)
14.8%NZ+85.2%CDMBGF
Diff. MC
θH
%
d)
10.5%HP+89.5%CDMBGF
Diff. MC
θH
%
10 -3
10 -2
10 -1
1
10
10 2
-4 -2 0 2 4
10 -3
10 -2
10 -1
1
10
10 2
-4 -2 0 2 4
1
10
10 2
0 1 2
1
10
10 2
0 1 2
Figure 4: Percentage of DIS data as a function of ηmax and θH. The data are described by the sum of
the diffractive and non-diffractive contributions obtained from Monte Carlo simulation, with relative
fractions determined by a fit to the data. The dashed line corresponds to the diffractive contribution
and the sum of the diffractive and non-diffractive Monte Carlo models is indicated by the full line.
24
x
Events
ZEUS 1993
NZ
HP
HP+SP
Non Diff. DIS
Q2 [GeV2]
Events
W [GeV]
Events
xIP
Events
Mx [GeV]
Events
β
Events
0
500
10 -4 10 -3 10 -2 0
500
10 102
0
250
500
100 200 300 0
200
400
10 -3 10 -2
10 2
0 10 20 0
200
0 0.5
Figure 5: Observed distributions of x,Q2,W,xIP ,MXand βfor the selected (MX, y) intervals.
Uncorrected data are indicated by the dots. The errors are the statistical errors combined in quadrature
with 50% of the non-diffractive DIS background. The predictions from HP (full line), HP+SP (dashed
line) and NZ (dotted line) models are shown. The non-diffractive DIS background which has been
subtracted from the data is indicated by the shaded area.
25
β
Events
Non Diff. DIS
NZ
HP
HP+SP
a) Mx<20 GeV b) Mx<20 GeV
β
Events
β
Events
c) Mx<16 GeV
β
Events
d) Mx<16 GeV
β
Events
e) Mx<10 GeV
β
Events
f) Mx<10 GeV
Q2 [GeV2]
ZEUS 1993
y
|| |
208 160
--
--
--
--
0.2
0.08
0.3
0.8
0
200
0 0.5 0
100
0 0.5
0
100
0 0.5 0
50
0 0.5
0
100
0 0.5 0
50
0 0.5
Figure 6: Observed βdistribution as a function of (y, Q2, MX). The Q2intervals are 8-20 and 20-160
GeV2, the yintervals are 0.08-0.2, 0.2-0.3 and 0.3-0.8, and the MXintervals are (a,b) 0-20, (c,d) 0-16
and (e,f) 0-10 GeV. Uncorrected data are indicated by the dots. The errors are the statistical errors
combined in quadrature with 50% of the non-diffractive DIS background. The predictions from HP
(full line), HP+SP (dashed line) and NZ (dotted line) models are shown. The non-diffractive DIS
background which has been subtracted from the data is indicated by the shaded area.
26
ZEUS 1993
WDA [GeV]
% of diff. events
<Q2>=13 GeV2
<Q2>=39 GeV2
a)
b)
xDA [10-3]
% of diff. events
0
5
10
15
20
25
30
35
60 80 100 120 140 160 180 200 220 240
0
5
10
15
20
25
30
35
0 0.5 1 1.5 2 2.5 3
Figure 7: Observed fraction of diffractive events as a function of WDA and xDA in two Q2intervals.
The data are fitted to the NZ model for diffractive processes and the CDMBGF model for the non-
diffractive contribution. The errors are the statistical errors combined in quadrature with 50% of the
non-diffractive DIS background.
27
ZEUS 1993
1
10
10 -3 10 -2
xIP
F2
D(3)
1
10
F2
D(3)
1
10
F2
D(3)
10 -3 10 -2
xIP
10 -3 10 -2
xIP
10 -3 10 -2
xIP
8 12 20 40 100
0.1
0.25
0.5
0.8
Q2 [GeV2]
β
Figure 8: The results of FD(3)
2(β, Q2, xIP ) compared to the parametrisation discussed in the text.
The inner error bars show the statistical errors, the outer bars correspond to the statistical and DIS
event selection systematic errors added in quadrature, and the full line corresponds to the statistical
and total systematic errors added in quadrature. Note that the data include an estimated 15%
contribution due to double dissociation. The overall normalisation uncertainty of 3.5% due to the
luminosity uncertainty is not included.
28
ZEUS 1993
0
0.1
F2
D
~
Q2=10 GeV2
0
0.1
Q2=16 GeV2
0
0.1
Q2=28 GeV2
0
0.1
0 0.2 0.4 0.6 0.8 1
Q2=63 GeV2
β
0
0.1
F
~
2
D
β=0.175
0
0.1
β=0.375
0
0.1
10
β=0.65
Q2 [GeV2]
Figure 9: The results of ˜
FD
2(β, Q2) compared to the parametrisation discussed in the text, indicated
by the full line, and the β(1 −β) hard contribution, indicated by the dashed line. The inner error bars
show the statistical errors, the outer bars correspond to the statistical and systematic errors added in
quadrature. The systematic errors combine in quadrature the fits of the xIP dependence due to each
of the systematic checks discussed in the text. Note that the overall normalisation is arbitrary and
is determined by the experimental integration limits over xIP (6.3·10−4< xIP <10−2). The data
include an estimated 15% contribution due to double dissociation.
29
ZEUS 1993
1
10
10 -3 10 -2
xIP
F2
D(3)
1
10
F2
D(3)
1
10
F2
D(3)
10 -3 10 -2
xIP
10 -3 10 -2
xIP
10 -3 10 -2
xIP
8 12 20 40 100
0.1
0.25
0.5
0.8
Q2 [GeV2]
β
DL
NZ
Capella et al.
Figure 10: The results of FD(3)
2compared to various models discussed in the text. Note that the
estimated 15% contribution due to double dissociation has been subtracted in order to compare with
models for the single dissociation cross section. The inner error bars show the statistical errors, the
outer bars correspond to the statistical and DIS event selection systematic errors added in quadrature,
and the full line corresponds to the statistical and total systematic errors added in quadrature. The
overall normalisation uncertainty of 3.5% due to the luminosity and 10% due to the subtraction of the
double dissociation background is not included.
30
ZEUS 1993
1
10
10 -3 10 -2
xIP
F2
D(3)
1
10
F2
D(3)
1
10
F2
D(3)
10 -3 10 -2
xIP
10 -3 10 -2
xIP
10 -3 10 -2
xIP
8 12 20 40 100
0.1
0.25
0.5
0.8
Q2 [GeV2]
β
MSR Goul.
MSR DL
MSR IS
Figure 11: The results of FD(3)
2compared to an Ingelman-Schlein type model for which the momentum
sum rule (MSR) for quarks within the pomeron is assumed. The βdependence is taken from the
parametrisation discussed in the text. Note that the estimated 15% contribution due to double
dissociation has been subtracted in order to compare with models for the single dissociation cross
section. The inner error bars show the statistical errors, the outer bars correspond to the statistical
and DIS event selection systematic errors added in quadrature, and the full line corresponds to the
statistical and total systematic errors added in quadrature. The overall normalisation uncertainty of
3.5% due to the luminosity and 10% due to the subtraction of the double dissociation background is
not included.
31
