# Evidence for a Large Dust/Ice Ratio in the Nucleus of Comet 9P/Tempel 1

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-EP/2003-02

10th January 2003

Measurement of the inclusive D∗±

production

in γγ collisions at LEP

The ALEPH Collaboration∗)

Abstract

The inclusive production of D∗±mesons in two-photon collisions is measured with

the ALEPH detector at e+e−centre-of-mass energies from 183GeV to 209GeV. A

total of 360 ± 27 D∗±meson events were observed from an integrated luminosity

of 699pb−1. Contributions from direct and single-resolved processes are separated

using the ratio of the transverse momentum pD∗±

mass Wvisof the event. Differential cross sections of D∗±production as functions of

pD∗±

t

and the pseudorapidity |ηD∗±| are measured in the range 2GeV/c < pD∗±

12GeV/c and |ηD∗±| < 1.5. They are compared to next-to-leading order (NLO)

perturbative QCD calculations. The extrapolation of the integrated visible D∗±

cross section to the total charm cross section, based on the Pythia Monte Carlo

program, yields σ(e+e−→ e+e−c¯ c)<√s>=197GeV= 731±74stat±47syst±157extrpb.

t

of the D∗±to the visible invariant

t

<

Submitted to European Physical Journal C

∗) See next pages for the list of authors

Page 2

The ALEPH Collaboration

A. Heister, S. Schael

Physikalisches Institut das RWTH-Aachen, D-52056 Aachen, Germany

R. Barate, R. Bruneli` ere, I. De Bonis, D. Decamp, C. Goy, S. Jezequel, J.-P. Lees, F. Martin, E. Merle,

M.-N. Minard, B. Pietrzyk, B. Trocm´ e

Laboratoire de Physique des Particules (LAPP), IN2P3-CNRS, F-74019 Annecy-le-Vieux Cedex,

France

S. Bravo, M.P. Casado, M. Chmeissani, J.M. Crespo, E. Fernandez, M. Fernandez-Bosman, Ll. Garrido,15

M. Martinez, A. Pacheco, H. Ruiz

Institut de F´isica d’Altes Energies, Universitat Aut` onoma de Barcelona, E-08193 Bellaterra

(Barcelona), Spain7

A. Colaleo, D. Creanza, N. De Filippis, M. de Palma, G. Iaselli, G. Maggi, M. Maggi, S. Nuzzo, A. Ranieri,

G. Raso,24F. Ruggieri, G. Selvaggi, L. Silvestris, P. Tempesta, A. Tricomi,3G. Zito

Dipartimento di Fisica, INFN Sezione di Bari, I-70126 Bari, Italy

X. Huang, J. Lin, Q. Ouyang, T. Wang, Y. Xie, R. Xu, S. Xue, J. Zhang, L. Zhang, W. Zhao

Institute of High Energy Physics, Academia Sinica, Beijing, The People’s Republic of China8

D. Abbaneo, P. Azzurri, T. Barklow,26O. Buchm¨ uller,26M. Cattaneo, F. Cerutti, B. Clerbaux,23

H. Drevermann, R.W. Forty, M. Frank, F. Gianotti, J.B. Hansen, J. Harvey, D.E. Hutchcroft, P. Janot,

B. Jost, M. Kado,2P. Mato, A. Moutoussi, F. Ranjard, L. Rolandi, D. Schlatter, G. Sguazzoni, W. Tejessy,

F. Teubert, A. Valassi, I. Videau, J.J. Ward

European Laboratory for Particle Physics (CERN), CH-1211 Geneva 23, Switzerland

F. Badaud, S. Dessagne, A. Falvard,20D. Fayolle, P. Gay, J. Jousset, B. Michel, S. Monteil, D. Pallin,

J.M. Pascolo, P. Perret

Laboratoire de Physique Corpusculaire, Universit´ e Blaise Pascal, IN2P3-CNRS, Clermont-Ferrand,

F-63177 Aubi` ere, France

J.D. Hansen, J.R. Hansen, P.H. Hansen, A. Kraan, B.S. Nilsson

Niels Bohr Institute, 2100 Copenhagen, DK-Denmark9

A. Kyriakis, C. Markou, E. Simopoulou, A. Vayaki, K. Zachariadou

Nuclear Research Center Demokritos (NRCD), GR-15310 Attiki, Greece

A.

H. Videau

Laoratoire Leprince-Ringuet, Ecole Polytechnique, IN2P3-CNRS, F-91128 Palaiseau Cedex, France

Blondel,12

J.-C. Brient, F.Machefert, A.Roug´ e, M.Swynghedauw,R.Tanaka

V. Ciulli, E. Focardi, G. Parrini

Dipartimento di Fisica, Universit` a di Firenze, INFN Sezione di Firenze, I-50125 Firenze, Italy

A. Antonelli, M. Antonelli, G. Bencivenni, F. Bossi, G. Capon, V. Chiarella, P. Laurelli, G. Mannocchi,5

G.P. Murtas, L. Passalacqua

Laboratori Nazionali dell’INFN (LNF-INFN), I-00044 Frascati, Italy

J. Kennedy, J.G. Lynch, P. Negus, V. O’Shea, A.S. Thompson

Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ,United Kingdom10

S. Wasserbaech

Page 3

Department of Physics, Haverford College, Haverford, PA 19041-1392, U.S.A.

R. Cavanaugh,4S. Dhamotharan,21C. Geweniger, P. Hanke, V. Hepp, E.E. Kluge, G. Leibenguth,

A. Putzer, H. Stenzel, K. Tittel, M. Wunsch19

Kirchhoff-Institut f¨ ur Physik, Universit¨ at Heidelberg, D-69120 Heidelberg, Germany16

R. Beuselinck, W. Cameron, G. Davies, P.J. Dornan, M. Girone,1R.D. Hill, N. Marinelli, J. Nowell,

S.A. Rutherford, J.K. Sedgbeer, J.C. Thompson,14R. White

Department of Physics, Imperial College, London SW7 2BZ, United Kingdom10

V.M. Ghete, P. Girtler, E. Kneringer, D. Kuhn, G. Rudolph

Institut f¨ ur Experimentalphysik, Universit¨ at Innsbruck, A-6020 Innsbruck, Austria18

E. Bouhova-Thacker, C.K. Bowdery, D.P. Clarke, G. Ellis, A.J. Finch, F. Foster, G. Hughes,

R.W.L. Jones, M.R. Pearson, N.A. Robertson, M. Smizanska

Department of Physics, University of Lancaster, Lancaster LA1 4YB, United Kingdom10

O. van der Aa, C. Delaere,28V. Lemaitre29

Institut de Physique Nucl´ eaire, D´ epartement de Physique, Universit´ e Catholique de Louvain, 1348

Louvain-la-Neuve, Belgium

U. Blumenschein, F. H¨ olldorfer, K. Jakobs, F. Kayser, K. Kleinknecht, A.-S. M¨ uller, B. Renk, H.-

G. Sander, S. Schmeling, H. Wachsmuth, C. Zeitnitz, T. Ziegler

Institut f¨ ur Physik, Universit¨ at Mainz, D-55099 Mainz, Germany16

A. Bonissent, P. Coyle, C. Curtil, A. Ealet, D. Fouchez, P. Payre, A. Tilquin

Centre de Physique des Particules de Marseille, Univ M´ editerran´ ee, IN2P3-CNRS, F-13288 Marseille,

France

F. Ragusa

Dipartimento di Fisica, Universit` a di Milano e INFN Sezione di Milano, I-20133 Milano, Italy.

A. David, H. Dietl, G. Ganis,27K. H¨ uttmann, G. L¨ utjens, W. M¨ anner, H.-G. Moser, R. Settles, G. Wolf

Max-Planck-Institut f¨ ur Physik, Werner-Heisenberg-Institut, D-80805 M¨ unchen, Germany16

J. Boucrot, O. Callot, M. Davier, L. Duflot, J.-F. Grivaz, Ph. Heusse, A. Jacholkowska,6L. Serin,

J.-J. Veillet, C. Yuan

Laboratoire de l’Acc´ el´ erateur Lin´ eaire, Universit´ e de Paris-Sud, IN2P3-CNRS, F-91898 Orsay Cedex,

France

G. Bagliesi, T. Boccali, L. Fo` a, A. Giammanco, A. Giassi, F. Ligabue, A. Messineo, F. Palla,

G. Sanguinetti, A. Sciab` a, R. Tenchini,1A. Venturi,1P.G. Verdini

Dipartimento di Fisica dell’Universit` a, INFN Sezione di Pisa, e Scuola Normale Superiore, I-56010

Pisa, Italy

O. Awunor, G.A. Blair, G. Cowan, A. Garcia-Bellido, M.G. Green, L.T. Jones, T. Medcalf, A. Misiejuk,

J.A. Strong, P. Teixeira-Dias

Department of Physics, Royal Holloway & Bedford New College, University of London, Egham, Surrey

TW20 OEX, United Kingdom10

R.W. Clifft, T.R. Edgecock, P.R. Norton, I.R. Tomalin

Particle Physics Dept., Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 OQX, United

Kingdom10

B. Bloch-Devaux, D. Boumediene, P. Colas, B. Fabbro, E. Lan¸ con, M.-C. Lemaire, E. Locci, P. Perez,

J. Rander, B. Tuchming, B. Vallage

CEA, DAPNIA/Service de Physique des Particules, CE-Saclay, F-91191 Gif-sur-Yvette Cedex,

France17

N. Konstantinidis, A.M. Litke, G. Taylor

Institute for Particle Physics, University of California at Santa Cruz, Santa Cruz, CA 95064, USA22

C.N. Booth, S. Cartwright, F. Combley,25P.N. Hodgson, M. Lehto, L.F. Thompson

Page 4

Department of Physics, University of Sheffield, Sheffield S3 7RH, United Kingdom10

A. B¨ ohrer, S. Brandt, C. Grupen, J. Hess, A. Ngac, G. Prange, U. Sieler30

Fachbereich Physik, Universit¨ at Siegen, D-57068 Siegen, Germany16

C. Borean, G. Giannini

Dipartimento di Fisica, Universit` a di Trieste e INFN Sezione di Trieste, I-34127 Trieste, Italy

H. He, J. Putz, J. Rothberg

Experimental Elementary Particle Physics, University of Washington, Seattle, WA 98195 U.S.A.

S.R. Armstrong, K. Berkelman, K. Cranmer, D.P.S. Ferguson, Y. Gao,13S. Gonz´ alez, O.J. Hayes,

H. Hu, S. Jin, J. Kile, P.A. McNamara III, J. Nielsen, Y.B. Pan, J.H. von Wimmersperg-Toeller,

W. Wiedenmann, J. Wu, Sau Lan Wu, X. Wu, G. Zobernig

Department of Physics, University of Wisconsin, Madison, WI 53706, USA11

G. Dissertori

Institute for Particle Physics, ETH H¨ onggerberg, 8093 Z¨ urich, Switzerland.

1Also at CERN, 1211 Geneva 23, Switzerland.

2Now at Fermilab, PO Box 500, MS 352, Batavia, IL 60510, USA

3Also at Dipartimento di Fisica di Catania and INFN Sezione di Catania, 95129 Catania, Italy.

4Now at University of Florida, Department of Physics, Gainesville, Florida 32611-8440, USA

5Also Istituto di Cosmo-Geofisica del C.N.R., Torino, Italy.

6Also at Groupe d’Astroparticules de Montpellier, Universit´ e de Montpellier II, 34095, Montpellier,

France.

7Supported by CICYT, Spain.

8Supported by the National Science Foundation of China.

9Supported by the Danish Natural Science Research Council.

10Supported by the UK Particle Physics and Astronomy Research Council.

11Supported by the US Department of Energy, grant DE-FG0295-ER40896.

12Now at Departement de Physique Corpusculaire, Universit´ e de Gen` eve, 1211 Gen` eve 4, Switzerland.

13Also at Department of Physics, Tsinghua University, Beijing, The People’s Republic of China.

14Supported by the Leverhulme Trust.

15Permanent address: Universitat de Barcelona, 08208 Barcelona, Spain.

16Supported by Bundesministerium f¨ ur Bildung und Forschung, Germany.

17Supported by the Direction des Sciences de la Mati` ere, C.E.A.

18Supported by the Austrian Ministry for Science and Transport.

19Now at SAP AG, 69185 Walldorf, Germany

20Now at Groupe d’ Astroparticules de Montpellier, Universit´ e de Montpellier II, 34095 Montpellier,

France.

21Now at BNP Paribas, 60325 Frankfurt am Mainz, Germany

22Supported by the US Department of Energy, grant DE-FG03-92ER40689.

23Now at Institut Inter-universitaire des hautes Energies (IIHE), CP 230, Universit´ e Libre de Bruxelles,

1050 Bruxelles, Belgique

24Also at Dipartimento di Fisica e Tecnologie Relative, Universit` a di Palermo, Palermo, Italy.

25Deceased.

26Now at SLAC, Stanford, CA 94309, U.S.A

27Now at INFN Sezione di Roma II, Dipartimento di Fisica, Universit` a di Roma Tor Vergata, 00133

Roma, Italy.

28Research Fellow of the Belgium FNRS

29Research Associate of the Belgium FNRS

30Now at Verdi Information Consult GmbH, 53757 Sankt Augustin, Germany

Page 5

1Introduction

Heavy flavour production in two-photon events at LEP 2 centre-of-mass energies is dom-

inated by charm production processes in which both of the photons couple directly (di-

rect processes) or in which one photon couples directly and the other appears resolved

(single-resolved processes) (Fig. 1) [1]. These two contributions are of the same order

of magnitude within the experimental acceptance. Because the single-resolved process

is dominated by γg fusion, the measurement of the cross section can give access to the

gluon content of the photon. Moreover, the large masses of the c and b quarks provide

a cutoff for perturbative QCD calculations, allowing a good test of QCD predictions for

the corresponding reactions. Contributions from processes in which both photons appear

resolved (double-resolved processes) are suppressed by more than two orders of magnitude

compared to the total cross section [1]. The production of b quark is expected to be

suppressed by a large factor compared to charm quark because of the heavier mass and

smaller absolute charge.

In the present analysis charm production is measured in two steps. A high-purity γγ

sample is first selected, then examined for its charm content via reconstruction of D∗+

mesons in their decay to D0π+. This letter is organized as follows. A short descrip-

tion of the ALEPH detector is given in Section 2. Monte Carlo simulations for signal

and background processes are described in Section 3. In Section 4, event selection and

reconstruction of D∗+mesons are discussed. The results of the analysis are presented

in Section 5. Finally, in Section 6 a summary is given. Throughout this letter charge-

conjugated particles and their decays are implicitly included.

2ALEPH Detector

The ALEPH detector has been described in detail in [2, 3]. Here, only the parts essential

to the present analysis are covered briefly. The central part of the ALEPH detector is

dedicated to the reconstruction of the trajectories of charged particles. The trajectory

of a charged particle emerging from the interaction point is measured by a two-layer

silicon strip vertex detector (VDET), a cylindrical drift chamber (ITC) and a large time

projection chamber (TPC). The three tracking detectors are immersed in a 1.5T axial

magnetic field provided by a superconducting solenoidal coil. Together they measure

charged particle transverse momenta with a resolution of δpt/pt= 6×10−4pt⊕0.005 (ptin

GeV/c). The TPC also provides a measurement of the specific ionization dE/dxmeas. An

estimator χh= (dE/dxmeas− dE/dxexp,h)/σexp,his formed to test a particle hypothesis,

where dE/dxexp,h and σexp,h denote the expected specific ionization and the estimated

uncertainty for the particle hypothesis h, respectively. A mass hypothesis may be tested

by means of the χhvalues themselves or by calculating χ2

Photons are identified in the electromagnetic calorimeter (ECAL), situated between

the TPC and the coil.The ECAL is a lead/proportional-tube sampling calorimeter

segmented in 0.9◦× 0.9◦projective towers and read out in three sections in depth. It

has a total thickness of 22 radiation lengths and yields a relative energy resolution of

hconfidence levels Ph.

1

Page 6

0.18/√E + 0.009, with E in GeV, for isolated photons. Electrons are identified by their

transverse and longitudinal shower profiles in ECAL and their specific ionization in the

TPC.

The iron return yoke is instrumented with 23 layers of streamer tubes and forms the

hadron calorimeter (HCAL). The latter provides a relative energy resolution of charged

and neutral hadrons of 0.85/√E, with E in GeV. Muons are distinguished from hadrons

by their characteristic pattern in HCAL and by the muon chambers, composed of two

double-layers of streamer tubes outside HCAL.

Two small-angle calorimeters, the luminosity calorimeter (LCAL) and the silicon lu-

minosity calorimeter (SICAL), are particularly important for this analysis to veto events

with detected scattered electrons. The LCAL is a lead/proportional-tube calorimeter,

similar to ECAL, placed around the beam pipe at each end of the detector. It monitors

angles from 45 to 160 mrad with an energy resolution of 0.15

uses 12 silicon/tungsten layers to sample showers. It is mounted around the beam pipe

in front of the LCAL, covering angles from 34 to 58 mrad, with an energy resolution of

0.225

E(GeV).

The information from the tracking detectors and the calorimeters are combined in an

energy-flow algorithm [3]. For each event, the algorithm provides a set of charged and

neutral reconstructed particles, called energy-flow objects.

?

E(GeV). The SICAL

?

3Monte Carlo Simulations

In order to simulate the process e+e−→ e+e−γγ → e+e−c¯ c → e+e−D∗±X, the leading-

order (LO) PYTHIA 6.121 Monte Carlo [4] is used. Events are generated at e+e−centre-

of-mass energies ranging from 183GeV to 209GeV using the corresponding integrated

luminosities for weighting. Two different samples, direct and single-resolved processes,

were generated for each of the considered D∗+decay modes using matrix elements for

the massive charm quark. The charm quark mass mcis chosen to be 1.5GeV/c2and the

parameter ΛQCDis set to 0.291GeV/c2. The γγ invariant mass Wγγis required to be at

least 3.875GeV/c2, which is the D¯D threshold. In order to ensure that both photons are

quasi-real, the maximum squared four-momentum transfer Q2

In the single-resolved process, the SaS-1D [5] parametrization is used for the partonic

distribution of the resolved photon. The Peterson et al. parametrization [6] is adopted as

the fragmentation function of the charm quark with the nonperturbative parameter ?c=

0.031. The background process e+e−→ e+e−γγ → e+e−b¯b is simulated using PYTHIA

6.121 with Wγγ being required to be at least 10.5GeV/c2, which is the B¯B threshold.

The b quark mass is set to 4.5GeV/c2. Again the Peterson et al. parametrization is

adopted with ?b = 0.0035. Other possible background processes have been simulated

using appropriate Monte Carlo generators as listed in Table 1.

maxis limited to 4.5GeV/c2.

2

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4Event Selection and Reconstruction of D∗+Mesons

4.1Selection of γγ Events

The data analyzed were collected by the ALEPH detector at e+e−centre-of-mass energies

ranging from 183GeV to 209GeV with an integrated luminosity L = 699pb−1. The event

variables used for the event preselection are based on the ALEPH energy-flow objects.

The following cuts, derived from Monte Carlo studies, were applied to select two-photon

events.

• The event must contain at least 3 charged particles. This cut reduces the background

from leptonic events.

• The visible invariant mass Wvisof the event must lie between 4GeV/c2and 55GeV/c2

while the total energy of charged particles Echshould not exceed 35GeV in order

to reject the e+e−annihilation background.

• The visible transverse momentum pt,vis of the event is required to be less than

8GeV/c, as the pt,visdistribution has a much longer tail for all considered back-

ground processes.

• To reject further background processes a cut combining the number of charged tracks

and the visible energy Evisof the event is applied: Nch< 40 −2

• Finally, in order to retain only events with almost on-shell photons an anti-tagging

condition was applied, i.e., tagged events were rejected. A tag in this analysis is

defined as an energy-flow object in the luminosity calorimeters (LCAL and SICAL)

with an energy of at least 30GeV.

3Evis(GeV).

This selection retains a sample of 4.9 million events. Monte Carlo studies of possible

background sources predict a γγ purity of 98.8%.

4.2Reconstruction of D∗+Mesons

Charm quarks are detected using exclusively reconstructed D∗+mesons which decay via

D∗+→ D0π+, with the D0being identified in three decay modes, (1) K−π+, (2) K−π+π0,

and (3) K−π+π−π+. As a basis for possible K±and π±candidates reconstructed tracks

of charged particles which fulfill the following quality conditions are used:

p> 100MeV/c(momentum of track),

|d0|

|z0|

NTPC≥ 4

|cosθ|< 0.94

A track surviving these cuts is classified as a kaon if the measured specific energy loss

dE/dx of the track is consistent with the expectation value for the kaon mass hypothesis,

i.e., if the corresponding confidence level PKis greater than 10%. The track is classified

as a pion if Pπis at least 1%. Thus, each track can be flagged as a kaon or pion or both

or neither.

< 2cm

< 8cm

(distance to beam axis at closest approach),

(z coordinate at closest approach),

(number of hits in TPC),

(θ = polar angle with respect to beam axis).

3

Page 8

The π0candidates are formed from pairs of photons found in ECAL with an energy of

at least 250MeV each and an invariant mass within 85MeV/c2of the nominal π0mass.

In order to improve the energy resolution of these π0’s the energies of the photons are

refitted using the π0mass as constraint. If the confidence level of this fit is greater than

5% and if |cosθπ0| < 0.93, where θπ0 is the polar angle of the π0candidate with respect

to the beam axis, the π0candidate is retained.

The D0candidates are formed from appropriate combinations of identified kaons and

pions according to three considered decay modes. The D0candidate is retained if it has

an invariant mass within 20MeV/c2, 65MeV/c2, and 20MeV/c2of the nominal D0mass

for decay mode (1), (2), and (3), respectively. These mass ranges correspond to about

three times the mass resolution. In order to reduce the combinatorial background in mode

(3), the four tracks composing the D0are fitted to a common vertex and the confidence

level of this fit is required to be greater than 0.2%. The combination of each D0with one

of the remaining π+candidates is considered to be a D∗+candidate. In order to reduce

combinatorial background from soft processes and to limit the kinematic range of the D∗+

to the acceptance range of the detector with reasonable efficiency, cuts were applied to

the transverse momentum ptand the pseudorapidity η = −ln(tan(θ/2)) of the D∗+:

2GeV/c < pD∗+

t

< 12GeV/c,

|ηD∗+| < 1.5.(1)

If there are several D∗+candidates found in one event the corresponding D0candidates

are compared in mass and only the candidate with D0mass nearest the nominal D0mass

is retained. If two or more D∗+candidates share the same D0candidate, all of them are

retained. Figure 2 shows the mass difference ∆m = mD∗+ − mD0 for the selected D∗+

candidates for all three decay modes together. The spectrum rises at the lower threshold

given by the pion mass. A clear peak is seen around 145.5MeV/c2. In order to extract the

number of D∗+events the data distribution is fitted with the following parametrization:

F(∆m) = N

1

√2πσexp

?

−1

2

?∆m − 145.5MeV/c2

σ

?2 ?

+ C (∆m − mπ+)P

.(2)

In order to exclude systematic binning effects an unbinned maximum likelihood fit is

performed where C and P are used as free parameters. The normalization N follows from

the constraint that the integral of F(∆m) over the range of the fit, 130MeV/c2< ∆m <

200MeV/c2, must be equal to the number of entries in the histogram. The width σ of the

Gaussian describing the peak is fixed to 0.5MeV/c2, as determined in Monte Carlo. The

number of D∗+events is then obtained by integrating the Gaussian part of (2) in the range

of 145.5MeV/c2± 3σ. As the result a total of 360.0 ± 27.0statD∗+events are observed

for all three D∗+decay modes together. Among the possible background processes, only

the contribution from γγ → b¯b → D∗±X is found to be sizeable. This contribution is

estimated to be 20.5 ± 1.6statD∗+events from a γγ → b¯b → D∗±X Monte Carlo sample

and the total cross section σ(e+e−→ e+e−b¯b) measured in [11]. After subtraction of this

background, a total of 339.5±27.0statD∗+events are found in the data sample analyzed.

The mass difference distributions for three channels separately are shown in Fig. 3.

4

Page 9

5 Cross Section Measurements

5.1Relative Fractions of Direct and Single-resolved Contribu-

tions

As mentioned in the introduction, open charm production in γγ collisions is dominated

by contributions from direct and single-resolved processes. In the direct case the c¯ c pair

makes up the final state of the γγ system (in LO) whereas in the single-resolved case the

partons of the resolved photon (photon residue) in addition to the c¯ c pair make up the final

state. The transverse momentum pD∗+

t

of the D∗+is correlated with the invariant mass

of the c¯ c system and the total visible invariant mass Wvisis in turn correlated with the

invariant mass of the total γγ system. The ratio pD∗+

at higher values for the direct case compared to the distribution of single-resolved events.

Figure 4 shows the distribution of pD∗+

t

/Wvisin data for all events found in the signal re-

gion of the mass-difference spectrum. Combinatorial background has been subtracted us-

ing events of the upper sideband 0.16GeV/c2< ∆m < 0.2GeV/c2of the mass-difference

spectrum. Background from b¯b production has also been subtracted. The relative frac-

tions are determined by fitting the sum of the direct and single-resolved Monte Carlo

distributions to data with the relative fraction as a free parameter of the fit. The total

number of entries in this Monte Carlo sum is required to be equal to the number of entries

in the data distribution. The fit yields a direct contribution of rdir= (62.6 ± 4.2)% and

a single-resolved contribution of rres= 1 − rdir= (37.4 ± 4.2)%.

t

/Wvisshould therefore be distributed

5.2 Differential Cross Sections

Two differential cross sections for the production of D∗+mesons are determined: the first

one as a function of the transverse D∗+momentum pD∗+

of pseudorapidity |ηD∗+|. Both are restricted to the range defined in Eq. (1). The former

is measured in three pD∗+

t

bins: [2–3], [3–5], [5–12] GeV/c, and the latter in three |ηD∗+|

bins: [0–0.5], [0.5–1.0], [1.0–1.5]. All considered D∗+decay modes were treated separately.

The average differential cross section dσ/dpD∗+

is obtained by

t

, and the second as a function

t

for a given pD∗+

t

bin and |ηD∗+| < 1.5

dσ

dpD∗+

t

=

ND∗+

found

LB∗B0?pD∗+

∆pD∗+

t

t

.(3)

Analogously one obtains dσ/d|ηD∗+| for a given bin in |ηD∗+| and 2GeV/c < pD∗+

12GeV/c

dσ

d|ηD∗+|=

where

t

<

ND∗+

found

∆|ηD∗+|LB∗B0?|ηD∗+|

,

• ND∗+

background (determined as described in Section 4.2) with the width of the fitted

foundis the number of D∗+found in the considered bin after subtracting the b¯b

5

Page 10

Gaussian (2) being fixed to 0.5MeV/c2for decay modes (1) and (3) and 0.7MeV/c2

for decay mode (2),

• ∆pD∗+

• L = 699pb−1is the integrated luminosity of the data analyzed,

• B∗is the branching ratio BR(D∗+→ D0π+) = (68.3 ± 1.4)% [10],

• B0is the branching ratio of the considered D0decay mode [10],

• ?pD∗+

(|ηD∗+|) bin in the considered decay mode. Since efficiencies are determined sep-

arately for direct and single-resolved processes (?dir

total efficiency is a weighted combination using the fractions as determined in Sec-

tion 5.1,

?pD∗+

t

t

?|ηD∗+|= rdir?dir

t

, ∆|ηD∗+| are the considered intervals in pD∗+

t

and |ηD∗+|,

t

(?|ηD∗+|) is the efficiency of reconstructing a D∗+candidate in the given pD∗+

t

pD∗+

t

and ?res

pD∗+

t

, respectively) the

= rdir?dir

pD∗+

+ rres?res

pD∗+

t

,

|ηD∗+|+ rres?res

|ηD∗+|

.

Tables 2 and 3 show the number of D∗+mesons found in the chosen pD∗+

respectively, as well as the derived differential cross sections dσ/dpD∗+

with their statistical and systematic errors. The resulting cross sections for the different

D∗+decay modes are consistent with each other for all bins in pD∗+

taking into account the statistical uncertainties. The weighted average over all of the

considered D∗+decay modes is given in Table 4 for each pD∗+

the dominating statistical uncertainties are used for weighting.

t

and |ηD∗+| bins

and dσ/d|ηD∗+|

as well as in |ηD∗+|,

and |ηD∗+| bin, where only

t

t

t

5.2.1 Systematic Errors on Differential Cross Sections

The study of systematic errors was performed separately for each pD∗+

for each of the considered D∗+decay modes, unless otherwise specified.

The systematic error introduced by the event selection was studied by varying the cuts

within the resolution obtained from the Monte Carlo detector simulation. The systematic

uncertainty was estimated from the resulting relative variation of the efficiency. This

yields an uncertainty of 0.6%–6.4%, depending on the considered pD∗+

on the D∗+decay mode.

The selection of pion and kaon candidates depends essentially on the dE/dx measure-

ment as well as on the expectation values dE/dxexp,hused to calculate the probability

for a given mass hypothesis mh. The uncertainty of the dE/dx calibration changes the

efficiency by 0.5%–5.8%. These deviations are used as an estimate of the systematic error.

The systematic error due to the accepted mass range used to classify D0candidates

was examined by comparison of the mass distributions of D0candidates which contributed

to the D∗+signal in data and Monte Carlo for each D0decay mode separately. A Gaussian

fit was applied to these distributions. The fraction of the fitted Gaussian which lies within

the accepted mass range differs between data and Monte Carlo by less than 0.6%. Thus,

the uncertainty due to this source can be neglected.

In order to estimate the error introduced by the method for extracting the number

of D∗+events (Section 4.2) the mean of the fitted Gaussian in Eq. (2) was varied by

t

and |ηD∗+| bin and

t

or |ηD∗+| bin and

6

Page 11

±0.05MeV/c2, and the width was varied by 10% about its values as obtained in Monte

Carlo. The resulting relative error on the efficiencies was 0.8%–2.1%.

A variation of the interval that defines the upper sideband yields a variation in rdir

of less than 0.05%. Hence, this source is negligible. The present analysis assumes the

fraction rdir to be constant over the considered kinematic range. Monte Carlo studies

show a variation of this fraction of up to 12% in this range, depending on the bin in

pD∗+

t

and |ηD∗+|. A relative uncertainty of 10% is therefore added in quadrature to the

statistical uncertainty of rres. A variation of rdir/reswithin these uncertainties yields a

variation in the cross section of 0.3%–3.4%, which is used to estimate the introduced

uncertainty.

The statistical error of b¯b background subtraction and the uncertainties of the total

cross section σ(e+e−→ e+e−b¯b) yield a systematic error of 1.2%–3.4% on the differential

cross sections.

The overall trigger efficiency of the selected D∗+events is estimated to be consistent

with 100% with a statistical uncertainty of 1%. Thus no correction is made for this source.

The relative errors on the branching ratios given in [10] are used to estimate the

corresponding relative systematic uncertainties in the cross sections.

Similarly the relative uncertainties in the efficiencies due to finite statistics in the

Monte Carlo samples, 0.5%–2.3%, are taken into account.

All systematic errors are assumed to be uncorrelated and therefore added in quadra-

ture. Table 5 shows a summary of the systematic uncertainties.

5.2.2Comparison to Theory

Figures 5 and 6 show the measured dσ/dpD∗+

ferent NLO perturbative QCD calculations, the fixed-order (FO) NLO (also known as

massive approach) [12] and the resummed (RES) NLO (massless approach) [13]. In both

cases, the charm quark mass mcis set to 1.5GeV/c2, the renormalization scale µRand

the factorization scale µFare chosen such that µ2

pt(c) is the transverse momentum of the charm quark. For the resolved contribution the

photonic parton densities of the GRS-HO parametrization are chosen [14] in the FO NLO

calculation, whereas the RES NLO uses GRV-HO [15]. The fragmentation of the charm

quark to the D∗+is modelled by the fragmentation function suggested by Peterson et

al. [6], with ?c= 0.035 in the case of FO NLO. The RES NLO calculation uses ?c= 0.185,

which was determined by using nonperturbative fragmentation functions fitted [13] to

ALEPH measurements of inclusive D∗+production in e+e−annihilation [16]. The results

of the two NLO QCD calculations are represented by the dashed lines (for RES NLO)

and solid lines (for FO NLO) in both Fig. 5 and Fig. 6. In order to estimate the the-

oretical uncertainties, the FO NLO calculation was repeated with the charm mass and

the renormalization scale varied as described in the figures. The RES NLO calculation is

also repeated using the AFG [17] ansatz as an alternative for parton density function and

varying the renormalization and factorization scales. The resulting theoretical uncertain-

ties are indicated by the bands around the corresponding default values in Figs. 5 and

6.

Altogether, the measurement of dσ/dpD∗+

t

t

and dσ/d|ηD∗+| in comparison to two dif-

F= 4µ2

R= m2

T≡ m2

c+ pt(c)2, where

seems to favour a harder pD∗+

t

spectrum

7

Page 12

than predicted. The RES NLO calculation clearly overestimates the measurement in

the low pD∗+

t

region, while the FO NLO calculation slightly underestimates it in the

pD∗+

t

> 3.0GeV/c region. The measured dσ/d|ηD∗+| is consistent with the almost flat

distribution predicted by both NLO calculations, but the measurement of dσ/d|ηD∗+| is

again overestimated by the RES NLO calculation and somewhat underestimated by the

FO NLO calculation.

5.3Visible Cross Section

The visible cross section σD∗+

tance range [Eq. (1)] for the three considered decay modes by

vis(e+e−→ e+e−D∗+X) is calculated separately in the accep-

σD∗+

vis(e+e−→ e+e−D∗+X) =

ND∗+

found

LB∗B0?

,(4)

where the notation is as the same as in Eq. (3). The numbers of D∗+found and the

efficiencies of reconstructing a D∗+candidate for direct and single-resolved processes are

listed in Table 6 together with the derived visible cross sections σD∗+

and their uncertainties for the three decay modes. The systematic error is determined

in the same way as for differential cross sections (Section 5.2.1). The weighted average

over all of the considered decay modes using the dominating statistical uncertainties for

weighting is

vis(e+e−→ e+e−D∗+X)

σD∗+

vis(e+e−→ e+e−D∗+X) = 23.39 ± 1.64stat± 1.52systpb

The theoretically predicted cross section [12] is

.(5)

σD∗+

vis(e+e−→ e+e−D∗+X) = 17.3+5.1

−2.9pb,(6)

and is consistent with this measurement within the given uncertainties.

5.4Total Cross Section

The total cross section for the reaction e+e−→ e+e−c¯ c is given by

σ(e+e−→ e+e−c¯ c) =

σD∗+

vis

2Pc→D∗+(rdirRdir+ rresRres),(7)

where the symbols are as follows:

• σD∗+

• Pc→D∗+ is the probability for a charm quark to fragment into a D∗+meson (taking

the combined quantity Pc→D∗+ ×BR(D∗+→ D0π+) = 0.1631±0.0050 from [18] and

using BR(D∗+→ D0π+) = (68.3 ± 1.4)% [10] yields Pc→D∗+ = 0.2388 ± 0.0088);

• the factor 2 in the denominator takes into account that, for the single inclusive cross

sections, both the D∗+and the D∗−mesons were counted;

vis

is the visible inclusive D∗+cross section determined in the previous section;

8

Page 13

• rdirand rresare the fractions of the direct and single-resolved contributions in the

considered acceptance range, as described in Section 5.1;

• Rdiris the ratio

Rdir=σD∗+

tot,dir

σD∗+

vis,dir

of the total D∗+cross section to the visible cross section in the range of Eq. (1) for

direct processes. It describes the extrapolation of the measured cross section to the

total phase space available. Rresis the corresponding quantity for the single-resolved

case.

Separate Monte Carlo samples are used to estimate Rdirand Rresfor direct and single-

resolved processes. The parameters used to determine Rdir and Rres are described in

Section 3. This yields Rdir= 12.74 ± 0.45statand Rres= 18.62 ± 0.80stat.

The main theoretical uncertainties entering the calculation of the extrapolation factors

stem from the uncertainty of the charm quark mass. A variation of the charm mass to

mc= 1.3GeV and mc= 1.7GeV yields relative errors on Rdirof ±10% and on Rresof

+43% and −19%, respectively.

In the single-resolved case an additional uncertainty enters Rresby the choice of the

parton density functions describing the resolved photon. Alternatively to the default

choice the GRV-LO parametrization [19] was used to calculate Rres. This yields a relative

deviation of 12% and is added in quadrature to the other systematic uncertainties on Rres.

The following values are therefore obtained:

Rdir= 12.7 ± 1.3

Rres= 18.6+8.3

−4.2

.

The uncertainties in rdir, σD∗+

taken into account in the estimation of the statistical and systematic error on the total

cross section by Gaussian error propagation. This procedure yields a total cross section

for the reaction e+e−→ e+e−c¯ c at e+e−centre-of-mass energies√s = (183 − 209)GeV,

corresponding to the luminosity weighted average of 197GeV,

vis, and Pc→D∗+, which are assumed to be uncorrelated, are

σ(e+e−→ e+e−c¯ c)<√s>=197GeV= 731 ± 74stat± 47syst+157

−86extrpb.(8)

Alternatively, the total cross section is determined by means of the NLO calculation

referenced in the previous section; in this case the cross section is given by

σ(e+e−→ e+e−c¯ c) =

σD∗+

vis

2Pc→D∗+Rtot

. (9)

The value Rtot= 22.2 is extracted from [12] by determining the ratio of the calculated

total charm cross section to the charm cross section calculated for the visible D∗+range

considered in the present analysis. Variation of the parameters entering the calculation

9

Page 14

yields deviations in the range from −33% to +72%, which are used as an estimate of the

systematic error due to the extrapolation. This results in a total cross section

σ(e+e−→ e+e−c¯ c)<√s>=197GeV= 1087 ± 86stat± 70syst+783

−357extrpb.(10)

The measured total cross section [Eq. (8)] is shown in Fig. 7 in comparison to the

NLO QCD prediction of Drees et al. [1] and to results from other experiments [20, 21, 22,

23]. Within the uncertainties, this NLO QCD prediction is in good agreement with our

measurement and others [24].

6 Conclusions

The inclusive production of D∗+mesons in two-photon collisions was measured using the

ALEPH detector at LEP 2 energies in the reaction D∗+→ D0π+. The D0mesons were

identified in the decay modes K−π+, K−π+π0, and K−π+π−π+. A total of 339.5 ± 27.0

D∗+events from γγ → c¯ c was found in the kinematic region 2GeV/c < pD∗+

and |ηD∗+| < 1.5.

The fractions of the main contributing processes, direct and single-resolved, were de-

termined using the event variable pD∗+

t

/Wvisto be rdir= (62.6±4.2)% and rres= 1−rdir=

(37.4 ± 4.2)%, within the acceptance.

The differential cross sections dσ/dpD∗+

t

and dσ/d|ηD∗+| were measured and compared

to the fixed-order (FO) NLO QCD calculation [12] and the resummed (RES) NLO QCD

calculation [13]. While the data show a slightly harder spectrum in the pD∗+

tion compared to both calculations, the almost flat distribution of dσ/d|ηD∗+| which is

predicted by the NLO calculations for the visible D∗+region is in agreement with the

measurement. Overall, the measurements of dσ/dpD∗+

derestimated by the FO NLO calculation and overestimated by the RES NLO calculation.

For the integrated visible D∗+cross section a value of σD∗+

1.52systpb is obtained which is consistent with the FO NLO calculation.

The extrapolation of the visible D∗+cross section to the total cross section of charm

production introduces large theoretical uncertainties and has a large relative uncertainty.

Using the LO calculation of the Pythia Monte Carlo we obtain

t

< 12GeV/c

t

distribu-

t

and dσ/d|ηD∗+| were slightly un-

vis

= 23.39 ± 1.64stat±

σ(e+e−→ e+e−c¯ c)<√s>=197GeV= 731 ± 74stat± 47syst

A different method using the results from the FO NLO calculation [12] yields a higher

cross section and a larger error.

+157

−86extrpb.

Acknowledgements

We wish to thank our colleagues in the CERN accelerator divisions for the successful

operation of LEP. We are indebted to the engineers and technicians in all our institutions

for their contribution to the excellent performance of ALEPH. Those of us from non-

member countries thank CERN for its hospitality. We would like to thank Stefano Frixione

and Bernd Kniehl for fruitful discussions.

10

Page 15

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