15 November 2001

Physics Letters B 520 (2001) 191–203www.elsevier.com/locate/npe

D∗± meson production in deep-inelastic diffractive interactions atHERA

H1 Collaboration

C. Adloff ag, V. Andreevx, B. Andrieuaa, T. Anthonisd, V. Arkadovai,A. Astvatsatourovai, A. Babaevw, J. Bährai, P. Baranovx, E. Barreletab, W. Bartelj,

P. Bateu, J. Beckerak, A. Beglarianah, O. Behnkem, C. Beiern, A. Belousovx,T. Benischj, Ch. Bergera, T. Berndtn, J.C. Bizotz, J. Boehme, V. Boudryaa,

W. Braunschweiga, V. Brissonz, H.-B. Brökerb, D.P. Brownj, W. Brücknerl,D. Brunckop, J. Bürgerj, F.W. Büsserk, A. Bunyatyanl,ah, A. Burrager, G. Buschhorny,L. Bystritskayaw, A.J. Campbellj, J. Caoz, S. Carona, F. Cassol-Brunnerv, D. Clarkee,

B. Clerbauxd, C. Collardd, J.G. Contrerasg,4,18, Y.R. Coppensc, J.A. Coughlane,M.-C. Cousinouv, B.E. Coxu, G. Cozzikai, J. Cvachac, J.B. Daintonr, W.D. Dauo,

K. Daumag,2, M. Davidssont, B. Delcourtz, N. Deleruev, R. Demirchyanah,A. De Roeckj,6, E.A. De Wolfd, C. Diaconuv, J. Dingfelderm, P. Dixons, V. Dodonovl,

J.D. Dowellc, A. Droutskoiw, A. Dubaky, C. Duprelb, G. Eckerlinj, D. Ecksteinai,V. Efremenkow, S. Egliaf, R. Eichleraj, F. Eiselem, E. Eisenhandlers, M. Ellerbrockm,E. Elsenj, M. Erdmannj,3,5, W. Erdmannaj, P.J.W. Faulknerc, L. Favartd, A. Fedotovw,

R. Felstj, J. Ferenceij, S. Ferronaa, M. Fleischerj, Y.H. Flemingc, G. Flüggeb,A. Fomenkox, I. Forestiak, J. Formánekad, G. Frankej, E. Gabathulerr, K. Gabathuleraf,

J. Garveyc, J. Gassneraf, J. Gaylerj, R. Gerhardsj, C. Gerlichm, S. Ghazaryand,ah,L. Goerlichf, N. Gogitidzex, M. Goldbergab, C. Grabaj, H. Grässlerb, T. Greenshawr,

G. Grindhammery, T. Hadigm, D. Haidtj, L. Hajdukf, J. Hallerm, W.J. Haynese,B. Heinemannr, G. Heinzelmannk, R.C.W. Hendersonq, S. Hengstmannak,

H. Henschelai, R. Heremansd, G. Herrerag,7,18, I. Herynekac, M. Hildebrandtak,M. Hilgersaj, K.H. Hiller ai, J. Hladkýac, P. Hötingb, D. Hoffmannv, R. Horisbergeraf,

S. Hurlingj, M. Ibbotsonu, Ç. Isseverg, M. Jacquetz, M. Jaffrez, L. Janauscheky,X. Janssend, V. Jemanovk, L. Jönssont, C. Johnsonc, D.P. Johnsond, M.A.S. Jonesr,

H. Jungt,j , D. Kants, M. Kapichineh, M. Karlssont, O. Karschnickk, F. Keil n,N. Kellerak, J. Kennedyr, I.R. Kenyonc, S. Kermichev, C. Kieslingy, P. Kjellbergt,

M. Klein ai, C. Kleinwortj, T. Klugea, G. Kniesj, B. Koblitz y, S.D. Kolyau, V. Korbelj,P. Kostkaai, S.K. Kotelnikovx, R. Koutouevl, A. Koutovh, H. Krehbielj, J. Krosebergak,

K. Krügerj, A. Küpperag, T. Kuhrk, T. Kurcap, R. Lahmannj, D. Lambc,

0370-2693/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PII: S0370-2693(01)01155-8

192 H1 Collaboration / Physics Letters B 520 (2001) 191–203

M.P.J. Landons, W. Langeai, T. Laštovickaad,ai, P. Laycockr, E. Lebaillyz, A. Lebedevx,B. Leißnera, R. Lemranij, V. Lendermanng, S. Levonianj, M. Lindstroemt, B. List aj,E. Lobodzinskaj,f , B. Lobodzinskif,j , A. Loginovw, N. Loktionovax, V. Lubimovw,

S. Lüdersaj, D. Lükeg,j , L. Lytkin l, H. Mahlke-Krügerj, N. Maldenu, E. Malinovskix,I. Malinovskix, R. Maraceky, P. Maraged, J. Marksm, R. Marshallu, H.-U. Martyna,

J. Martyniakf, S.J. Maxfieldr, D. Meeraj, A. Mehtar, K. Meiern, A.B. Meyerk,H. Meyerag, J. Meyerj, P.-O. Meyerb, S. Mikockif, D. Milsteadr, T. Mkrtchyanah,

R. Mohry, S. Mohrdieckk, M.N. Mondragong, F. Moreauaa, A. Morozovh,J.V. Morrise, K. Müller ak, P. Murínp,5, V. Nagovizinw, B. Naroskak, J. Naumanng,

Th. Naumannai, G. Nelleny, P.R. Newmanc, T.C. Nichollse, F. Niebergallk,C. Niebuhrj, O. Nixn, G. Nowakf, J.E. Olssonj, D. Ozerovw, V. Panassikh,

C. Pascaudz, G.D. Patelr, M. Peezv, E. Perezi, J.P. Phillipsr, D. Pitzlj , R. Pöschlz,I. Potachnikoval, B. Povhl, K. Rabbertza, G. Rädela, J. Rauschenbergerk, P. Reimerac,

B. Reiserty, D. Reynaj, C. Rislery, E. Rizvic, P. Robmannak, R. Roosend,A. Rostovtsevw, S. Rusakovx, K. Rybicki f, D.P.C. Sankeye, J. Scheinsa,

F.-P. Schillingj, P. Schleperj, D. Schmidtag, D. Schmidtj, S. Schmidty, S. Schmittj ,M. Schneiderv, L. Schoeffeli, A. Schöningaj, T. Schörnery, V. Schröderj,

H.-C. Schultz-Coulong, C. Schwanenbergerj, K. Sedlákac, F. Sefkowak, V. Shekelyany,I. Sheviakovx, L.N. Shtarkovx, Y. Siroisaa, T. Sloanq, P. Smirnovx, Y. Solovievx,

D. Southu, V. Spaskovh, A. Speckaaa, H. Spitzerk, R. Stameng, B. Stellaae, J. Stiewen,U. Straumannak, M. Swartn, M. Taševskýac, V. Tchernyshovw, S. Tchetchelnitskiw,

G. Thompsons, P.D. Thompsonc, N. Tobienj, D. Traynors, P. Truölak, G. Tsipolitisj,1,I. Tsurinai, J. Turnauf, J.E. Turneys, E. Tzamariudakiy, S. Udlufty, M. Urbanak,

A. Usik x, S. Valkárad, A. Valkárováad, C. Valléev, P. Van Mechelend, S. Vassilievh,Y. Vazdikx, A. Vichnevskih, K. Wackerg, R. Wallnyak, B. Waughu, G. Weberk,M. Webern, D. Wegenerg, C. Wernerm, M. Wernerm, N. Wernerak, G. Whiteq,

S. Wiesandag, T. Wilksenj, M. Windeai, G.-G. Winterj, Ch. Wissingg, M. Wobischj,E.-E. Woehrlingc, E. Wünschj, A.C. Wyattu, J. Žácekad, J. Zálešákad, Z. Zhangz,

A. Zhokinw, F. Zomerz, J. Zsemberyi, M. zur Neddenj

a I. Physikalisches Institut der RWTH, Aachen, Germany9

b III. Physikalisches Institut der RWTH, Aachen, Germany9

c School of Physics and Space Research, University of Birmingham, Birmingham, UK8

d Inter-University Institute for High Energies ULB-VUB, Brussels; Universitaire Instelling Antwerpen, Wilrijk; Belgium10

e Rutherford Appleton Laboratory, Chilton, Didcot, UK8

f Institute for Nuclear Physics, Cracow, Poland11

g Institut für Physik, Universität Dortmund, Dortmund, Germany9

h Joint Institute for Nuclear Research, Dubna, Russiai CEA, DSM/DAPNIA, CE-Saclay, Gif-sur-Yvette, France

j DESY, Hamburg, Germanyk II. Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany9

l Max-Planck-Institut für Kernphysik, Heidelberg, Germanym Physikalisches Institut, Universität Heidelberg, Heidelberg, Germany9

H1 Collaboration / Physics Letters B 520 (2001) 191–203 193

n Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg, Germany9

o Institut für experimentelle und Angewandte Physik, Universität Kiel, Kiel, Germanyp Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic12,13

q School of Physics and Chemistry, University of Lancaster, Lancaster, UK8

r Department of Physics, University of Liverpool, Liverpool, UK8

s Queen Mary and Westfield College, London, UK8

t Physics Department, University of Lund, Lund, Sweden14

u Physics Department, University of Manchester, Manchester, UK8

v CPPM, CNRS/IN2P3, Univ. Mediterranee, Marseille, Francew Institute for Theoretical and Experimental Physics, Moscow, Russia19

x Lebedev Physical Institute, Moscow, Russia12,15

y Max-Planck-Institut für Physik, München, Germanyz LAL, Université de Paris-Sud, IN2P3-CNRS, Orsay, France

aaLPNHE, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, Franceab LPNHE, Universités Paris VI and VII, IN2P3-CNRS, Paris, France

ac Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic12,16

ad Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic12,16

aeDipartimento di Fisica, Università di Roma Tre and INFN Roma 3, Roma, Italyaf Paul Scherrer Institut, Villigen, Switzerland

ag Fachbereich Physik, Bergische Universität Gesamthochschule Wuppertal, Wuppertal, Germanyah Yerevan Physics Institute, Yerevan, Armenia

ai DESY, Zeuthen, Germanyaj Institut für Teilchenphysik, ETH, Zürich, Switzerland17

ak Physik-Institut der Universität Zürich, Zürich, Switzerland17

Received 31 August 2001; accepted 20 September 2001Editor: W.-D. Schlatter

E-mail address:eckhard.elsen@desy.de (E. Elsen).1 Also at Physics Department, National Technical University, Zografou Campus, GR-15773 Athens, Greece.2 Also at Rechenzentrum, Bergische Universität Gesamthochschule Wuppertal, Germany.3 Also at Institut für Experimentelle Kernphysik, Universität Karlsruhe, Karlsruhe, Germany.4 Also at Dept. Fis. Ap. CINVESTAV, Mérida, Yucatán, México.5 Also at University of P.J. Šafárik, Košice, Slovak Republic.6 Also at CERN, Geneva, Switzerland.7 Also at Dept. Fis. CINVESTAV, México City, México.8 Supported by the UK Particle Physics and Astronomy Research Council, and formerly by the UK Science and Engineering Research

Council.9 Supported by the Bundesministerium für Bildung und Forschung, FRG, under contract numbers 05 H1 1GUA/1, 05 H1 1PAA/1, 05 H1

1PAB/9, 05 H1 1PEA/6, 05 H1 1VHA/7 and 05 H1 1VHB/5.10 Supported by FNRS-NFWO, IISN-IIKW.11 Partially supported by the Polish State Committee for Scientific Research, grant no. 2P0310318 and SPUB/DESY/P03/DZ-1/99, and by

the German Bundesministerium für Bildung und Forschung, FRG.12 Supported by the Deutsche Forschungsgemeinschaft.13 Supported by VEGA SR grant no. 2/1169/2001.14 Supported by the Swedish Natural Science Research Council.15 Supported by Russian Foundation for Basic Research grant no. 96-02-00019.16 Supported by the Ministry of Education of the Czech Republic under the projects INGO-LA116/2000 and LN00A006, by GA AVCR grant

no B1010005 and by GAUK grant no 173/2000.17 Supported by the Swiss National Science Foundation.18 Supported by CONACyT.19 Partially supported by Russian Foundation for Basic Research, grant no. 00-15-96584.

194 H1 Collaboration / Physics Letters B 520 (2001) 191–203

Abstract

A measurement is presented of the cross section forD∗± meson production in diffractive deep-inelastic scattering for the firsttime at HERA. The cross section is given for the processep→ eXY , where the systemX contains at least oneD∗± meson andis separated by a large rapidity gap from a low mass proton remnant systemY . The cross section is presented in the diffractivedeep-inelastic region defined by 2<Q2< 100 GeV2, 0.05< y < 0.7, xP < 0.04,MY < 1.6 GeV and|t |< 1 GeV2. TheD∗±mesons are restricted to the rangepT,D∗ > 2 GeV and|ηD∗ |< 1.5. The cross section is found to be 246±54±56 pb and formsabout 6% of the corresponding inclusiveD∗± cross section. The cross section is presented as a function of various kinematicvariables, includingzobs

Pwhich is an estimate of the fraction of the momentum of the diffractive exchange carried by the parton

entering the hard-subprocess. The data show a large component of the cross section at lowzobsP

where the contribution of theboson–gluon-fusion process is expected to dominate. The data are compared with several QCD-based calculations. 2001Elsevier Science B.V. All rights reserved.

1. Introduction

The observation of events with a large rapiditygap in the distribution of the final state hadrons atHERA [1] allows the nature of colour singlet exchangein strong interactions to be investigated. Colour singletexchange interactions have been successfully mod-elled [2] in terms of phenomenological Regge the-ory [3] and, at high energy, are attributed to diffractiveor pomeron exchange. HERA allows the partonic na-ture of diffraction to be investigated in deep-inelasticscattering (DIS) using the virtual photon as a probe.

The inclusive diffractive DIS structure functionFD2is directly sensitive to the quark content of the diffrac-tive exchange [4,5]. Information about the gluon con-tent can be inferred indirectly from scaling violations.However, the measurement of the hadronic final statein diffraction gives further, more direct, informationabout the gluon content [6–9]. The production of opencharm is expected to be particularly sensitive to thegluon content because studies in inclusive DIS revealthat the dominant contribution comes from the boson–gluon-fusion (BGF) mechanism [10]. The presence ofthe hard scale, provided by the charm quark mass, al-lows a variety of perturbative QCD-based models ofdiffraction to be tested.

This Letter describes the measurement of diffractiveopen charm production in DIS at HERA, which wasperformed using the H1 detector. Measurements of thetotalD∗± cross section and of differential distributionswhich explore the dynamics of diffractive charmproduction are presented. The ratio of the diffractive

D∗± cross section to the inclusiveD∗± cross sectionis also measured.

The Letter is organised as follows. The kinematicsof diffractive DIS are introduced in Section 2. Thedifferent theoretical approaches to diffractive charmproduction are summarised in Section 3. In Section 4,the H1 detector, the data selection, the cross sectionmeasurement procedure and the evaluation of thesystematic uncertainties are explained. The results, inthe form of the total and differential cross sections arepresented and discussed in Section 5.

2. Kinematics

The process studied in this Letter isep→ eXY →e(D∗±X′)Y and is shown in Fig. 1. The positronproduces a virtual photonγ � (with four-momentumq)which interacts with the proton (with four-momentumP ). If the interaction takes place via colour singletexchange, the photon and proton dissociate into twodistinct hadronic systemsX and Y , with invariantmassesMX andMY , respectively. The systemY isthat which is closest to the outgoing proton direction.In the case whereM

XandM

Yare small compared

with the photon–proton centre of mass energyW , thetwo systems are separated by a large rapidity gap. Inaddition to the standard DIS kinematic variablesQ2,y and Bjorkenx the following variables are defined

xP = q · (P − pY )q · P ,

t = (P − pY )2,

H1 Collaboration / Physics Letters B 520 (2001) 191–203 195

Fig. 1. The process under study in this article isep → eXY →e(D∗±X′)Y . The positron (e) couples to a photon (γ �) whichinteracts with the proton (p) via colour singlet exchange, producingtwo distinct final state hadronic systemsX andY . The systemsXandY are separated by the largest gap in rapidity in the final statehadrons.

(1)β = Q2

2q · (P − pY ) = x

xP

,

where pY is the four-momentum ofY . The quan-tity xP may be interpreted as the longitudinal mo-mentum fraction, with respect to the incoming pro-ton, of the colourless exchange andt is the squaredfour-momentum transferred at the proton vertex. In theanalysis presented in this Letter,t andM

Yare con-

strained to be small by the experimental selection andare integrated over implicitly.

In a QCD interpretation in which a partonic struc-ture is ascribed to the colourless exchange the low-est order (i.e.,O(α0

s )) contribution to the diffractivecross section in the proton infinite momentum frame isquark scattering (γ �q → q). In this caseβ can be in-terpreted as the fractional longitudinal momentum ofthe exchange carried by the struck quark. TheO(αs)contributions are the BGF (γ �g → qq) and QCD-Compton (γ �q → qg) processes. In theO(αs) casethe invariant mass squareds of the partons emergingfrom the hard subprocess is non-zero. Therefore, thequantityzP is introduced

(2)zP = β ·(

1+ s

Q2

)

which corresponds to the longitudinal momentumfraction of the colourless exchange carried by the par-ton (quark or gluon) which enters the hard interaction.

3. Models of diffractive D∗± production

A detailed description of the models used in thisLetter is given in [9]. A brief summary focusing onthe production of open charm in each of the modelsis given here. For ease of comparison with the data inthis Letter the models are divided into three groups:the ‘resolved pomeron’ model, ‘2-gluon exchange’models and ‘soft colour neutralisation’ models.

In the ‘resolved pomeron’ model [11] the diffrac-tive cross section factorises into deep-inelastic scatter-ing from the pomeron and a pomeron flux factor, moti-vated by Regge theory, which describes the probabilityfor finding a pomeron in the proton. Within this pic-ture, the partonic content of the pomeron has been de-termined by QCD analyses of HERA diffractive data[4,12]. The parton distributions, obtained from fits tothe data, contain a dominant gluon distribution. Opencharm is produced in the resolved pomeron model bythe BGF process, where the photon interacts with agluon of the pomeron carrying a fractionzP of thepomeron longitudinal momentum.

In ‘2-gluon exchange’ models diffractive DIS isstudied in the proton rest frame by consideringqq andqqg photon fluctuations as colour dipoles scatteringoff the proton. Open charm can be produced when thephoton fluctuates intocc or ccg states. The simplestrealisation of net colour singlet exchange betweenthese partonic fluctuations and the proton at the par-ton level is a pair of gluons with opposite colour [13].In perturbative QCD, the cross section for 2-gluon ex-change is related to the square of thekT -unintegratedgluon density of the protonF(x, k2

T ) [14,15], wherekT is the parton transverse momentum relative to theproton direction. In the ‘saturation’ model [16] the cal-culation of theqqg cross section is made under the as-sumption of strongkT ordering of the final state par-tons, wherek(g)T � k

(q,q)

T . In an alternative approach[17,18] (hereafter referred to as ‘BJLW’) the calcu-lation of theqqg final state includes configurationswithout strongkT ordering. In this model all outgoingpartons are required to have highkT and the minimumvalue for the final state gluon transverse momentumkcutT ,g is a free parameter which can be tuned to describe

the data. The 2-gluon exchange calculations are per-formed under the assumption of lowxP (xP < 0.01)

196 H1 Collaboration / Physics Letters B 520 (2001) 191–203

to avoid contributions from secondary reggeon ex-changes which correspond to quark exchange in themodels.

In ‘soft colour neutralisation’ models an alterna-tive approach to diffractive DIS is given which leadsto very similar properties of inclusive and diffractiveDIS final states. In the soft colour interaction model(SCI) [19], open charm is produced via BGF from thegluon distribution of the proton. It is then assumed thatthe partons produced in the hard interactions can ex-change soft gluons with the background colour field ofthe incoming proton leaving all momenta unchanged.Large rapidity gap events may be produced this waywhen the soft interactions lead to a net colour singletexchange. The probability for soft colour exchangeis assumed to be independent of the kinematics ofthe hard scattering process. The generalised area law(GAL) [20] approach is a modification of the Lundstring model [21]. The production mechanism for opencharm is similar to that in the SCI model except thatit is formulated in terms of interactions between thecolour strings connecting the partons in an event. Inthis model the probability for a soft colour interac-tion is not constant but is exponentially suppressed bythe difference between the areas in momentum spacespanned by the strings before and after the colour re-arrangement. The ‘semi-classical’ model [22] is a non-perturbative model based on the dipole approach. Inthe proton rest frame the photon fluctuations scatteroff a superposition of soft colour fields representingthe proton. In this approach, theqqg fluctuation is ex-pected to be dominant for open charm production [23].If the gluon is the lowestkT parton, then the contribu-tion can be related to BGF in the proton infinite mo-mentum frame.

Comparison of the data with the ‘resolved pomeron’,the ‘2-gluon exchange’ and the ‘semi-classical’ mod-els is facilitated by their implementation within theRAPGAP Monte Carlo generator [24]. The predic-tions of the SCI and GAL models are calculated us-ing the AROMA Monte Carlo generator [25]. Thecross section predictions in this Letter are all calcu-lated assuming a charm quark massmc = 1.5 GeV.For the hadronisation fractionf (c→D∗±) the value0.233± 0.010± 0.011 [26] is used. The momentumfraction of the charm quark carried by theD∗± is cal-culated using the Peterson et al. model [27] with thefragmentation parameterε = 0.078.

4. Experimental procedure

The data presented in this analysis were collectedover the years 1996 and 1997, when HERA collidedpositrons with energyEe = 27.5 GeV with protons ofenergyEp = 820 GeV. Requiring all essential detectorcomponents to be operational the available integratedluminosity is 19.1 pb−1. Further details of this analysisbeyond those given here can be found in [28].

4.1. The H1 detector

A short overview of the detector components mostrelevant for the present analysis is given here. A de-tailed description of the H1 detector can be foundin [29]. The z-axis of the H1 detector is taken alongthe beam direction such that positivez values refer tothe direction of the outgoing proton beam, referred toas the ‘forward’ direction.

Charged particles emerging from the interactionregion are measured by the central tracking device(CTD) in the range−1.5 < η < 1.5.20 The CTDcomprises two large cylindrical central jet drift cham-bers (CJC) and twoz chambers situated concentricallyaround the beam-line within a solenoidal magneticfield of 1.15 T. The resolution achieved by the CTDis σ(pT )/pT 0.01pT /GeV. The CTD also providestriggering information based on track segments in ther–φ plane from the CJC and the position of the ver-tex using a double layer of multi-wire proportionalchambers (MWPC). The energies of final state parti-cles are measured in the Liquid Argon (LAr) calorime-ter which surrounds the tracking chambers and cov-ers the range−1.5< η < 3.4. The backward region(−4.0< η < −1.4) is covered by a lead-scintillatingfibre calorimeter (SPACAL [30]) with electromagneticand hadronic sections. In front of the SPACAL, theBackward Drift Chamber (BDC) [31] provides tracksegments of charged particles.

Detectors close to the beam pipe in the directionof the outgoing proton are used in the selection oflarge rapidity gap events. These are the Forward MuonDetector (FMD), the Proton Remnant Tagger (PRT)and the Plug calorimeter (PLUG). The FMD is located

20 The pseudorapidityη of an object detected with polar angleθis defined asη= − ln tan(θ/2).

H1 Collaboration / Physics Letters B 520 (2001) 191–203 197

at z = 6.5 m and covers the pseudorapidity range1.9 < η < 3.7 directly. The PLUG allows energymeasurements to be made over the range 3.5< η <5.5. Particles produced at largerη can also be detectedbecause of secondary scattering with the beam-pipe.The PRT, a set of scintillators surrounding the beampipe atz= 26 m, can tag hadrons in the region 6.0 �η� 7.5.

4.2. Event selection

The events were triggered by an electromagneticenergy cluster in the SPACAL, in coincidence witha charged track signal from both the MWPC andthe CJC. The positrons are identified in the SPACALas clusters with energyE′

e > 9 GeV which haveproperties consistent with electromagnetic deposition,and for which the centre of gravity of the clustermatches a charged track segment in the BDC to within2.5 cm. The selected events are also required to havea reconstructed vertex from the CTD within±35 cmof the nominal vertex. In order to suppress eventswith initial state photon radiation the summedE − pzof the event calculated using all reconstructed finalstate particles, including the positron, is required tobe greater than 35 GeV. The kinematic region coveredby the measurement is 2< Q2 < 100 GeV2 and0.05< y < 0.7. To minimise the correction due toQED radiative effects,Q2, y andx are reconstructedfrom the energy and angleθ ′ of the scattered positronand the hadronic final state using the ‘) method’ [32].

Diffractive events are selected experimentally bythe absence of activity in the outgoing proton region.No signal above noise thresholds is allowed in theFMD, the PRT, the PLUG and the most forward part(η > 3.3) of the LAr calorimeter. This ensures thatthere is a large rapidity gap covering at least 3.3< η�7.5 between the photon dissociation systemX and theproton remnant systemY . Monte Carlo studies showthat the absence of particles in the detectors close tothe beam pipe restricts the mass of the proton remnantsystem toMY < 1.6 GeV and the momentum transferto the proton to|t|< 1 GeV2.

The four-momentum of the systemX, which is wellcontained in the central detector, is reconstructed us-ing information from the LAr and SPACAL calorime-ters together with the CJC [33]. The variablexP is cal-

culated from

(3)xP =∑X+e′(E + pz)

2Ep,

where E and pz are the energy and longitudinalmomentum of each final state particle in the laboratoryframe, and the sum runs over the scattered positrone′and all detected particles in the photon dissociationsystemX. The quantityβ is calculated fromβ =x/xP. The cross section is restricted to the rangexP <

0.04 to suppress contributions from non-diffractivescattering and secondary reggeon exchanges.

In this Letter an hadronic observablezobsP

is con-structed which is analogous toxobs

g for inclusiveD∗±production which was measured in [34]. In the re-solved pomeron picturezobs

Pis an approximation to the

momentum fractionzP of the pomeron carried by theinteracting gluon (see Eq. (2)). The observablezobs

Pis

defined as

(4)zobsP

= M2cc +Q2

M2X

+Q2 ,

whereM2cc is a hadron level estimate ofs which is

constructed from the scattered positron and theD∗±meson in an identical manner to that used for thegluon momentum fractionxobs

g in [34]. Monte Carlosimulations show that the resolution in the hadronicvariablezobs

Pis approximately 30%, and that there is

a good correlation betweenzobsP

andzP as calculatedfrom the kinematics of the outgoing partons. Thevariablezobs

Pcan be interpreted as the fraction of the

energy of the systemX which is carried by thecc pairemerging from the hard scattering.

4.3. Reconstruction ofD∗± mesons

TheD∗± mesons are reconstructed using theD∗± −D0 mass difference method [35] in the decay channel

(5)D∗± →D0π+slow → (

K−π+)π+

slow(+c.c.),

which has a branching fraction of 2.59% [36]. Thereconstruction method is detailed in [37]. The decayproducts are detected in the CTD and are required tohave a transverse momentumpT of at least 140 MeVfor theπslow and 250 MeV for both theK andπ .

The invariant mass of theKπ combination has to beconsistent with theD0 mass within±80 MeV. After

198 H1 Collaboration / Physics Letters B 520 (2001) 191–203

Fig. 2. Distribution of the mass difference,M = M(K∓π±π±

slow) − M(K∓π±), with a curve fitted to the forma(,M −Mπ)

b+ Gaussian.

cuts on the direction (|η(Kππ)|< 1.5) and transversemomentum (pT (Kππ) > 2 GeV), the mass differencedistribution,M =M(Kππslow)−M(Kπ) is plottedin Fig. 2. The number ofD∗± candidates is determinedby fitting the histogram in Fig. 2 with a Gaussiandistribution for the signal plus a background functiona(,M − Mπ)

b, whereMπ denotes the mass of thepion. The position and width of the Gaussian arefixed to values taken from a higher statistics sampleof events where no diffractive cuts were applied [37].The normalisation of the Gaussian and the backgroundparametersa andb are allowed to vary. The resultingnumber of detectedD∗± mesons is 46± 10.

4.4. Cross section measurement

Monte Carlo simulations are used to correct the datafor the effects of losses and migrations due to the fi-nite resolution of the H1 detector. The efficiency iscalculated by running the H1 detector simulation pro-gram on a sample ofD∗± events from the diffractiveMonte Carlo generator RAPGAP [24] in the resolvedpomeron mode with thet dependence of the cross sec-tion parameterised ase−6|t |. The RAPGAP programis used to model events which contain an elastic pro-ton (MY = mp) in the kinematic rangexP < 0.1. Mi-grations fromxP > 0.1 or from large values ofMY(MY > 5 GeV) are modelled by using a simulation ofthe heavy quark generator AROMA [25] in the inclu-

sive mode. The contribution is of the order 5% to theselected sample of events. An additional correction of−8%± 6% is applied to account for the net smearingacross theM

Y= 1.6 GeV boundary. Since only elas-

tically scattered protons have been simulated in RAP-GAP, this correction is evaluated using the proton dis-sociation simulation in the DIFFVM [38] generator.21

A further correction of+4%± 1% takes into accountdiffractive events rejected due to fluctuations in thenoise level in the FMD. This correction is estimateddirectly from the data, using a sample of randomly se-lected events, not correlated with a physics trigger. Anadditional source of background is the contribution ofreflections in theD0 mass window, coming fromD0

channels other than that defined in Eq. (5). They areestimated, from simulations using the AROMA MonteCarlo, to be 3.5% [28]. The contribution from photo-production background is found to be negligible. QEDradiative corrections were calculated to be approxi-mately 2% using the RAPGAP program interfaced toHERACLES [39].

4.5. Systematic uncertainties

The following sources of systematic error are takeninto account

• The uncertainty in the physics model forD∗± pro-duction used to compute the efficiency correctionsis estimated by varying the shapes of the kinematicdistributions in the simulations beyond the limitsimposed by previous measurements or the presentdata. This is done by reweighting thexP distribu-tion to that observed in data; theβ distribution by(1 ± 0.3β) and thet distribution bye±2t . The re-sulting systematic uncertainties on the cross sectionmeasurements range between 10% and 20% withthe largest contribution originating from the vari-ation of thexP distribution. The uncertainties areverified using simulations of models with differentunderlying kinematic distributions.

• The total uncertainty due to the reconstructionefficiency, mass and momentum resolution of thecentral tracker for the three tracks was estimated in

21 For the correction, it is assumed that the ratio of diffractiveproton elastic to diffractive proton dissociative interactions is 1: 1.

H1 Collaboration / Physics Letters B 520 (2001) 191–203 199

the analysis of the inclusive DISD∗± cross sectionto be+9%

−4% [37].• An error of 8% is found by varying the details of the

fitting procedure used to obtain the number ofD∗±mesons.

• The uncertainty in the correction due to the smear-ing of events across the boundaryMY = 1.6 GeVis estimated by varying in the DIFFVM simulation:the efficiency of the forward detectors, the assumedMY

distribution, the ratio of double to single disso-ciation between 0.5 and 2 and the assumedt depen-dence for double dissociation. This contributes 6%to the systematic error.

• The uncertainty in the trigger efficiency gives acontribution of 5% to the systematic error.

• The uncertainty due to the assumed charm fragmen-tation scheme is estimated by using parameterisa-tions of the Peterson model and the standard Lundstring model in JETSET [21]. This leads to an aver-age uncertainty of 5% in the cross sections.

• The uncertainty in the correction due to QEDradiative effects is estimated as 3%.

• The number of events migrating into the samplefrom xP > 0.1 orMY > 5 GeV is varied by±50%,leading to an average systematic error of 3%.Other sources of systematic error are the uncertaintyin the measured energy and angle of the scatteredpositron, uncertainties in the hadronic energy scaleof the liquid argon and SPACAL calorimeters,the uncertainty in the luminosity measurement,the uncertainty on the fraction of events lost dueto noise in the FMD and the uncertainty in thebranching ratio for the measured decay channel.Each of them is responsible for an error of no morethan 2.5%.

The total systematic error for each point has beenobtained by adding all individual contributions inquadrature. It ranges between 20% and 30% andfor most data points is similar in magnitude to thestatistical error.

5. Results

The total D∗± production cross section for thekinematic region 2< Q2 < 100 GeV2, 0.05< y <0.7,xP < 0.04,MY < 1.6 GeV,|t|< 1 GeV2,pT,D∗ >

2 GeV and|ηD∗ |< 1.5 is

σ(ep→ e

(D∗±X′)Y )

(6)= 246± 54 (stat.)± 56 (syst.) pb.

The ratio of the diffractiveD∗± cross section tothe inclusiveD∗± cross section measured in the samekinematic range defined in terms ofQ2, y, pT,D∗ andηD∗ is found to be

(7)5.9± 1.1 (stat.)± 1.1 (syst.)%,

where the inclusiveD∗± cross section has been deter-mined as in [37]. The error in the ratio is dominatedby the uncertainties pertaining to the measurement ofthe diffractive cross section.

In Table 1 the total cross section is compared withsome of the phenomenological models discussed inSection 3. The first three rows of Table 1 show the pre-dictions for the cross section for three different sets ofparton parameterisations within the resolved pomeronmodel. The first two predictions are based on the par-ton distributions of the pomeron and sub-leading ex-change from the leading order DGLAP analysis ofFD2from H1 [4]. The ‘ACTW fit D’ parameterisation isthe best combined fit in [12] to H1 and ZEUSFD2data and ZEUS diffractive dijet data. All three sets ofparton parameterisations give acceptable descriptionsof FD2 . All of the predictions using the three partonparameterisations exceed the data although the para-meterisation with the flat gluon distribution (‘H1 fit2’) is closest. The predictions shown are calculated

Table 1The predictions for the total diffractiveD∗± cross section fortwo groups of models: the resolved pomeron and soft colourneutralisation approaches. The bottom row shows the cross sectionmeasured in the data

Model Cross section (pb)

Resolved H1 fit 2 368

pomeron H1 fit 3 433

ACTW fit D 481

Soft colour SCI 203

neutralisation GAL 328

semi-classical 196

H1 Data 246± 54 (stat.)± 56 (syst.)

200 H1 Collaboration / Physics Letters B 520 (2001) 191–203

Fig. 3. Cross sectionsσ(ep → e(D∗±X′)Y ) as a function of (a)xP; (b) log10β and (c)zobsP

. The data are points with error bars (inner:statistical, outer: total). Each distribution is plotted three times to allow comparison with the three groups of models described in the text.

with the factorisation and renormalisation scales set toµ2 ≡ µ2

f ≡ µ2r =Q2 +p2

T +4m2c . Changing this scale

to p2T + 4m2

c produces an increase of around 20% inthe predicted cross sections. Similarly, the variation ofthe charm quark mass by±0.1 GeV leads to an un-certainty of∓10% in the cross sections. Changingεin the Peterson model from 0.078 to 0.035 and to 0.1produces an uncertainty in the cross section predic-tions of +15

−5 %. The values shown in the table are cal-culated withΛQCD = 0.20 GeV and the number of ac-tive quark flavours in the first order expression forαsis Nf = 4. SelectingΛQCD = 0.25 GeV andNf = 5

leads to an increase of about 10% in the cross sections.The contribution ofD∗± production from meson ex-change in the predictions is less than 7%.

The cross section predictions from the semi-classical,SCI and GAL models are also shown in Table 1 andare in agreement with the data. However, none ofthese models can simultaneously reproduce the shapesand normalisations of the differential dijet cross sec-tions [9]. The semi-classical model prediction was cal-culated using the same factorisation scale as for the re-solved pomeron model. The SCI and GAL model pre-dictions useµ2 =Q2 + 2p2

T + 2m2c . For each of the

H1 Collaboration / Physics Letters B 520 (2001) 191–203 201

Fig. 4. Cross sectionsσ(ep→ e(D∗±X′)Y ) as a function of (a) log10Q2; (b) p∗

T ,D∗ and (c)ηD∗ . The data are points with error bars (inner:statistical, outer: total). Each distribution is plotted twice to allow comparison with two of the groups of models described in the text.

three models, the uncertainty in the predictions due tothe variation of the factorisation scale,mc andε aresimilar to those for the resolved pomeron model.

Differential cross sections are shown in Figs. 3and 4. They represent average values over the intervalsshown in the figures.

In Fig. 3 the cross section is shown as a function ofxP, log10β andzobs

Pand compared to the QCD-based

models described in Section 3. The cross sections dif-ferential inxP and log10β are flat within experimentalerrors. Fig. 3 shows that about 60% of charm produc-tion is in the regionzobs

P< 0.2 where the contribution

of the BGF process is expected to dominate.

The discrepancy between the resolved pomeronmodel predictions and the data is pronounced in thelow xP, high β and highzobs

Pregions which are all

correlated with low values ofMX

. Of the three partonparameterisations the calculations which use ‘H1 fit 2’are shown to come closest to the data in this region. Allthree parameterisations are consistent with the data inthe highM

Xregion.

The two gluon exchange models, directly applicablein the lowxP region (xP < 0.01) are also compared tothe data in Fig. 3. The sensitivity of this measurementto the value of the transverse momentum cut-offkcut

T ,g

of the gluon in theqqg state within the BJLW model

202 H1 Collaboration / Physics Letters B 520 (2001) 191–203

is also studied. Calculations which use cut-off valuesof 1.0 GeV and 1.5 GeV both give a fair descriptionof the data in the lowMX region (i.e., the lowxP,high β , high zobs

Pdomain). These data also offer

sensitivity to the relative contribution of the scatteringof the qq fluctuation, which is shown as a shadedzone, and forms a sizeable component of the total twogluon exchange cross section. The saturation modelreproduces reasonably well the normalisation of thedata in the lowxP range, in which it is expected to beapplicable, but also provides a good description of thedata in the remaining region of phase space.

The semi-classical model gives a good descriptionof the distributions shown in Fig. 3. Both the SCI andGAL models provide a satisfactory description of thespectra although the GAL model tends to overestimatethe data in the lowM

Xdomain.

In Fig. 4, theD∗± cross section is plotted differen-tially at 2 values of log10Q

2, p∗T ,D∗ andηD∗ , where

p∗T ,D∗ is the transverse momentum of theD∗± in theγ ∗p centre of mass system. The data tend to fall offwith higher values of each of these variables.

Since these distributions are integrated over thefull xP range of this measurement, a comparison ismade only with resolved pomeron calculations andsoft colour neutralisation models. Both sets of modelsprovide a reasonable description of the data.

6. Conclusion

The dynamics of open diffractive charm produc-tion in DIS have been studied for the first time atHERA. The totalD∗± production cross section inthe kinematic range 2< Q2 < 100 GeV2, 0.05<y < 0.7, xP < 0.04,MY < 1.6 GeV, |t| < 1 GeV2,pT,D∗ > 2 GeV and|ηD∗ |< 1.5 has been found to be246± 54 (stat.)± 56 (syst.) pb. In the studied regionabout 6% of the totalD∗± cross section is produceddiffractively.

The cross section has been measured as a functionof xP, log10β , zobs

P, log10Q

2, p∗T ,D∗ and ηD∗ . The

data show a sizeable component of charm productionin the low zobs

Pregion which is suggestive of the

dominance of the contribution from the boson–gluon-fusion process.

A number of QCD-based models which give a gooddescription of the inclusive diffractive cross section

were compared with the measurement. A reasonabledescription of the data is provided by a model basedon the resolved pomeron picture using various as-sumptions for the partonic composition of the colour-less exchange. A parton parameterisation containinga flat gluon dependence (‘H1 fit 2’) comes closest tothe data. Predictions of two gluon exchange processeswere found to match the data in the lowxP region.Soft colour neutralisation models give a satisfactorydescription of the data.

Acknowledgements

We are grateful to the HERA machine group whoseoutstanding efforts have made and continue to makethis experiment possible. We thank the engineers andtechnicians for their work in constructing and nowmaintaining the H1 detector, our funding agenciesfor financial support, the DESY technical staff forcontinual assistance and the DESY directorate forthe hospitality which they extend to the non DESYmembers of the collaboration.

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