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Available via license: CC BY-NC-ND 4.0
Content may be subject to copyright.
ELSEWIER
13June1996
Physics Letters B 377 (1996) 259-272
PHYSICS LE-ITERS B
Measurement of elastic 4 photoproduction at HERA
ZEUS Collaboration
M. Derrick, D. Krakauer, S. Magill, D. Mikunas, B. Musgrave, J.R. Okrasinski, J. Repond,
R. Stanek, R.L. Talaga, H. Zhang
Argonne National Laboratory, Argonne, IL, USA&
M.C.K. Mattingly
Andrews University. Berrien Springs, MI, USA
G. Bari, M. Basile, L. Bellagamba, D. Boscherini, A. Bruni, G. Bruni, P. Bruni,
G. Cara Romeo, G. Castellini i, L. Cifarelli2, F. Cindolo, A. Contin, M. Corradi, I. Gialas,
P. Giusti, G. Iacobucci, G. Laurenti, G. Levi, A. Margotti, T. Massam, R. Nania,
F. Palmonari, A. Polini, G. Sartorelli, Y. Zamora Garcia3, A. Zichichi
University and INFN Bologna. Bologna, ItaIy36
A. Bornheim, J. Crittenden, T. Doeker4, M. Eckert, L. Feld, A. Frey, M. Geerts, M. Grothe,
H. Hartmann, K. Heinloth, L. Heinz, E. Hilger, H.-P. Jakob, U.F. Katz, S. Mengel,
J. Mollen 5, E. Paul, M. Pfeiffer, Ch. Rembser, D. Schramm, J. Stamm, R. Wedemeyer
Physikalisches Institut der Universitiit Bonn, Bonn, Germany””
S. Campbell-Robson, A. Cassidy, W.N. Cottingham, N. Dyce, B. Foster, S. George,
M.E. Hayes, G.P. Heath, H.F. Heath, D. Piccioni, D.G. Roff, R.J. Tapper, R. Yoshida
H.H. Wilis Physics Laboratory University of Bristol, Bristol, UK45
M. Arneodo6, R. Ayad, M. Capua, A. Garfagnini, L. Iannotti, M. Schioppa, G. Susinno
Calabria University, Physics Dept. and INFN, Cosenza, Italy 36
A. Caldwel17, N. Cartiglia, Z. Jing, W. Liu, J.A. Parsons, S. Ritz8, F. Sciulli, P.B. Straub,
L. Wai9, S. Yang lo, Q. Zhu
Columbia University, Nevis Labs., Irvington on Hudson. N. E, USA 47
P. Borzemski, J. Chwastowski, A. Eskreys, M. Zachara, L. Zawiejski
Inst. of Nuclear Physics, Cracow, Polandm
L. Adamczyk, B. Bednarek, K. Jelen, D. Kisielewska, T. Kowalski, M. Przybycien,
E. Rulikowska-Zarebska, L. Suszycki, J. Zajac
Faculty of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Cracow, Poland4
0370-2693/96/$12.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved.
PII SO370-2693(96)00172-4
260
ZEUS Collaboration/Physics Letters B 377 (19%) 259-272
A. Kotanski
Jagellonian Univ., Dept. of Physics, Cracow, Poland4’
L.A.T. Bauerdick, U. Behrens, H. Beier, J.K. Bienlein, 0. Deppe, K. Desler, G. Drews,
M. Flasinski ” D J Gilkinson, C. Glasman, P. Gottlicher, J. GroDe-Knetter, T. Haas, . .
W. Hain, D. Hasell, H. Hefiling, Y. Iga, K.F. Johnson 12, P. Joos, M. Kasemann, R. Klanner,
W. Koch, U. K&z, H. Kowalski, J. Labs, A. Ladage, B. Lohr, M. Lowe, D. Luke,
J. Mainusch i3, 0. Manczak, T. Monteiro
i4, J.S.T. Ng, D. Notz, K. Ohrenberg,
K. Piotrzkowski, M. Roco, M. Rohde, J. Roldarr, U. Schneekloth, W. Schulz, F. Selonke,
B. Surrow, T. Vol.3, D. Westphal, G. Wolf, C. Youngman, W. Zeuner
Deutsches Elektronen-Synchrotron DESE Hamburg, Germany
H.J. Grabosch, A. Kharchilava 15, . .
S M Mari 16, A. Meyer, S. Schlenstedt, N. Wulff
DESY-I’ Zeuthen, Zeuthen, Germany
G. Barbagli, E. Gallo, P. Pelfer
University and INFN, Florence. Italy M
G. Maccarrone, S. De Pasquale, L. Votano
INFN, Laboratori Nazionali di Frascati, Frascati. Italy 36
A. Bamberger, S. Eisenhardt, T. Trefzger, S. Wijlfle
Fakultiit fur Physik der Universitiit Freiburg i. Br.. Freiburg i.Br., Germany j3
J.T. Bromley, N.H. Brook, P.J. Bussey, A.T. Doyle, D.H. Saxon, L.E. Sinclair, M.L. Utley,
AS. Wilson
Dept. of Physics and Astronomy, University of Glasgow. Glasgow, UK45
A. Dannemann, U. Holm, D. Horstmann, R. Sinkus, K. Wick
Hamburg University, 1. institute of Exp. Physics. Hamburg, Germany33
B.D. Burow “, L. Hagge , .
I3 E Lohrmann, J. Milewski, N. Pavel, G. Poelz, W. Schott,
F. Zetsche
Hamburg University. II. Institute of Exp. Physics. Hamburg, Germanyj’
T.C. Bacon, N. Bri.immer, I. Butterworth, V.L. Harris, G. Howell, B.H.Y. Hung,
L. Lamberti ‘*, K.R. Long, D.B. Miller, A. Prinias
I9 J.K. Sedgbeer, D. Sideris,
,
A.F. Whitfield
Imperial College London, High Energy Nuclear Physics Group, London, UK 45
U. Mallik, M.Z. Wang, S .M. Wang, J.T. Wu
University of Iowa Physics and Astronomy Dept., Iowa City, USA M
P. Cloth, D. Filges
Forschungszentrum Jiilich. lnstitut fur Kerphysik. Jiilich. Germany
S.H. An, G.H. Cho, B.J. Ko, S.B. Lee, S.W. Nam, H.S. Park, S.K. Park
ZEUS Collnboration/Physics Letters B 377 (19%) 259-272
Korea University, Seoul, South Korea 3x
261
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 46
F. Barreiro, G. Cases, J.P. Fernandez, R. Graciani, J.M. Hernandez, L. Hervas, L. Labarga,
M. Martinez, J. de1 Peso, J. Puga, J. Terron, J.F. de Troconiz
Univer. Autdnoma Madrid, Depto de Fisica Tedrica, Madrid, Spain 44
F. Corriveau, D.S. Hanna, J. Hartmann, L.W. Hung, J.N. Lim, C.G. Matthews 20, P.M. Patel,
M. Riveline, D.G. Stairs, M. St-Laurent, R. Ullmann, G. Zacek
McGill University, Dept. of Physics, Montreal, Quebec, Canada “J*
T. Tsurugai
Meiji Gakuin University, Faculty of General Education, K)kohama. Japan
V. Bashkirov, B.A. Dolgoshein, A. Stifutkin
Moscow Engineering Physics Institute. Moscow, Russia”
G.L. Bashindzhagyan , . . 21 PF 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 43
M. Botje, F. Chlebana, J. Engelen, M. de Kamps, P. Kooijman, A. Kruse, A. van Sighem,
H. Tiecke, W. Verkerke, J. Vossebeld, M. Vreeswijk, L. Wiggers, E. de Wolf,
R. van Woudenberg22
NIKHEF and University of Amsterdam. NetherlandsJg
D. Acosta, B. Bylsma, L.S. Durkin, J. Gilmore, C. Li, T.Y. Ling, P. Nylander, I.H. Park,
T.A. Romanowski 23
Ohio State University Physics Department, Columbus. Ohio, USA 4ci
D.S. Bailey, R.J. Cashmore , .
24 A M.
Cooper-Sarkar, R.C.E. Devenish, N. Harnew,
M. Lancaster, L. Lindemann, J.D. McFall, C. Nath, V.A. Noyes i9, A. Quadt, J.R. Tickner,
H. Uijterwaal, R. Walczak, D.S. Waters, F.F. Wilson, T. Yip
Department of Physics, University of Oxford, Oxford, UK45
G. Abbiendi, A. Bertolin, R. Brugnera, R. Carlin, F. Dal Corso, M. De Giorgi, U. Dosselli,
S. Limentani, M. Morandin, M. Posocco, L. Stance, R. Stroili, C. Voci, F. Zuin
Dipartimento di Fisica deli’ Universita and INFN, Padova. Italy’”
J. Bulmahn, R.G. Feild 25, B.Y. Oh, J.J. Whitmore
Pennsylvania State University, Dept. of Physics, University Park. PA, USA 4’
G. D’ Agostini, G. Marini, A. Nigro, E. Tassi
Dipartimento di Fisica. Univ. ‘LA Sapienza’ and INFN, Rome, fialyx6
262
ZEUS Colluborazion / Physics Letters B 377 (19%) 259-272
J.C. Hart, N.A. McCubbin, T.P. Shah
Rutherford Appleton Laboratory, Chiltn, Didcot, Oxon, UK 45
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 Caltfornia. Santa Cruz. CA, USA4
J. Biltzinger, R.J. Seifert, 0. Schwarzer, A.H. Walenta, G. Zech
Fachbereich Physik der Universitiit-Gesamthochschule Siegen, Germany”
H. Abramowicz, G. Briskin, S. Dagan26, A. Levy2’
School of Physics,Tel-Aviv University. Tel Aviv, Israel j5
J.I. Fleck 27, M. Inuzuka, T. Ishii, M. Kuze, S. Mine, M. Nakao, I. Suzuki, K. Tokushuku,
K. Umemori, S. Yamada, Y. Yamazaki
Institute for Nuclear Study, University of Tokyo, Tokyo, Japan 27
M. Chiba, R. Hamatsu, T. Hirose, K. Homma, S. Kitamura**, T. Matsushita, K. Yamauchi
Tokyo Metropolitan University, Dept. of Physics, Tokyo, Japan3’
R. Cirio, M. Costa, M.I. Ferrero, S. Maselli, C. Peroni, R. Sacchi, A. Solano, A. Staiano
Universita di ?irrino. Dipartimento di Fisica Sperimentale and INFN. 7orino. Italy 3h
M. Dardo
II Faculty of Sciences. Torinn University and INFN - Alessandria. Italy x6
D.C. Bailey, F. Benard, M. Brkic, G.F. Hartner, K.K. Joo, G.M. Levman, J.F. Martin,
R.S. Orr, S. Polenz, C.R. Sampson, D. Simmons, R.J. Teuscher
Univemity of Toronto, Dept. of Physics. Toronto, Ont.. CanadaJ’
J.M. Butterworth, C.D. Catterall, T.W. Jones, P.B. Kaziewicz, J.B. Lane, R.L. Saunders,
J. Shulman, M.R. Sutton
University College London. Physics and Astronomy Dept., London. UK”’
B. Lu, L.W. MO
Virginia Polytechnic Inst. and State University. Physics Dept., Blacksburg, VA, USA”
W. Bogusz, J. Ciborowski, J. Gajewski, G. Grzelak29, M. Kasprzak, M. Krzyianowski,
K. Muchorowski3’, R.J. Nowak, J.M. Pawlak, T. Tymieniecka, A.K. Wrbblewski,
J.A. Zakrzewski, A.F. Zarnecki
Warsaw University, Institute ($ Experimental Physics, Warsaw. Poland”’
M. Adamus
Institute fir Nuclear Studies. Warsaw. Polanda’
C. Coldewey, Y. Eisenberg 26, U. Karshon26, D. Reve126, D. Zer-Zion
Weiznumn Institute, Particle Physics Dept.. Rehovot, Israel j4
ZEUS Collaboration/Physics Letters B 377 (19%) 259-272
W.F. Badgett, J. Breitweg, D. Chapin, R. Cross, S. Dasu, C. Foudas, R.J. Loveless,
S. Mattingly, D.D. Reeder, S_ Silverstein, W.H. Smith, A. Vaiciulis, M. Wodarczyk
Universuy of Wisconsin. Dept. of Physics, Madison. WI0 USA 46
S. Bhadra, M.L. Cardy, C.-P. Fagerstroem, W.R. Frisken, M. Khakzad, W.N. Murray,
W.B. Schmidke
Rwk Univemity, Dept. of Physics, North York, ant., Canada”
Received 31 January 1996
Editor: L. Montanet
263
Abstract
The production of 4 mesons in the reaction e+p -+ e+~$p (4
-+ KtK-) at a median Q2 of 10P4 GeV2 has been studied
with the ZEUS detector at HERA. The differential 4 photoproduction cross section du/dt has an exponential shape and
has been determined in the kinematic range 0.1 < it/ < 0.5 GeV’ and 60 < W < 80 GeV. An integrated cross section of
flYI’
_-Q,, = 0.96 f O.l9~~:;~,k pb has been obtained by extrapolating to t = 0. When compared to lower energy data, the results
show a weak energy dependence of both u,~+$~
and the slope of the t distribution. The C$ decay angular distributions are
consistent with s-channel helicity conservation. From lower energies to HERA energies, the features of q5 photoproduction
are compatible with those of a soft diffractive process.
I Also at IROE Florence, Italy.
z Now 31 Univ. of Salerno and INFN Napoli, Italy.
’ Suppouted by Worldlab, Lausanne, Switzerland.
A Now as MINERVA-Fellow at Tel-Aviv University
’ Now at ELEKLUFT, Bonn
’ Also at University of Torino.
’ Alexandra- von Humboldt Fellow.
’ Alfred P Sloan Foundation Fellow.
” Now at University of Washington, Seattle.
I” Now at California Institute of Technology, Los Angeles.
” Now at Inst. of Computer Science, Jagellonian Univ., Cracow.
I? Visitor from Florida State University.
” Now at DESY Computer Center.
IJ Supported by European Community Program PRAXIS XXI.
” Now at Univ. de Strasbourg.
‘(’ Present address: Dipartimento di Fisica, Univ. “La Sapienza”,
Rome.
Ii Also supported by NSERC. Canada.
” Supported by an EC fellowship.
I” PPARC Post-doctoral Fellow.
?” Now at Park Medical Systems Inc., Lachine, Canada.
?’ Pnrtially supported by DESY.
?: Now at Philips Natlab, Eindhoven, NL.
?’ Now at Department of Energy, Washington.
?’ Also at University of Hamburg, Alexander von Humboldt Re-
search Award.
z Now at Yale University, New Haven, CT.
?‘# Supported by a MINERVA Fellowship.
z7 Supported by the Japan Society for the Promotion of Science
(JSPS1.
28 Present address: Tokyo Metropolitan College of Allied Medical
Sciences, Tokyo I 16, Japan.
*‘Supported by the Polish State Committee for Scientific Re-
search, grant No. 2PO3809308.
mSupported by the Polish State Committee for Scientific Re-
search, grant No. 2PO3B09208.
‘I Supported by the Natural Sciences and Engineering Research
Council of Canada ( NSERC)
j2 Supported by the FCAR of Qutbec, Canada.
33 Supported by the German Federal Ministry for Education and
Science, Research and Technology (BMBF), under contract num-
bers 056BN191, 056FR19P, 056HH191, 056HH291. 05681791.
34 Supported by the MlNERVA Gesellschafl fiir Forschung GmbH.
and by the Israel Academy of Science.
35 Supported by the German Israeli Foundation, and by the Israel
Academy of Science.
.16 Supported by the Italian National Institute for Nuclear Physics
(INFN).
I’ Supported by the Japanese Ministry of Education, Science and
Culture (the Monbusho) and its grants for Scientific Research.
3R Supported by the Korean Ministry of Education and Korea
Science and Engineering Foundation.
39 Supported by the Netherlands Foundation for Research on Mat-
ter (FOM).
4(1 Supported by the Polish State Committee for Scientific Re-
search, grants I 15&343/SPUB/PO3/ 109/95,2P03B 244 08~02.
~03, pO4 and ~05, and the Foundation for Polish-German Collab-
oration (proj. No. 506/92).
41 Supported by the Pohsh State Commitree for Scientific Research
(grant No. 2 PO3B 083 08).
264
ZEUS Collaboration/ Physics Letters B 377 (19%) 259-272
1. Introduction
Elastic photoproduction of 4 mesons, ‘yp -+ c)p,
has previously been studied at photon-proton centre-
of-mass energies up to W E 17 GeV in fixed tar-
get experiments [ l-31. At these energies the reaction
yp + +p has the characteristics of a soft diffractive
process: a cross section rising weakly with the centre-
of-mass energy, a steep forward diffractive peak in the
t distribution, where t is the four-momentum transfer
squared at the proton vertex, and s-channel helicity
conservation.
At the energies of the previous experiments, elas-
tic vector meson photoproduction is well described
as a soft diffractive process in the framework of the
Regge theory [ 41 and of the Vector Dominance Model
(VDM) [ 51. In this approach, this reaction is assumed
to proceed at high energy through the exchange of a
“soft” pomeron trajectory [ 61 with an effective inter-
cept of 1 + E = 1.08 and a slope of a’ = 0.25 GeV2.
Recent experimental results [ 71 extend the validity of
this approach to the high energies of HERA for elastic
p” photoproduction. This approach also provides pre-
dictions [ 61 for the total photoproductioncross section
consistent with the measurements made at HERA [ 81.
In contrast, the predictions of Regge theory fail to de-
scribe the recently measured rapidly rising cross sec-
tions at HERA for elastic J/$ photoproduction [9]
and for exclusive p” production ( y*p + pop) in deep
inelastic scattering (DIS) [ IO]. The measurements
for the latter two processes are consistent with per-
turbative QCD calculations [ 11,121. In these calcu-
lations the scale of the process is given by the virtu-
ality Q’ of the exchanged photon for exclusive DIS
p0 production or depends on the mass of the vector
meson for elastic J/lc, photoproduction. Perturbative
QCD calculations for the proton structure function F2
‘? Partially supported by the German Federal Ministry for Educa-
tion and Science, Research and Technology (BMBF).
A Supported by the German Federal Ministry for Education and
Science, Research and Technology (BMBF), and the Fund of Fun-
damental Research of Russian Ministry of Science and Education
and by INTAS-Grant No. 93-63.
4 Supported by the Spanish Ministry of Education and Science
through funds provided by CICYT.
jq Supported by the Particle Physics and Astronomy Research
Council.
A~ Supported by the US Department of Energy.
J7 Supported by the US National Science Foundation.
are consistent with the data [ 131 at HERA energies
for a scale as cmall as Q* = 1.5 GeV*. If the scale
of elastic vector meson photoproduction is given by
the mass of the vector meson, the scale of elastic 4
photoproduction is between that of elastic p” and J/$
photoproduction and between that of elastic p” pho-
toproduction and exclusive DIS p” production. It is
therefore of interest to measure elastic 4 photopro-
duction and to see whether the scale of the process is
large enough to cause a deviation from the behavior
of a soft diffractive process.
The expectations of Regge theory and VDM may
also be confronted by a measurement of elastic 4 pho-
toproduction at HERA energies. In the additive quark
model [ 141 and VDM, the reaction ‘yp --f c$p can
proceed only by pomeron exchange [ 151, and is thus
a particularly clean example of a diffractive reaction.
This paper reports a measurement with the ZEUS
detector at HERA of high energy production of 4
mesons in the reaction e+p -+ e++p using events with
Q2 < 4 GeV* in which neither the scattered proton
nor the scattered positron was observed in the detector.
The 4 was observed, via its decay into K+K-, in the
kinematic range 60 < W < 80 GeV and 0.1 < pg <
0.5 GeV2, where pr is the transverse momentum of
the 4 with respect to the beam axis.
2. Kinematics
Fig. 1 shows a schematic diagram for the reaction
e+(k)p(P) 4 e+tk’)4(v)p(P’),
where each quantity in parentheses is the four-
momentum of the particle.
The kinematics of the inclusive scattering of un-
polarised positrons and protons is described by the
positron-proton centre-of-mass energy and any two of
the following variables:
- Q2 = -q* = -( ,4 - id)*, the negative of the four-
momentum squared of the exchanged photon;
_
y = (q . P)/( k . P), the fraction of the positron
energy transferred to the hadronic final state in the
rest frame of the initial state proton;
- W2 = (q + P)* = -Q2 + 2v(k. P) + Mi, the
centre-of-mass energy squared of the photon-proton
system, where M,, is the proton mass.
ZEUS Collaboration/ Physics Letters B 377 (19%) 259-272
265
Fig. I. Schematic diagram of elastic q5 photoproduction in efp
interactions.
For the description of the exclusive reaction e+p +
e’4p (4 + K+K- ) the following additional vari-
ables are required:
- t = ( P - P’) 2, the four-momentum transfer squared
at the proton vertex;
-
the angle between the 4 production plane and the
positron scattering plane;
_
the polar and azimuthal angles of the decay kaons
in the 4 rest frame.
In the present analysis, events were selected in which
the final state positron was scattered at an angle too
small to be detected in the main ZEUS calorimeter.
Thus the angle between the 4 production plane and the
positron scattering plane was not measured. In such
untagged photoproduction events the Q2 value ranges
from the kinematic minimum Qii, = @y2/ ( 1 - y) M
10P9 GeV2, where M, is the electron mass, to the
detector limit Q,!&, x
4 GeV2, with a median Q2 of
approximately 10e4 GeV2. Because of this small Q*
value, the photon-proton centre-of-mass energy can be
expressed as:
W2 2 2(&j - pzd)E,,,
where E,, , E+ are the energies of the incoming proton
and the produced 4 meson and pz+ 48 is the longitu-
4R Throughout this paper use is made of the standard ZEUS right-
handed coordinate system in which the positive Z-axis points in
dinal momentum of the C#J meson. Similarly, the four-
momentum transfer squared, t, at the proton vertex for
Q2 = QL,, is given by:
t = (q - V)2 N -p; .
Non-zero values of Q2 cause t to differ from -p; by
less than Q2, as described elsewhere [ 71.
2. I. 4 photoproduction
The ‘yp cross section is related to the efp cross
section by:
d2ae” (Y 1
K
1+(1-y)2
dydQ2 = G@
Y
-
+ 2(1 -Y>
Y
@‘(KQ2)
1
*
l
where a; ” and ~1 I’
are the ‘yp cross sections for
transversely and longitudinally polarized photons, re-
spectively.
Using the VDM predictions [ 51:
f
u;qw,o) uY”( W)
+'(wQ2) = (1 +Q2/M$)2 = (1 +Q2/@)2
where Mg is the 4 meson mass, and using 6 = 1 [ 161
yields
d2&T
WQ2
= F(y,Q2)aYp(W)
where the function:
F(y,Q’) = 2;
1 +(l -y)2
y
-
is the effective photon flux.
the direction of flight of the protons (referred to as the forward
direction) and the X-axis is horizontal, pointing towards the center
of HERA. The nominal interaction point is at X = Y = Z = 0.
266
ZEUS Collaboration/ Physics Letters B 377 (19%) 259-272
Assuming no strong W dependence, the yp cross
section at the average W measured in the experiment
is obtained as the ratio of the corresponding e+p cross
section, integrated over they and Q* ranges covered by
the measurement, and the photon flux factor F(y, Q*)
integrated over the same y and Q2 ranges.
to 176.2”, respectively. Each part consists of towers
which are longitudinally subdivided into electromag-
netic (EMC) and hadronic (HAC) readout cells. The
transverse sizes are typically 5 x 20 cm2 for the EMC
cells ( 10 x 20 cm2 in RCAL) and 20 x 20 cm* for the
HAC cells. From test beam data, energy resolutions
with E in GeV of aE/E = 0.18/a for electrons and
u.E/E = 0.35/a for hadrons have been obtained.
3. Experimental setup
3.1. HERA
During 1994 HERA operated with a proton beam
energy of 820 GeV and a positron beam energy of 27.5
GeV. In the positron and the proton beams 153 collid-
ing bunches were stored together with an additional 17
proton and 15 positron unpaired bunches. These addi-
tional bunches were used for background studies. The
time between bunch crossings was 96 ns. The typical
instantaneous luminosity was 1.5 . 1030 cm-*s-l.
Proton-gas events occuring upstream of the nominal
e+p interaction point are out of time with respect to the
e+p interactions and may thus be rejected by timing
measurement made by the scintillation counter arrays
Veto Wall, C5 and SRTD respectively situated along
the beam line at Z = -730 cm, Z = -315 cm and
Z = -150cm.
The luminosity is determined [ 211 from the rate
of the Bethe-Heitler process efp + efyp where the
photon is measured by the LUMI calorimeter located
in the HERA tunnel in the direction of the positron
beam.
3.2. The ZEUS detector
3.3. Trigger
A detailed description of the ZEUS detector can be
found elsewhere [ 171. The main components used in
this analysis are outlined below.
Charged particle momenta are reconstructed by
the vertex detector (VXD) [ 181, the central tracking
detector (CTD) [ 191 and the rear tracking detector
(RTD) [ 171. The VXD and the CTD are cylindri-
cal drift chambers placed in a magnetic field of 1.43
T produced by a thin superconducting coil. The ver-
tex detector surrounds the beam pipe and consists of
120 radial cells, each with 12 sense wires. The CTD
surrounds the vertex detector and consists of 72 cylin-
drical layers, organized in 9 superlayers covering the
polar angular region 15’ < 0 < 164”. The RTD is a
planar drift chamber located at the rear of the CTD
covering the polar angular region 162” < 8 < 170”.
Using the information from the VXD, the CTD and
the RTD for the two-track events of this analysis, the
primary event vertex was reconstructed with a resolu-
tion of 1.4 cm in Z and 0.2 cm in the transverse plane.
ZEUS has a three level trigger system. The data used
in this analysis were taken with the “untagged vector
meson photoproduction trigger” described in this sec-
tion. The photoproduction events are “untagged” since
the scattered positron escapes undetected through the
beam pipe hole in the RCAL.
The first level trigger (FLT) required:
-
a minimum energy deposit of 464 MeV in the elec-
tromagnetic section of the RCAL, excluding the
towers immediately surrounding the beam pipe;
-
at least one track candidate in the CTD;
- less than 1250 MeV deposited in the FCAL towers
surrounding the beam pipe.
-
the time of any energy deposited in the Veto Wall,
the C5 and the SRTD to be consistent with an e+p
interaction and not with a proton-gas event.
The second level trigger (SLT) rejected background
events exploiting the excellent time resolution of the
calorimeter.
The high resolution uranium-scintillator calorime-
ter CAL [ 201 is divided into three parts, the forward
calorimeter (FCAL), the barrel calorimeter (BCAL)
and the rear calorimeter (RCAL) , which cover polar
angles from 2.6” to 36.7’, 36.7’ to 129.1”, and 129.1”
The third level trigger (TLT) used information from
the CTD to select events with a reconstructed vertex,
at most 4 reconstructed tracks and an invariant mass
less than 1.5 GeV for at least one two-track combi-
nation assuming that the particles are pions. The rate
of the untagged vector meson photoproduction trigger
ZEUS Collaborarion / Physics Letters B 377 (19%) 259-272
261
leaving the TLT was about 2 Hz. Because of this high
rate the trigger was prescaled. The recorded data col-
lected during 1994 from this trigger correspond to an
effective integrated luminosity of 887 f 31 nb-‘.
4. Event selection
The following offline cuts were applied to select the
reaction yp + @( -+ K+K-)p:
exactly two oppositely charged tracks associated
with a reconstructed vertex;
each track within the pseudorapidity range 171 <
2.0 and with a transverse momentum greater than
150 MeV. These cuts select the high efficiency and
well understood region of the tracking detector;
the Z coordinate of the vertex within f30 cm of the
nominal interaction point;
in BCAL and RCAL, not more than 200 MeV in
any EMC (HAC) calorimeter cell which is more
than 30 cm (50 cm) away from the extrapolated
impact position of either of the two tracks. This cut
rejects events with additional neutral particles;
energy deposit in FCAL less than 0.8 GeV. This cut
reduces the contamination from diffractive proton
dissociation, yp -+ 4X.
Since the detector geometry and the trigger limit
the observable kinematic range for the reaction yp -+
4~. the selected events were restricted to the region:
60~ W<80GeV
0. I < ps < 0.5 GeV2,
where the acceptance is well understood and the back-
ground contamination due to proton dissociation is
relatively small.
5. Monte Carlo simulation and acceptance
calculation
The acceptance for untagged elastic 4 photoproduc-
tion was calculated by Monte Carlo methods. The re-
action P+P + e+& was simulated using two differ-
ent event generators. The first one, DIPSI, is based on a
model by Ryskin [ 111. It describes elastic vector me-
son production by the exchange of a pomeron which
4Y The pseudorapidity 11 is defined as 7 = -In[tan( $ ) 1.
The acceptance as a function of MKK, the invariant
ZEUS 1994
Fig. 2. Acceptance for the reaction e+p + e+~$p as a function
ofW(for0.1<p~<0.5GeV2)andofp~(for60<W<80
GeV) obtained for the two event generators described in the text.
interacts with the quark-antiquark pair into which the
incoming virtual photon fluctuates. The second gener-
ator, JETPHI, uses a VDM approach and was written
in the framework of the JETSET package [ 221.
Events were generated in the W range from 50 to
90 GeV and the Q2 range between Q,$, and 4 GeV2.
The 4 decay angular distributions in both programs
were simulated assuming s-channel helicity conserva-
tion. To reproduce the ps distribution of the data, the
t dependence was taken to be of the form e-‘lrl with
b = 7 GeVm2. The input vertex distribution was sim-
ulated in accordance with that measured using non-
diffractive photoproduction events.
The generated events were processed through the
ZEUS detector and trigger simulation programs as
well as through the analysis chain. The same offline
cuts were used for the Monte Carlo events and for the
data. The reconstructed W, p; and decay angular dis-
tributions of the Monte Carlo sample agree well with
those of the data.
The acceptance as a function of W and p+ is shown
in Fig, 2. The acceptance drops at low values of W be-
cause the decay kaons enter BCAL, not RCAL, thus
providing no trigger. At high W as well as at low
pr values the acceptance decreases because the decay
kaons emerge at a large polar angle and are not de-
tected by the CTD.
268
ZEUS Collaboration/Physics Letters B 377 (19%) 259-272
50
ZEUS 1994
Fig. 3. Uncorrected K+K- invariant mass distribution for all
events passing the final selection cuts. The curve is the result of
the fit described in the text.
mass of the two decay kaons, is flat in the Cp mass
region.
6. Results
6.1. Extraction of the 4 signal
After applying all selection cuts, the two particle
invariant mass was computed for each event, assuming
that the two charged particles are kaons. The invariant
mass distribution is shown in Fig. 3. The line is a fit
to the function:
where the functions BW and BG describe the reso-
nance shape and background, respectively. The res-
onance shape was described by a relativistic p-wave
Breit-Wigner function convoluted with a Gaussian.
The width of the Breit-Wigner function was fixed
at the Particle Data Group value of 4.43 & 0.06
MeV [ 231. The background, mainly due to the reac-
tion yp + pop, was taken to be of the form:
BG = (Y( MKK - ~MK)~,
where MK is the kaon mass.
The fit yields 566 & 31 q5 -+ KfK- mesons after
background subtraction. The 4 mass obtained from the
fit is M,#, = 1.020 f 0.001 GeV, with an r.m.s. of the
Gaussian of 4 MeV, compatible with the experimental
resolution. The value of the free parameter p obtained
from the fit is p = 0.97 f. 0.09.
6.2. qi~ Events from background reactions
The main source of background to the elastic q5 re-
action is the process yp + q5X, where the proton
diffractively dissociates into a hadronic final state X
which is not detected in the main calorimeter. The
background was evaluated by comparing the number
of 4 events in the data, without the E~AL < 0.8 GeV
cut, to a Monte Carlo simulation using the PYTHIA
generator [ 241 of the diffractive proton dissociation
reaction ‘yp + 4X. The mass spectrum of the diffrac-
tive events was simulated according to a da/dM$ cx
( 1 /Mx) 2.25 distribution [ 251. The t dependence was
parametrized with the form eehlrl with b = 4 GeV-*.
The contamination of the elastic 4 photoproduction
sample from proton dissociations0 was estimated to
be (24&7(stat) f6(syst))% in the& range between
0.1 and 0.5 GeV*. The systematic error was estimated
by varying the exponent in the diffractive Mx distri-
bution between 2 and 2.5. Similarly, the uncertainty
due to varying the generated t slope in the MC sam-
ple from 4 GeV-* to 3 GeV-* has been included in
the systematic error.
For each bin in p;,
the number of events in the
q!~ peak was corrected for the background from the
diffractive proton dissociation reaction ‘yp --f q5X. The
p; behaviour of this background was taken from the
PYTHIA MC simulation.
The background due to a I$ meson produced in a
beam-gas interaction was estimated from the analysis
of events coming from unpaired bunches. The values
found are 1% for positron- and < 1% for proton-gas
interactions.
H, The proton diffractive dissociation contamination in this mea-
surement and in elastic p” photoproduction [ 7 1 of ( 1 I f 1 (stat) f
6(syst) )% are compatible, taking into account the different ac-
ceptance at low p: and the different p? regions of the two
measurements.
ZEUS Collaboration/Physics Letters B 377 (19%) 259-272
269
-1
10 1 ““I ‘/ ““I j ” ” ” “j ’
0
0.1
0.2
0.3
0.4 It( (t&V;
_A 10 L
I
‘I_‘l$.1::j..i
0 fixed target experiments [2.261
ot
I I
10
w ccc:;
1
Fig. 4. (a) Acceptance corrected f distribution for the reaction
71, - I$/, at < W >= 70 GeV. The dots are the ZEUS data, while
the line is the result of the exponential fit described in the text.
(b) Compilation of measurementi of the slope parameter b as a
function of W for the reaction yp -+ tip. The different data are
measured in various I intervals. The line shows the Regge theory
prediction b,, + 4cu’lnW with cz’ = 0.25 GeV-2. The value for bo
is chosen such that the line intercepts the ZEUS measurement.
6.3. Elastic C#I photoproduction cross section
The cross section for the reaction yp ---) dp is given
bY
where N$ is the number of acceptance corrected 4
events, BR is the branching ratio of the 4 decay into
K.’ K- (49.1 f 0.9%) [ 231, L is the effective inte-
grated luminosity and F = 0.025 is the photon flux
factor integrated over the phase space determined by
the selection cuts.
An exponential fit to the acceptance corrected p;
distribution in the range 0.1 < p; < 0.5 GeV* gives
the slope value of 6.5 Z!Z 1 .O(stat) GeV-*.
The acceptance corrected t distribution was recon-
structed from the measured pg spectrum using a bin-
by-bin correction, given by the ratio of the generated t
and the reconstructed p; distributions in the MC sam-
ple. The acceptance corrected t distribution is shown
in Fig. 4a. An exponential fit of the form du/dltl =
du/dltlI,=O. 4”
in the 1 tl range between 0.1 and 0.5
GeV* yields:
b = 7.3 f 1 .O( stat) f 0.8( syst) GeV-’
dcr,f4P
44
r=O = 7.2 f 2.1 (stat) f 1.8( syst) pb/GeV*
The systematic error of the slope parameter b includes
uncertainties from the acceptance calculation (6%)
and the applied cuts (9%). The systematic error for
da/dtl,,o is due to the acceptance calculation ( 14%))
the applied cuts (15%) and a normalization uncer-
tainty due to the calorimeter trigger ( 12%)) the signal
fitting procedure (7%) and the luminosity measure-
ment (3.5%).
Fig. 4b shows the value of the slope parameter b
measured by this experiment together with the results
of lower energy photoproduction experiments [ 2,261.
The ZEUS measurement, when compared to the fixed
target measurements, shows a weak energy depen-
dence of b, as predicted by Regge theory [ 41. The
slope parameter for elastic p” photoproduction [ 7 ] is
b, = 9.9 * 1.2 f 1.4 GeV-* measured in the range
I tl < 0.5 GeV* using a fit of the form e-bltl+CrZ. In the
framework of geometric diffractive models, the slope
obtained here for the 4 meson, compared to that of
the p”, indicates that the radius of 4p interaction is
smaller than that of pop.
6.4. Total elastic 4 photoproduction cross section
The total elastic cross section was obtained by ex-
trapolating the differential cross section to t = 0 as-
suming a simple exponential t dependence. The result-
ing value of the cross section is:
a,,,+,, = 0.96 & O.l9(stat)~~.,:~(syst) pb
integrated over the range ItI < 0.5 GeV* and at an
average W of 70 GeV.
The systematic error includes uncertainties from the
acceptance calculation (8%)) the applied cuts (8%)
and the normalization as described in Section 6.3. The
uncertainty from the proton dissociation background
subtraction made in each bin of the ps distribution has
been included in the statistical error. The uncertainty of
the t extrapolation has been estimated by using a fit of
the form e-blrl+cr2 with different values of c. Changing
the parameter c from 0 to 3 GeVm4 increases the cross
section by 10%. The range of the variation for the
parameter c was taken in accordance with the results
ZEUS Collaborahon / Physics Letters B 377 (19%) 259-272
I
I
ID II
DZ
W (GeV)
ZEUS 1994
0 fixed target experiments [2,271
Fig. 5. Elastic q5 photoproduction cross sections as a function of W.
The solid dot is the ZEUS measurement, while the open circles are
the lower energy data. The line shown is a description of the fixed
target data using a,p_+P 0: Wt’.32 16 1. It is inspired from Regge
theory, wtuch predicts (T,,,,+,~ cx W4’/b( W), where I +r = 1.08
is the intercept of the Regge trajectory and b(W) is the energy
dependent exponential slope of the differential cross section. This
energy dependence however is ignored in the parametrisation.
obtained in high energy p” photoproduction [ 71. This
uncertainty has been included in the systematic error.
The cross section for the process yp --f 4~ from
this analysis is compared in Fig. 5 to results at lower
yp centre-of-mass energies [ 2,271. The data show a
weak energy dependence of the cross section from 2
GeV to 70 GeV, as predicted by Regge theory [4].
The cross section ratio of elastic r$ and p” [ 71 pho-
toproduction at W = 70 GeV is 0.065 ZIZ 0.013( stat).
The same ratio measured at W = 17 GeV [3] is
0.076 10.010. These results show that there is no sig-
nificant energy dependence of the $1~’ photoproduc-
tion cross section ratio in this W range.
6.5. Total +p cross section
Using VDM and the optical theorem the 4 photo-
production cross section at f = 0 can be related to the
total 4p cross section by:
where 71 is the ratio of the real to the imaginary part
of the forward 4~ elastic scattering amplitude, f$/4~
is the ~4 coupling constant and Q is the fine structure
constant. For pure pomeron exchange 7 = 0. Taking
,f$/4r= 18.4 (seee.g. [l],p. 393) yields:
a$‘= 19&7mb.
Using a parametrisation [6] based on Regge the-
ory, this result is in agreement with the additive quark
model which predicts (see e.g. [ 281) g$ 2 a::” +
K-II
utot
rr+[,
- utot
= 19.9 mb at W = 70 GeV. The com-
parison of a$$
to the total pop cross section, c&” =
28.0 f 1.2(stat) f 2.8(syst) mb [7], indicates that
the @p interaction radius is smaller than that of pop.
This is consistent with the comparison in Section 6.3
of the 4 and p” slopes.
6.6. Decay angular distributions
The 4 decay angular distributions can be used to
determine elements of the 4 spin-density matrix [ 291.
In the s-channel helicity frame the decay angle 0h is
defined as the angle between the K+ and the direction
of the recoil proton in the 4 centre-of-mass frame,
while the azimuthal angle & is the angle between the
4 decay plane and the ~4 plane in the yp centre-of-
mass frame.
Since in the present experiment the scattered
positron and proton were not detected, the decay an-
gles are determined by approximating the direction of
the virtual photon by that of the incoming positron.
It has been verified by Monte Carlo calculations that
this is a good approximation.
The acceptance corrected $ decay angular distribu-
tions in the kinematic range 0.1 < p+ < 0.5 GeV*
are shown in Fig. 6. They have been fitted with the
functions [ 291:
1 dN
--
=
3 [l -
r;; +
(3r$
-
N dcos&,
4
1) cos2e,,]
1 dN
--
N dh,
= $1 -by?, COS&bh),
where rg and I:“_,
are two of the 4 spin-density ma-
trix elements.
Assuming VDM and s-channel helicity conserva-
tion, the P$ spin-density matrix element can be ex-
pressed as:
where E is the ratio of the longitudinally to the trans-
versely polarised photon fluxes. Assuming the Q2 de-
ZEUS Collaboration/Physics Letters B 377 (19%) 259-272
271
CO&,
4+, b-ad)
Fig. 6. Acceptance corrected decay angular distributions for the 4 meson in the reaction yp
--t qip at < W >= 70 GeV. The curves are
the results of the fits described in the text.
pendence given in Section 2.1, on average E 2 0.998
and r$i N 0.03 in the kinematic region under study.
The spin-density matrix element 17”~ is expected to be
zero under the assumption of s-channel helicity con-
servation.
The fitted values obtained from the distributions in
Fig. 6 are rg$ = -0.01 f 0.04 and $:I = 0.03 XII 0.05,
consistent with VDM and s-channel helicity conser-
vation.
7. Summary and conclusions
The photoproduction of C#J mesons has been mea-
sured with the ZEUS detector at HERA. The cross
. .
sechon IS LT~,,_&~ = 0.96 f O.l9z$.:g pb at < W >=
70 GeV and for ItI < 0.5 GeV*. In comparison to
lower energy measurements this result is consistent
with Regge theory which predicts a weak rise of this
cross section with increasing W from the exchange of
a soft pomeron.
The differential cross section du/dt, determined in
the kinematic range 0.1 < JtJ < 0.5 GeV*, falls ex-
ponentially with the slope value b = 7.3 f 1.0 f 0.8
GeV-‘. The comparison with lower energy data is
consistent with the logarithmic rise of the t slope with
W expected by Regge theory.
The spin-density matrix elements measured from
the C$ decay angular distributions are in argeement
with s-channel helicity conservation.
At HERA energies, elastic 4 photoproduction
shows the features typical of a soft diffractive reac-
tion. The Regge theory expectations for elastic vector
meson production at HERA energies are thus corrob-
orated at the scale given by elastic C#J photoproduction.
Acknowledgement
We thank the DESY Directorate for their strong
support and encouragement. The remarkable achieve-
ments of the HERA machine group were essential for
the successful completion of this work and are grate-
fully appreciated.
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