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DESY 01-105 ISSN 0418-9833July 2001

D∗± Meson Production in Deep–Inelastic Diffractive

Interactions at HERA

H1 Collaboration

Abstract

A measurement is presented of the cross section forD∗± meson production in diffractivedeep–inelastic scattering for the first time at HERA. The cross section is given for theprocessep → eXY , where the systemX contains at least oneD∗± meson and is separatedby a large rapidity gap from a low mass proton remnant systemY . The cross sectionis presented in the diffractive deep–inelastic region defined by 2 < Q2 < 100 GeV2,0.05 < y < 0.7, xIP < 0.04, MY < 1.6 GeV and |t| < 1 GeV2. TheD∗± mesons arerestricted to the rangepT,D∗ > 2 GeV and|ηD∗ | < 1.5. The cross section is found to be246 ± 54 ± 56 pb and forms about6% of the corresponding inclusiveD∗± cross section.The cross section is presented as a function of various kinematic variables, includingzobs

IP

which is an estimate of the fraction of the momentum of the diffractive exchange carriedby the parton entering the hard-subprocess. The data show a large component of the crosssection at lowzobs

IP where the contribution of the Boson–Gluon–Fusion process is expectedto dominate. The data are compared with several QCD–based calculations.

Submitted toPhys. Lett. B.

C. Adloff33, V. Andreev24, B. Andrieu27, T. Anthonis4, V. Arkadov35, A. Astvatsatourov35,A. Babaev23, J. Bahr35, P. Baranov24, E. Barrelet28, W. Bartel10, P. Bate21, J. Becker37,A. Beglarian34, O. Behnke13, C. Beier14, A. Belousov24, T. Benisch10, Ch. Berger1,T. Berndt14, J.C. Bizot26, J. Boehme, V. Boudry27, W. Braunschweig1, V. Brisson26,H.-B. Broker2, D.P. Brown10, W. Bruckner12, D. Bruncko16, J. Burger10, F.W. Busser11,A. Bunyatyan12,34, A. Burrage18, G. Buschhorn25, L. Bystritskaya23, A.J. Campbell10,J. Cao26, S. Caron1, F. Cassol-Brunner22, D. Clarke5, B. Clerbaux4, C. Collard4,J.G. Contreras7,41, Y.R. Coppens3, J.A. Coughlan5, M.-C. Cousinou22, B.E. Cox21,G. Cozzika9, J. Cvach29, J.B. Dainton18, W.D. Dau15, K. Daum33,39, M. Davidsson20,B. Delcourt26, N. Delerue22, R. Demirchyan34, A. De Roeck10,43, E.A. De Wolf4,C. Diaconu22, J. Dingfelder13, P. Dixon19, V. Dodonov12, J.D. Dowell3, A. Droutskoi23,A. Dubak25, C. Duprel2, G. Eckerlin10, D. Eckstein35, V. Efremenko23, S. Egli32, R. Eichler36,F. Eisele13, E. Eisenhandler19, M. Ellerbrock13, E. Elsen10, M. Erdmann10,40,e, W. Erdmann36,P.J.W. Faulkner3, L. Favart4, A. Fedotov23, R. Felst10, J. Ferencei10, S. Ferron27,M. Fleischer10, Y.H. Fleming3, G. Flugge2, A. Fomenko24, I. Foresti37, J. Formanek30,G. Franke10, E. Gabathuler18, K. Gabathuler32, J. Garvey3, J. Gassner32, J. Gayler10,R. Gerhards10, C. Gerlich13, S. Ghazaryan4,34, L. Goerlich6, N. Gogitidze24, M. Goldberg28,C. Grab36, H. Grassler2, T. Greenshaw18, G. Grindhammer25, T. Hadig13, D. Haidt10,L. Hajduk6, J. Haller13, W.J. Haynes5, B. Heinemann18, G. Heinzelmann11,R.C.W. Henderson17, S. Hengstmann37, H. Henschel35, R. Heremans4, G. Herrera7,44,I. Herynek29, M. Hildebrandt37, M. Hilgers36, K.H. Hiller35, J. Hladky29, P. Hoting2,D. Hoffmann22, R. Horisberger32, S. Hurling10, M. Ibbotson21, C. Issever7, M. Jacquet26,M. Jaffre26, L. Janauschek25, X. Janssen4, V. Jemanov11, L. Jonsson20, C. Johnson3,D.P. Johnson4, M.A.S. Jones18, H. Jung20,10, D. Kant19, M. Kapichine8, M. Karlsson20,O. Karschnick11, F. Keil14, N. Keller37, J. Kennedy18, I.R. Kenyon3, S. Kermiche22,C. Kiesling25, P. Kjellberg20, M. Klein35, C. Kleinwort10, T. Kluge1, G. Knies10, B. Koblitz25,S.D. Kolya21, V. Korbel10, P. Kostka35, S.K. Kotelnikov24, R. Koutouev12, A. Koutov8,H. Krehbiel10, J. Kroseberg37, K. Kruger10, A. Kupper33, T. Kuhr11, T. Kurca16, R. Lahmann10,D. Lamb3, M.P.J. Landon19, W. Lange35, T. Lastovicka30,35, P. Laycock18, E. Lebailly26,A. Lebedev24, B. Leißner1, R. Lemrani10, V. Lendermann7, S. Levonian10, M. Lindstroem20,B. List36, E. Lobodzinska10,6, B. Lobodzinski6,10, A. Loginov23, N. Loktionova24,V. Lubimov23, S. Luders36, D. Luke7,10, L. Lytkin12, H. Mahlke-Kruger10, N. Malden21,E. Malinovski24, I. Malinovski24, R. Maracek25, P. Marage4, J. Marks13, R. Marshall21,H.-U. Martyn1, J. Martyniak6, S.J. Maxfield18, D. Meer36, A. Mehta18, K. Meier14,A.B. Meyer11, H. Meyer33, J. Meyer10, P.-O. Meyer2, S. Mikocki6, D. Milstead18,T. Mkrtchyan34, R. Mohr25, S. Mohrdieck11, M.N. Mondragon7, F. Moreau27, A. Morozov8,J.V. Morris5, K. Muller37, P. Murın16,42, V. Nagovizin23, B. Naroska11, J. Naumann7,Th. Naumann35, G. Nellen25, P.R. Newman3, T.C. Nicholls5, F. Niebergall11, C. Niebuhr10,O. Nix14, G. Nowak6, J.E. Olsson10, D. Ozerov23, V. Panassik8, C. Pascaud26, G.D. Patel18,M. Peez22, E. Perez9, J.P. Phillips18, D. Pitzl10, R. Poschl26, I. Potachnikova12, B. Povh12,K. Rabbertz1, G. Radel1, J. Rauschenberger11, P. Reimer29, B. Reisert25, D. Reyna10,C. Risler25, E. Rizvi3, P. Robmann37, R. Roosen4, A. Rostovtsev23, S. Rusakov24, K. Rybicki6,D.P.C. Sankey5, J. Scheins1, F.-P. Schilling10, P. Schleper10, D. Schmidt33, D. Schmidt10,S. Schmidt25, S. Schmitt10, M. Schneider22, L. Schoeffel9, A. Schoning36, T. Schorner25,V. Schroder10, H.-C. Schultz-Coulon7, C. Schwanenberger10, K. Sedlak29, F. Sefkow37,V. Shekelyan25, I. Sheviakov24, L.N. Shtarkov24, Y. Sirois27, T. Sloan17, P. Smirnov24,

1

Y. Soloviev24, D. South21, V. Spaskov8, A. Specka27, H. Spitzer11, R. Stamen7, B. Stella31,J. Stiewe14, U. Straumann37, M. Swart14, M. Tasevsky29, V. Tchernyshov23,S. Tchetchelnitski23, G. Thompson19, P.D. Thompson3, N. Tobien10, D. Traynor19, P. Truol37,G. Tsipolitis10,38, I. Tsurin35, J. Turnau6, J.E. Turney19, E. Tzamariudaki25, S. Udluft25,M. Urban37, A. Usik24, S. Valkar30, A. Valkarova30, C. Vallee22, P. Van Mechelen4,S. Vassiliev8, Y. Vazdik24, A. Vichnevski8, K. Wacker7, R. Wallny37, B. Waugh21, G. Weber11,M. Weber14, D. Wegener7, C. Werner13, M. Werner13, N. Werner37, G. White17, S. Wiesand33,T. Wilksen10, M. Winde35, G.-G. Winter10, Ch. Wissing7, M. Wobisch10, E.-E. Woehrling3,E. Wunsch10, A.C. Wyatt21, J.Zacek30, J. Zalesak30, Z. Zhang26, A. Zhokin23, F. Zomer26,J. Zsembery9, and M. zur Nedden10

1 I. Physikalisches Institut der RWTH, Aachen, Germanya

2 III. Physikalisches Institut der RWTH, Aachen, Germanya

3 School of Physics and Space Research, University of Birmingham, Birmingham, UKb4 Inter-University Institute for High Energies ULB-VUB, Brussels; Universitaire InstellingAntwerpen, Wilrijk; Belgiumc5 Rutherford Appleton Laboratory, Chilton, Didcot, UKb

6 Institute for Nuclear Physics, Cracow, Polandd

7 Institut fur Physik, Universitat Dortmund, Dortmund, Germanya

8 Joint Institute for Nuclear Research, Dubna, Russia9 CEA, DSM/DAPNIA, CE-Saclay, Gif-sur-Yvette, France10 DESY, Hamburg, Germany11 II. Institut fur Experimentalphysik, Universitat Hamburg, Hamburg, Germanya

12 Max-Planck-Institut fur Kernphysik, Heidelberg, Germany13 Physikalisches Institut, Universitat Heidelberg, Heidelberg, Germanya

14 Kirchhoff-Institut fur Physik, Universitat Heidelberg, Heidelberg, Germanya

15 Institut fur experimentelle und Angewandte Physik, Universitat Kiel, Kiel, Germany16 Institute of Experimental Physics, Slovak Academy of Sciences, Kosice, Slovak Republice,f

17 School of Physics and Chemistry, University of Lancaster, Lancaster, UKb18 Department of Physics, University of Liverpool, Liverpool, UKb

19 Queen Mary and Westfield College, London, UKb

20 Physics Department, University of Lund, Lund, Swedeng

21 Physics Department, University of Manchester, Manchester, UKb

22 CPPM, CNRS/IN2P3 - Univ Mediterranee, Marseille - France23 Institute for Theoretical and Experimental Physics, Moscow, Russial24 Lebedev Physical Institute, Moscow, Russiae,h

25 Max-Planck-Institut fur Physik, Munchen, Germany26 LAL, Universite de Paris-Sud, IN2P3-CNRS, Orsay, France27 LPNHE, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France28 LPNHE, Universites Paris VI and VII, IN2P3-CNRS, Paris, France29 Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republice,i

30 Faculty of Mathematics and Physics, Charles University, Praha, Czech Republice,i

31 Dipartimento di Fisica Universita di Roma Tre and INFN Roma 3, Roma, Italy32 Paul Scherrer Institut, Villigen, Switzerland33 Fachbereich Physik, Bergische Universitat Gesamthochschule Wuppertal, Wuppertal,Germany

2

34 Yerevan Physics Institute, Yerevan, Armenia35 DESY, Zeuthen, Germany36 Institut fur Teilchenphysik, ETH, Zurich, Switzerlandj37 Physik-Institut der Universitat Zurich, Zurich, Switzerlandj

38 Also at Physics Department, National Technical University, Zografou Campus, GR-15773Athens, Greece39 Also at Rechenzentrum, Bergische Universitat Gesamthochschule Wuppertal, Germany40 Also at Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, Karlsruhe, Germany41 Also at Dept. Fis. Ap. CINVESTAV, Merida, Yucatan, Mexicok42 Also at University of P.J.Safarik, Kosice, Slovak Republic43 Also at CERN, Geneva, Switzerland44 Also at Dept. Fis. CINVESTAV, Mexico City, Mexicok

a Supported by the Bundesministerium fur Bildung und Forschung, FRG, under contractnumbers 05 H1 1GUA /1, 05 H1 1PAA /1, 05 H1 1PAB /9, 05 H1 1PEA /6,05 H1 1VHA /7 and05 H1 1VHB /5b Supported by the UK Particle Physics and Astronomy ResearchCouncil, and formerly by theUK Science and Engineering Research Councilc Supported by FNRS-NFWO, IISN-IIKWd 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 furBildung und Forschung, FRGe Supported by the Deutsche Forschungsgemeinschaftf Supported by VEGA SR grant no. 2/1169/2001g Supported by the Swedish Natural Science Research Councilh Supported by Russian Foundation for Basic Research grant no. 96-02-00019i Supported by the Ministry of Education of the Czech Republicunder the projectsINGO-LA116/2000 and LN00A006, by GA AVCR grant no B1010005 and by GAUK grant no173/2000j Supported by the Swiss National Science Foundationk Supported by CONACyTl Partially Supported by Russian Foundation for Basic Research, grant no. 00-15-96584

3

1 Introduction

The observation of events with a large rapidity gap in the distribution of the final state hadronsat HERA [1] allows the nature of colour singlet exchange in strong interactions to be investi-gated. Colour singlet exchange interactions have been successfully modelled [2] in terms ofphenomenological Regge theory [3] and, at high energy, are attributed to diffractive or pomeronexchange. HERA allows the partonic nature of diffraction tobe investigated in deep–inelasticscattering (DIS) using the virtual photon as a probe.

The inclusive diffractive DIS structure functionFD2 is directly sensitive to the quark content

of the diffractive exchange [4,5]. Information about the gluon content can be inferred indirectlyfrom scaling violations. However, the measurement of the hadronic final state in diffractiongives further, more direct, information about the gluon content [6–9]. The production of opencharm is expected to be particularly sensitive to the gluon content because studies in inclusiveDIS reveal that the dominant contribution comes from the boson–gluon–fusion (BGF) mecha-nism [10]. The presence of the hard scale, provided by the charm quark mass, allows a varietyof perturbative QCD-based models of diffraction to be tested.

This article describes the measurement of diffractive opencharm production in DIS atHERA, which was performed using the H1 detector. Measurements of the totalD∗± crosssection and of differential distributions which explore the dynamics of diffractive charm pro-duction are presented. The ratio of the diffractiveD∗± cross section to the inclusiveD∗± crosssection is also measured.

The paper is organised as follows. The kinematics of diffractive DIS are introduced insection 2. The different theoretical approaches to diffractive charm production are summarisedin section 3. In section 4, the H1 detector, the data selection, the cross section measurementprocedure and the evaluation of the systematic uncertainties are explained. The results, in theform of the total and differential cross sections are presented and discussed in section 5.

2 Kinematics

The process studied in this paper isep → eXY → e(D∗±X ′)Y and is shown in figure 1. Theelectron produces a virtual photonγ⋆ (with four–momentumq) which interacts with the proton(with four–momentumP ). If the interaction takes place via colour singlet exchange, the photonand proton dissociate into two distinct hadronic systemsX andY , with invariant massesM

X

andMY

, respectively. The systemY is that which is closest to the outgoing proton direction. Inthe case whereM

XandM

Yare small compared with the photon-proton centre of mass energy

W , the two systems are separated by a large rapidity gap. In addition to the standard DISkinematic variablesQ2, y and Bjorkenx the following variables are defined

xIP =q · (P − pY )

q · P; t = (P − pY )2 ; β =

Q2

2q · (P − pY )=

x

xIP

, (1)

wherepY is the four–momentum ofY . The quantityxIP may be interpreted as the longitudinalmomentum fraction, with respect to the incoming proton, of the colourless exchange andt is

4

ee

γ*

pY

c

XX

Figure 1: The process under study in this article isep → eXY → e(D∗±X ′)Y . The electron(e) couples to a photon (γ⋆) which interacts with the proton (p) via colour singlet exchange, pro-ducing two distinct final state hadronic systemsX andY . The systemsX andY are separatedby the largest gap in rapidity in the final state hadrons.

the squared four–momentum transferred at the proton vertex. In the analysis presented in thispaper,t andM

Yare constrained to be small by the experimental selection and are integrated

over implicitly.

In a QCD interpretation in which a partonic structure is ascribed to the colourless exchangethe lowest order (i.e.O(α0

s) ) contribution to the diffractive cross section in the proton infinitemomentum frame is quark scattering (γ⋆q → q). In this caseβ can be interpreted as thefractional longitudinal momentum of the 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)case the invariant mass squareds of the partons emerging from the hard subprocess is non-zero.Therefore, the quantityzIP is introduced

zIP = β ·

(

1 +s

Q2

)

(2)

which corresponds to the longitudinal momentum fraction ofthe colourless exchange carriedby the parton (quark or gluon) which enters the hard interaction.

3 Models of Diffractive D∗± Production

A detailed description of the models used in this paper is given in [9]. A brief summary focusingon the production of open charm in each of the models is given here. For ease of comparisonwith the data in this paper 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 diffractive cross section factorises into deep–inelastic scattering from the pomeron and a pomeron flux factor, motivated by Regge theory,

5

which describes the probability for finding a pomeron in the proton. Within this picture, thepartonic content of the pomeron has been determined by QCD analyses of HERA diffractivedata [4, 12]. The parton distributions, obtained from fits tothe data, contain a dominant gluondistribution. Open charm is produced in the resolved pomeron model by the BGF process,where the photon interacts with a gluon of the pomeron carrying a fractionzIP of the pomeronlongitudinal momentum.

In ‘2-gluon exchange’ models diffractive DIS is studied in the proton rest frame by consid-ering qq andqqg photon fluctuations as colour dipoles scattering off the proton. Open charmcan be produced when the photon fluctuates intocc or ccg states. The simplest realisation ofnet colour singlet exchange between these partonic fluctuations and the proton at the partonlevel is a pair of gluons with opposite colour [13]. In perturbative QCD, the cross section for2-gluon exchange is related to the square of thekT –unintegrated gluon density of the protonF(x, k2

T ) [14,15], wherekT is the parton transverse momentum relative to the proton direction.In the ‘saturation’ model [16] the calculation of theqqg cross section is made under the as-sumption of strongkT ordering of the final state partons, wherek(g)

T ≪ k(q,q)T . In an alternative

approach [17,18] (hereafter referred to as ‘BJLW’) the calculation of theqqg final state includesconfigurations without strongkT ordering. In this model all outgoing partons are required tohave highkT and the minimum value for the final state gluon transverse momentumkcut

T,g is afree parameter which can be tuned to describe the data. The 2-gluon exchange calculations areperformed under the assumption of lowxIP ( xIP < 0.01 ) to avoid contributions from secondaryreggeon exchanges which correspond to quark exchange in themodels.

In ‘soft colour neutralisation’ models an alternative approach to diffractive DIS is givenwhich leads to very similar properties of inclusive and diffractive DIS final states. In the softcolour interaction model (SCI) [19], open charm is producedvia BGF from the gluon distri-bution of the proton. It is then assumed that the partons produced in the hard interactionscan exchange soft gluons with the background colour field of the incoming proton leaving allmomenta unchanged. Large rapidity gap events may be produced this way when the soft in-teractions lead to a net colour singlet exchange. The probability for soft colour exchange isassumed to be independent of the kinematics of the hard scattering process.

The generalised area law (GAL) [20] approach is a modification of the Lund String model[21]. The production mechanism for open charm is similar to that in the SCI model exceptthat it is formulated in terms of interactions between the colour strings connecting the partonsin an event. In this model the probability for a soft colour interaction is not constant but isexponentially suppressed by the difference between the areas in momentum space spanned bythe strings before and after the colour rearrangement.

The ‘semi-classical’ model [22] is a non-perturbative model based on the dipole approach.In the proton rest frame the photon fluctuations scatter off asuperposition of soft colour fieldsrepresenting the proton. In this approach, theqqg fluctuation is expected to be dominant foropen charm production [23]. If the gluon is the lowestkT parton, then the contribution can berelated to BGF in the proton infinite momentum frame.

Comparison of the data with the ‘resolved pomeron’, the ‘2-gluon exchange’ and the ‘semi-classical’ models is facilitated by their implementation within the RAPGAP Monte Carlo gen-erator [24]. The predictions of the SCI and GAL models are calculated using the AROMA

6

Monte Carlo generator [25]. The cross section predictions in this article are all calculated as-suming a charm quark massmc = 1.5 GeV. For the hadronisation fractionf(c → D∗±) thevalue0.233 ± 0.010 ± 0.011 [26] is used. The momentum fraction of the charm quark carriedby theD∗± is calculated using the Petersonet al. model [27] with the fragmentation parameterǫ = 0.078.

4 Experimental Procedure

The data presented in this analysis were collected over the years 1996 and 1997, when HERAcollided positrons with energyEe = 27.5 GeV with protons of energyEp = 820 GeV. Re-quiring all essential detector components to be operational the available integrated luminosityis 19.1pb−1. Further details of this analysis beyond those given here can be found in [28].

4.1 The H1 Detector

A short overview of the detector components most relevant for the present analysis is givenhere. A detailed description of the H1 detector can be found in [29]. Thez–axis of the H1detector is taken along the beam direction such that positive z values refer to the direction ofthe outgoing proton beam, referred to as the ‘forward’ direction.

Charged particles emerging from the interaction region aremeasured by the central track-ing device (CTD) in the range−1.5 < η < 1.51. The CTD comprises two large cylindri-cal central jet drift chambers (CJC) and twoz chambers situated concentrically around thebeam-line within a solenoidal magnetic field of 1.15 T. The resolution achieved by the CTDis σ(pT )/pT ≃ 0.01pT/GeV. The CTD also provides triggering information based on tracksegments in ther− φ plane from the CJC and the position of the vertex using a double layer ofmulti-wire proportional chambers (MWPC). The energies of final state particles are measuredin the Liquid Argon (LAr) calorimeter which surrounds the tracking chambers and covers therange−1.5 < η < 3.4. The backward region (−4.0 < η < −1.4) is covered by a lead–scintillating fibre calorimeter (SPACAL [30]) with electromagnetic and hadronic sections. Infront of the SPACAL, the Backward Drift Chamber (BDC) [31] provides track segments ofcharged particles.

Detectors close to the beam pipe in the direction of the outgoing proton are used in the se-lection of large rapidity gap events. These are the Forward Muon Detector (FMD), the ProtonRemnant Tagger (PRT) and the Plug calorimeter (PLUG). The FMD is located atz = 6.5 mand covers the pseudorapidity range1.9 < η < 3.7 directly. The PLUG allows energy mea-surements to be made over the range3.5 < η < 5.5. Particles produced at largerη can alsobe detected because of secondary scattering with the beam-pipe. The PRT, a set of scintillatorssurrounding the beam pipe atz = 26 m, can tag hadrons in the region6.0 <∼ η <∼ 7.5.

1The pseudorapidityη of an object detected with polar angleθ is defined asη = − ln tan(θ/2).

7

4.2 Event Selection

The events were triggered by an electromagnetic energy cluster in the SPACAL, in coincidencewith a charged track signal from both the MWPC and the CJC. Thepositrons are identifiedin the SPACAL as clusters with energyE ′

e > 9 GeV which have properties consistent withelectromagnetic deposition, and for which the centre of gravity of the cluster matches a chargedtrack segment in the BDC to within2.5 cm. The selected events are also required to have areconstructed vertex from the CTD within±35 cm of the nominal vertex. In order to suppressevents with initial state photon radiation the summedE − pz of the event calculated using allreconstructed final state particles, including the positron, is required to be greater than35 GeV.The kinematic region covered by the measurement is2 < Q2 < 100 GeV2 and0.05 < y < 0.7.To minimise the correction due to QED radiative effects,Q2, y andx are reconstructed from theenergy and angleθ′ of the scattered positron and the hadronic final state using the ‘Σ method’[32].

Diffractive events are selected experimentally by the absence of activity in the outgoingproton region. No signal above noise thresholds is allowed in the FMD, the PRT, the PLUG andthe most forward part (η > 3.3) of the LAr calorimeter. This ensures that there is a large rapiditygap covering at least3.3 < η ≤ 7.5 between the photon dissociation systemX and the protonremnant systemY . Monte Carlo studies show that the absence of particles in the detectors closeto the beam pipe restricts the mass of the proton remnant system toM

Y< 1.6 GeV and the

momentum transfer to the proton to|t| < 1 GeV2.

The four–momentum of the systemX, which is well contained in the central detector, isreconstructed using information from the LAr and SPACAL calorimeters together with the CJC[33]. The variablexIP is calculated from

xIP =

∑

X+e′(E + pz)

2Ep

(3)

whereE andpz are the energy and longitudinal momentum of each final state particle in thelaboratory frame, and the sum runs over the scattered positrone′ and all detected particles in thephoton dissociation systemX. The quantityβ is calculated fromβ = x/xIP . The cross sectionis restricted to the rangexIP < 0.04 to suppress contributions from non-diffractive scatteringand secondary reggeon exchanges.

In this paper an hadronic observablezobsIP is constructed which is analogous toxobs

g for in-clusiveD∗± production which was measured in [34]. In the resolved pomeron picturezobs

IP is anapproximation to the momentum fractionzIP of the pomeron carried by the interacting gluon(see equation 2). The observablezobs

IP is defined as

zobsIP =

M2cc +Q2

M2X

+Q2. (4)

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 the gluon momentum fractionxobsg in [34].

Monte Carlo simulations show that the resolution in the hadronic variablezobsIP is approximately

30%, and that there is a good correlation betweenzobsIP andzIP as calculated from the kinematics

of the outgoing partons. The variablezobsIP can be interpreted as the fraction of the energy of the

systemX which is carried by thecc pair emerging from the hard scattering.

8

4.3 Reconstruction ofD∗± Mesons

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

D∗± → D0 π+slow → (K− π+) π+

slow (+c.c.), (5)

which has a branching fraction of2.59% [36]. The reconstruction method is detailed in [37].The decay products are detected in the CTD and are required tohave a transverse momentumpT of at least140 MeV for theπslow and250 MeV for both theK andπ.

M (Kππs) - M (Kπ) [ GeV ]

En

trie

s p

er M

eV

H1 Data

0

10

20

30

0.14 0.15 0.16 0.17

Figure 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.

The invariant mass of theKπ combination has to be consistent with theD0 mass within±80 MeV. After cuts on the direction (|η(Kππ)| < 1.5) and transverse momentum (pT (Kππ) >2 GeV), the mass difference distribution∆M = M(Kππslow) −M(Kπ) is plotted in figure 2.The number ofD∗± candidates is determined by fitting the histogram in figure 2 with a Gaussiandistribution for the signal plus a background functiona(∆M −Mπ)b, whereMπ denotes the

9

mass of the pion. The position and width of the Gaussian are fixed to values taken from a higherstatistics sample of events where no diffractive cuts were applied [37]. The normalisation of theGaussian and the background parametersa andb are allowed to vary. The resulting number ofdetectedD∗± mesons is46 ± 10.

4.4 Cross Section Measurement

Monte Carlo simulations are used to correct the data for the effects of losses and migrationsdue to the finite resolution of the H1 detector. The efficiencyis calculated by running theH1 detector simulation program on a sample ofD∗± events from the diffractive Monte Carlogenerator RAPGAP [24] in the resolved pomeron mode with thet dependence of the crosssection parameterised ase−6|t|. The RAPGAP program is used to model events which containan elastic proton (M

Y= mp) in the kinematic rangexIP < 0.1. Migrations fromxIP > 0.1

or from large values ofMY (MY > 5 GeV) are modelled by using a simulation of the heavyquark generator AROMA [25] in the inclusive mode. The contribution is of the order5% tothe selected sample of events. An additional correction of−8% ± 6% is applied to account forthe net smearing across theM

Y= 1.6 GeV boundary. Since only elastically scattered protons

have been simulated in RAPGAP, this correction is evaluatedusing the proton dissociationsimulation in the DIFFVM [38] generator2. A further correction of+4%±1% takes into accountdiffractive events rejected due to fluctuations in the noiselevel in the FMD. This correction isestimated directly from the data, using a sample of randomlyselected events, not correlatedwith a physics trigger. An additional source of background is the contribution of reflections intheD0 mass window, coming fromD0 channels other than that defined in equation 5. They areestimated, from simulations using the AROMA Monte Carlo, tobe3.5% [28]. The contributionfrom photoproduction background is found to be negligible.QED radiative corrections werecalculated to be approximately2% using the RAPGAP program interfaced to HERACLES [39].

4.5 Systematic Uncertainties

The following sources of systematic error are taken into account

• The uncertainty in the physics model forD∗± production used to compute the efficiencycorrections is estimated by varying the shapes of the kinematic distributions in the sim-ulations beyond the limits imposed by previous measurements or the present data. Thisis done by reweighting thexIP distribution to that observed in data; theβ distribution by(1 ± 0.3β) and thet distribution bye±2t. The resulting systematic uncertainties on thecross section measurements range between10% and20% with the largest contributionoriginating from the variation of thexIP distribution. The uncertainties are verified usingsimulations of models with different underlying kinematicdistributions.

• The total uncertainty due to the reconstruction efficiency,mass and momentum resolutionof the central tracker for the three tracks was estimated in the analysis of the inclusive DISD∗± cross section to be+9%

−4% [37].2For the correction, it is assumed that the ratio of diffractive proton elastic to diffractive proton dissociative

interactions is1 : 1.

10

• An error of8% is found by varying the details of the fitting procedure used to obtain thenumber ofD∗± mesons.

• The uncertainty in the correction due to the smearing of events across the boundaryMY =1.6 GeV is estimated by varying in the DIFFVM simulation: the efficiency of the forwarddetectors, the assumedM

Ydistribution, the ratio of double to single dissociation between

0.5 and 2 and the assumedt dependence for double dissociation. This contributes6% tothe systematic error.

• The uncertainty in the trigger efficiency gives a contribution of5% to the systematic error.

• The uncertainty due to the assumed charm fragmentation scheme is estimated by usingparameterisations of the Peterson model and the standard Lund string model in JETSET[21]. This leads to an average uncertainty of5% in the cross sections.

• The uncertainty in the correction due to QED radiative effects is estimated as3%.

• The number of events migrating into the sample fromxIP > 0.1 orMY > 5 GeV is variedby ±50%, leading to an average systematic error of3%.

Other sources of systematic error are the uncertainty in themeasured energy and angle ofthe scattered positron, uncertainties in the hadronic energy scale of the liquid argon andSPACAL calorimeters, the uncertainty in the luminosity measurement, the uncertainty onthe fraction of events lost due to noise in the FMD and the uncertainty in the branchingratio for the measured decay channel. Each of them is responsible for an error of no morethan2.5%.

The total systematic error for each point has been obtained by adding all individual contri-butions in quadrature. It ranges between20% and30% and for most data points is similar inmagnitude to the statistical error.

5 Results

The totalD∗± production cross section for the kinematic region2 < Q2 < 100 GeV2, 0.05 <y < 0.7, xIP < 0.04,MY < 1.6 GeV, |t| < 1 GeV2, pT,D∗ > 2 GeV and|ηD∗| < 1.5 is

σ(ep→ e(D∗±X ′)Y ) = 246 ± 54 (stat.) ± 56 (syst.) pb . (6)

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

5.9 ± 1.1 (stat.) ± 1.1 (syst.)%, (7)

where the inclusiveD∗± cross section has been determined as in [37]. The error in theratio isdominated by the uncertainties pertaining to the measurement of the diffractive cross section.

11

Model cross section (pb)resolved H1 fit 2 368pomeron H1 fit 3 433

ACTW fit D 481soft colour SCI 203

neutralisation GAL 328semi-classical 196

H1 Data 246 ± 54 (stat.) ± 56 (syst.) pb

Table 1: The predictions for the total diffractiveD∗± cross section for two groups of models:the resolved pomeron and soft colour neutralisation approaches. The bottom row shows thecross section measured in the data.

In table 1 the total cross section is compared with some of thephenomenological modelsdiscussed in section 3. The first three rows of table 1 show thepredictions for the cross sectionfor three different sets of parton parameterisations within the resolved pomeron model. The firsttwo predictions are based on the parton distributions of thepomeron and sub-leading exchangefrom the leading order DGLAP analysis ofFD

2 from H1 [4]. The ‘ACTW fit D’ parameterisationis the best combined fit in [12] to H1 and ZEUSFD

2 data and ZEUS diffractive dijet data. Allthree sets of parton parameterisations give acceptable descriptions ofFD

2 . All of the predictionsusing the three parton parameterisations exceed the data although the parameterisation with theflat gluon distribution (‘H1 fit 2’) is closest. The predictions shown are calculated with thefactorisation and renormalisation scales set toµ2 ≡ µ2

f ≡ µ2r = Q2 + p2

T + 4m2c . Changing

this scale top2T + 4m2

c produces an increase of around20% in the predicted cross sections.Similarly, the variation of the charm quark mass by±0.1 GeV leads to an uncertainty of∓10%in the cross sections. Changingǫ in the Peterson model from0.078 to 0.035 and to0.1 producesan uncertainty in the cross section predictions of+15

−5 %. The values shown in the table arecalculated withΛQCD = 0.20 GeV and the number of active quark flavours in the first orderexpression forαs isNf = 4. SelectingΛQCD = 0.25 GeV andNf = 5 leads to an increase ofabout10% in the cross sections. The contribution ofD∗± production from meson exchange inthe predictions is less than7%.

The cross section predictions from the semi-classical, SCIand GAL models are also shownin table 1 and are in agreement with the data. However, none ofthese models can simultaneouslyreproduce the shapes and normalisations of the differential dijet cross sections [9]. The semi-classical model prediction was calculated using the same factorisation scale as for the resolvedpomeron model. The SCI and GAL model predictions useµ2 = Q2 + 2p2

T + 2m2c . For each

of the three models, the uncertainty in the predictions due to the variation of the factorisationscale,mc andǫ are similar to those for the resolved pomeron model.

Differential cross sections are shown in figures 3 and 4. Theyrepresent average values overthe intervals shown in the figures.

In figure 3 the cross section is shown as a function ofxIP , log10 β andzobsIP and compared to

the QCD-based models described in section 3. The cross sections differential inxIP andlog10 βare flat within experimental errors. Figure 3 shows that about 60% of charm production is inthe regionzobs

IP < 0.2 where the contribution of the BGF process is expected to dominate.

12

0

10000

20000

0.01 0.02 0.03xIP

dσ

/ dx IP

[p

b]

(a)

res. IP (H1 fit 2)

ACTW fit Dres. IP (H1 fit 3)

0.01 0.02 0.03xIP

Saturation model

BJLW (qq only)

BJLW (kT,g=1.5 GeV)BJLW (kT,g=1.0 GeV)

cut

cut

0.01 0.02 0.03xIP

Semi-Cl. modelSCIGALH1 Data

H1

0

100

200

300

-2 -1log10β

dσ

/ dlo

g10

β [p

b]

(b)

-2 -1log10β

-2 -1log10β

10

10 2

10 3

0.25 0.5 0.75z

IP obs

dσ

/ dz IP o

bs [p

b]

(c)

0.25 0.5 0.75z

IP obs

0.25 0.5 0.75z

IP obs

Figure 3:Cross sectionsσ(ep→ e(D∗±X ′)Y ) as a function of (a)xIP ; (b) log10 β and (c)zobsIP .

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

13

0

200

400

600

0.5 1 1.5log10Q

2

dσ

/ dlo

g10

Q2 [

pb

]

(a)

res. IP (H1 fit 2)

ACTW fit Dres. IP (H1 fit 3)

H1 Data

0.5 1 1.5log10Q

2

Semi-Cl. modelSCIGAL

H1

10

10 2

2 4 6 8p

T, D* * [GeV]

dσ

/ dp

T, D

* *

[pb

/GeV

]

(b)

2 4 6 8p

T, D* * [GeV]

0

100

200

-1 0 1ηD*

dσ

/ dη D

* [p

b]

(c)

-1 0 1ηD*

Figure 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 isplotted twice to allow comparison with two of the groups of models described in the text.

14

The discrepancy between the resolved pomeron model predictions and the data is pro-nounced in the lowxIP , highβ and highzobs

IP regions which are all correlated with low values ofM

X. Of the three parton parameterisations the calculations which use ‘H1 Fit 2’ are shown to

come closest to the data in this region. All three parameterisations are consistent with the datain the highM

Xregion.

The two gluon exchange models, directly applicable in the low xIP region (xIP < 0.01)are also compared to the data in figure 3. The sensitivity of this measurement to the value ofthe transverse momentum cut-offkcut

T,g of the gluon in theqqg state within the BJLW model isalso studied. Calculations which use cut-off values of1.0 GeV and1.5 GeV both give a fairdescription of the data in the lowM

Xregion (i.e. the lowxIP , highβ, highzobs

IP domain). Thesedata also offer sensitivity to the relative contribution ofthe scattering of theqq fluctuation, whichis shown as a shaded zone, and forms a sizeable component of the total two gluon exchangecross section. The saturation model reproduces reasonablywell the normalisation of the data inthe lowxIP range, in which it is expected to be applicable, but also provides a good descriptionof the data in the remaining region of phase space.

The semi-classical model gives a good description of the distributions shown in figure 3.Both the SCI and GAL models provide a satisfactory description of the spectra although theGAL model tends to overestimate the data in the lowM

Xdomain.

In figure 4, theD∗± cross section is plotted differentially at 2 values oflog10Q2, p∗T,D∗ and

ηD∗, wherep∗T,D∗ is the transverse momentum of theD∗± in theγ∗p centre of mass system. Thedata tend to fall off with higher values of each of these variables.

Since these distributions are integrated over the fullxIP range of this measurement, a com-parison is made only with resolved pomeron calculations andsoft colour neutralisation models.Both sets of models provide a reasonable description of the data.

6 Conclusion

The dynamics of open diffractive charm production in DIS have been studied for the first timeat HERA. The totalD∗± production cross section in the kinematic range2 < Q2 < 100 GeV2,0.05 < y < 0.7, xIP < 0.04, MY < 1.6 GeV, |t| < 1 GeV2, pT,D∗ > 2 GeV and|ηD∗| < 1.5has been found to be246 ± 54 (stat.) ± 56 (syst.) pb. In the studied region about6% of thetotalD∗± cross section is produced diffractively.

The cross section has been measured as a function ofxIP , log10 β, zobsIP , log10Q

2, p∗T,D∗ andηD∗. The data show a sizeable component of charm production in the low zobs

IP region which issuggestive of the dominance of the contribution from the boson–gluon–fusion process.

A number of QCD-based models which give a good description ofthe inclusive diffractivecross section were compared with the measurement. A reasonable description of the data isprovided by a model based on the resolved pomeron picture using various assumptions for thepartonic composition of the colourless exchange. A parton parameterisation containing a flatgluon dependence (‘H1 Fit 2’) comes closest to the data. Predictions of two gluon exchangeprocesses were found to match the data in the lowxIP region. Soft colour neutralisation modelsgive a satisfactory description of the data.

15

Acknowledgements

We are grateful to the HERA machine group whose outstanding efforts have made and continueto make this experiment possible. We thank the engineers andtechnicians for their work inconstructing and now maintaining the H1 detector, our funding agencies for financial support,the DESY technical staff for continual assistance and the DESY directorate for the hospitalitywhich they extend to the non DESY members of the collaboration.

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