EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
10th January 2003
Measurement of the inclusive D∗±
in γγ collisions at LEP
The ALEPH Collaboration∗)
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
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.
of the D∗±to the visible invariant
Submitted to European Physical Journal C
∗) See next pages for the list of authors
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,
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
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
Laoratoire Leprince-Ringuet, Ecole Polytechnique, IN2P3-CNRS, F-91128 Palaiseau Cedex, France
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
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
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,
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,
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
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
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,
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
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
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,
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,
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.
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
28Research Fellow of the Belgium FNRS
29Research Associate of the Belgium FNRS
30Now at Verdi Information Consult GmbH, 53757 Sankt Augustin, Germany
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) . 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 . 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.
2 ALEPH 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.
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
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
The information from the tracking detectors and the calorimeters are combined in an
energy-flow algorithm . For each event, the algorithm provides a set of charged and
neutral reconstructed particles, called energy-flow objects.
E(GeV). The SICAL
3 Monte 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  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  parametrization is used for the partonic
distribution of the resolved photon. The Peterson et al. parametrization  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.
4 Event 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
• 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-
• 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.
This selection retains a sample of 4.9 million events. Monte Carlo studies of possible
background sources predict a γγ purity of 98.8%.
4.2 Reconstruction 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),
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
(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).
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∗+
|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
?∆m − 145.5MeV/c2
+ C (∆m − mπ+)P
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 . 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.
5 Cross Section Measurements
5.1 Relative Fractions of Direct and Single-resolved Contribu-
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∗+
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∗+
/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)%.
/Wvisshould therefore be distributed
5.2Differential 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∗+
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
, and the second as a function
for a given pD∗+
bin and |ηD∗+| < 1.5
Analogously one obtains dσ/d|ηD∗+| for a given bin in |ηD∗+| and 2GeV/c < pD∗+
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
Gaussian (2) being fixed to 0.5MeV/c2for decay modes (1) and (3) and 0.7MeV/c2
for decay mode (2),
• L = 699pb−1is the integrated luminosity of the data analyzed,
• B∗is the branching ratio BR(D∗+→ D0π+) = (68.3 ± 1.4)% ,
• B0is the branching ratio of the considered D0decay mode ,
(|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-
, ∆|ηD∗+| are the considered intervals in pD∗+
(?|ηD∗+|) is the efficiency of reconstructing a D∗+candidate in the given pD∗+
, respectively) the
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.
and |ηD∗+| bins
as well as in |ηD∗+|,
and |ηD∗+| bin, where only
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
and |ηD∗+| bin and
or |ηD∗+| bin and
±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
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
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
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  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.
5.2.2 Comparison 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)  and the resummed (RES) NLO (massless approach) . 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  in the FO NLO
calculation, whereas the RES NLO uses GRV-HO . The fragmentation of the charm
quark to the D∗+is modelled by the fragmentation function suggested by Peterson et
al. , 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  to
ALEPH measurements of inclusive D∗+production in e+e−annihilation . 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  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
Altogether, the measurement of dσ/dpD∗+
and dσ/d|ηD∗+| in comparison to two dif-
c+ pt(c)2, where
seems to favour a harder pD∗+
than predicted. The RES NLO calculation clearly overestimates the measurement in
the low pD∗+
region, while the FO NLO calculation slightly underestimates it in the
> 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-
vis(e+e−→ e+e−D∗+X) =
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
vis(e+e−→ e+e−D∗+X) = 23.39 ± 1.64stat± 1.52systpb
The theoretically predicted cross section  is
vis(e+e−→ e+e−D∗+X) = 17.3+5.1
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) =
2Pc→D∗+(rdirRdir+ rresRres), (7)
where the symbols are as follows:
• 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  and
using BR(D∗+→ D0π+) = (68.3 ± 1.4)%  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;
is the visible inclusive D∗+cross section determined in the previous section;
• 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
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
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  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
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
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) =
The value Rtot= 22.2 is extracted from  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
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
The measured total cross section [Eq. (8)] is shown in Fig. 7 in comparison to the
NLO QCD prediction of Drees et al.  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 .
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∗+
/Wvisto be rdir= (62.6±4.2)% and rres= 1−rdir=
(37.4 ± 4.2)%, within the acceptance.
The differential cross sections dσ/dpD∗+
and dσ/d|ηD∗+| were measured and compared
to the fixed-order (FO) NLO QCD calculation  and the resummed (RES) NLO QCD
calculation . 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
and dσ/d|ηD∗+| were slightly un-
= 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  yields a higher
cross section and a larger error.
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.
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