- Email: [email protected]
Measurement of the inclusive D∗± production in γγ collisions at LEP
CxiA /---@
SUPPLEMENTS Nuclear Physics B (Proc. Suppl.) 126 (2004) 172-178
ELSEVIER
Measurement
of the inclusive D** production
www.cJhevierphysics.com
in yy collisions at LEP
J. Hel?, A. Ngac” “Fachbereich Physik, University 57068 Siegen, Germany
of Siegen,
collisions is measured with the ALEPH detector at The inclusive production of D** mesons in two-photon e+e- centre-of-mass energies from 183 GeV to 209 GeV. A total of 360 i 27 D*’ meson events are observed from an integrated luminosity of 699 pb-‘. Cont$>tions from direct and single-resolved processes are separated of the D** to the visible invariant mass Wyis of the event. using the ratio of the transverse momentum p, Differential cross sections of D** production as functions of pf** and the pseudorapidity (qD** ( are measured to next-to-leading order in the range 2GeV/c < pt*** < 12 GeV/c and IqD**/ < 1.5. They are compared The extrapolation of the integrated visible D** cross section to the (NLO) perturbative QCD calculations. total charm cross section, based on the Pythia Monte Carlo program, yields u(e+e-+ efe-cF)(fi))=leiGev = 731 i 74,tat k 47,,,t + 157,,t, pb.
1. INTRODUCTION Heavy flavour production in two-photon events at LEP 2 centre-of-mass energies is dominated by charm production processes in which both of the photons couple directly to the charm quark (direct processes) or in which one photon couples directly and the other appears resolved (singleresolved processes) [l]. These two contributions are of the same order of magnitude within the Because the singleexperimental acceptance. resolved process is dominated by yg 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 (doubleresolved processes) are suppressed by more than two orders of magnitude compared to the total cross section [l]. 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 yy sample is first selected, then examined for its charm content via reconstruction of D*” mesons in their 0920-5632/s - see front matter doi:10.1016/j.nuc1p1~ysbps.2003.11.029
0 2004 Published
by Elsevier
B.\!
decay to Don+. Throughout this note chargeconjugated particles and their decays are implicitly included.
2. MONTE
CARLO
SIMULATIONS
In order to simulate the process e+e- + e+e-yy -+ e+e-cc -+ e+e-D**X, the leadingorder (LO) PYTHIA 6.121 Monte Carlo [2] is used. Events are generated at e+e- centre-ofmass energies ranging from 183 GeV to 209 GeV 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 m, is chosen to be 1.5 GeV/c2 and the parameter &CD is set to 0.291GeV/c2 . The yy invariant mass W,, is required to be at least 3.875 GeV/c2, which is the DD threshold. In order to ensure that both photons are quasi-real, the maximum squared four-momentum transfer is limited to 4.5GeV/c2. In the singleSF&X resolved process, the SaS-1D [3] parametrization is used for the partonic distribution of the resolved photon. The Peterson et al. parametrization [4] is adopted as the fragmentation function of the charm quark with the nonperturbative parameter ec = 0.031. The background process
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Physics B (Proc. Suppl.) 126 (2004) 172-178
e+e- + e+e- yy --+ e+e-bb is simulated using PYTHIA 6.121 with W,, being required to be at least 10.5GeV/c2, which is the BB threshold. The b quark mass is set to 4.5 GeV/c2. Again the Peterson et al. parametrization is adopted with cb = 0.0035. The background processes e+e- -+ qq, e+e- -+ ~+r-, e+e- + e+e-r+rand e+e- -+ W+W- have been simulated using appropriate Monte Carlo generators. 3. DATA The ALEPH detector and its performance have been described in detail elsewhere [5,6]. Charged tracks and neutral calorimeter energy as defined by the ALEPH energy flow package [6] are used in this analysis. 3.1. Selection of yy 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 .C = 699pb-‘. Usual cuts on multiplicity, reconstructed invariant mass and transverse momentum are applied to select yy events. The selection retains a sample of 4.9 million events. Monte Carlo studies of possible background sources predict a yy purity of 98.8%. For more detaiIs see [7]. 3.2. Reconstruction of D*+ Mesons Charm quarks are detected using reconstructed D*+ mesons which decay via D*+ -+ D”rrTt, with the Do being identified in three decay modes, (1) K-r+, (2) Ke~+7r0, and (3) K-@n-r+. For tracks that fulfill certain quality conditions the measured specific energy loss dE/dx is used to identify K* and 7r* candidates. The x0 candidates are formed from pairs of photons found in ECAL with an energy of at least 250 MeV each and an invariant mass within 85MeV/c2 of the nominal no mass. The energy resolution could be improved by refitting the energies of the photons under a 7~~mass constraint. The Do candidates are formed from appropriate combinations of identified kaons and pions according to three considered decay modes. The Do candidate is retained if it has an invariant mass within 20 MeV/c2, 65 MeV/c2, and 20 MeV/c2 of
173
the nominal Do mass for decay mode (l), (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 Do are fitted to a common vertex and the confidence level of this fit is required to be greater than 0.2%. The combination of each Do with one of the remaining 7r.f 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 Pt and the pseudorapidity 77= - ln(tan(0/2)) of the D*+: 2GeV/c
< $‘+
< 12GeV/c,
]~o*~] < 1.5
.(l)
Figure 1 shows the mass difference Am = mDI+ 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 an appropriate parametrization. In order to exclude systematic binning effects an unbinned maximum likelihood fit is performed. The width a of the Gaussian describing the peak is fixed to 0.5MeV/c2, as determined in Monte Carlo. As the result a total of 360.0&27.0,t,t D*+ events are observed in the signal region for all three D*+ decay modes together. Among the possible background processes, only the contribution from yy -+ b6 -+ D**X is found to be sizeable. This contribution is estimated to be 20.5 f l.6,tat D*+ events. After subtraction of this background, a total of 339.5 f 27.0,tat D*+ events are found in the data sample analyzed. 4. CROSS
SECTION
MEASUREMENTS
4.1. Relative Fractions of Direct and Single-resolved Contributions As mentioned in the introduction, open charm production in yy collisions is dominated by contributions from direct and single-resolved processes. In the direct case the CS:pair makes up the final state of the yy system (in LO) whereas in the single-resolved case the partons of the resolved photon (photon residue) in addition to the
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Direct : (62.6 +_4.2)% Single-resolved : (37.4 + 4.2)%
80 60 40 20 n L “0.13
0.14
0.15 0.16 0.17 0.18 Am = m,*+ - mDO [GeV/c’]
0.19
0.2 0
Figure 1. Mass difference of reconstructed D*’ and Do candidates for all considered Do decay modes together. The points show data, the error bars represent statistical uncertainties, and the solid curve indicates the result of an unbinned maximum likelihood fit.
CE pair make up the final state. The transverse momentum pp* of the D*+ is correlated with the invariant mass of the CEsystem and the total visible invariant mass l&is is in turn correlated with the invariant mass of the total yy system. The ratio Py*+/Wvi, should therefore be distributed at higher values for the direct case compared to the distribution of single-resolved events. Figure 2 shows the distribution of Pp*+JW+, in data for all events found in the signal region of the mass-difference spectrum. Combinatorial background has been subtracted using events of the upper sideband 0.16 GeV/c2 < Am < 0.2 GeV/c2 of the mass-difference spectrum. Background from b6 production has also been subtracted. The relative fractions 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 f 4.2)% and a single-resolved contribution of T,,, = 1 - r&r = (37.4 f 4.2)X.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
FNvis
Figure 2. Pp*‘JWvis distribution for reconstructed D*+ events. The points with error bars show data. The relative contributions from direct (shaded histogram) and single-resolved (open histogram) processes are extracted by means of a fit.
4.2. 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 D*+ Pt F and the second as a function of pseudorapidity ]Q~*+). Both are restricted to the range defined in Eq. (1). The former is measured in three py*’ bins: [2-31, [3-51, [S-12] GeV/c, and the latter in three ]qD*+] bins: [O-0.5], [0.5-1.01, [l.O-1.51. All considered D*+ decay modes were treated separately. The efficiencies are determined separately for direct and single-resolved processes. The total efficiency is a weighted combination using the fractions as determined in Section 4.1. The resulting cross sections for the different D*+ decay modes are consistent with each other for all bins in p,D*+ as well as in [qD*+ 1, taking into account the statistical uncertainties. 4.3.
Systematic Errors on Differential Cross Sections The study of systematic errors was performed separately for each pF*’ and ]qD*’ ] bin and for each of the considered D*+ decay modes. Therefore ranges for the size of the particular uncer-
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Physics B (Proc. Suppl.) 126 (2004) 172-l 78
tainties are given. The systematic error introduced by the event selection was studied by varying the cuts within the resolution obtained from the Monte Carlo detector simulation. This yields an uncertainty of 0.6%-6.4%. The selection of pion and kaon candidates depends essentially on the dE/dx measurement. The uncertainty of the dE/dx calibration changes the efficiency by 0.5%-5.8%. The uncertainty due to the accepted mass range used to classify Do candidates was found to be negligible. In order to estimate the error introduced by the method for extracting the number of D*+ events (Section 3.2) the parameters of the fitted Gaussian were varied about its values as obtained in Monte Carlo. The resulting relative error on the efficiencies was 0.8%-2.1%. The present analysis assumes the fractions rdir/res to be constant over the considered kinematic range. Monte Carlo studies have been performed with varied fractions and an uncertainty in the cross section of 0.3%-3.4% is estimated. The statistical error of bb background subtraction and the uncertainties of the total cross section a(e’e- -+ e+e-bb) 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. Relative errors on the branching ratios given in [8] are used to estimate the corresponding uncertainties. Similarly the relative uncertainties in the efficiencies due to finite statistics in the Monte Carlo samples, 0.5%-2.3%, are taken into account. 43.1. Comparison to Theory Figures 3 and 4 show the measured dg/dpF*+ and da/dlqD*+ 1 in comparison to two different NLO perturbative QCD calculations, the fixedorder (FO) NLO (also known as massive approach) [lo] and the resummed (RES) NLO (massless approach) [ll]. In both cases, the charm quark mass m, is set to 1.5GeV/c2, the renormalization scale pn and the factorization
175
scale j.LF are chosen such that & = 4& ti rn$ 5 m,2 + pt (c12, where 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 [12] in the FO NLO calculation, whereas the RES NLO uses GRV-HO [13]. The fragmentation of the charm quark to the D*+ is modelled by the fragmentation function suggested by Peterson et al. [4], with E, = 0.035 in the case of FO NLO. The RES NLO calculation uses Ed = 0.185, which was determined by using nonperturbative fragmentation functions fitted [ll] to ALEPH measurements of inclusive D*+ production in e+eannihilation [14]. The results of the two NLO QCD calculations are represented by the dashed lines (for RES NLO) and solid lines (FO NLO) in both Fig. 3 and Fig. 4. In order to estimate the theoretical 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 [15] ansatz as an alternative for parton density function and varying the renormalization and factorization scales. The resulting theoretical uncertainties are indicated by the bands around the corresponding default values in Figs. 3 and 4. Altogether, the measurement of dcr/d#*‘+ seems to favour a harder py*+ spectrum than predicted. The RES NLO calculation clearly overestimates the measurement in the low p,““’ region, while the FO NLO calculation slightly underestimates it in the pp” > 3.0GeVjc region. The measured da/dlqD*+I is consistent with the almost flat distribution predicted by both NLO calculations, but the measurement of do/dJqD*+J is again overestimated by the RES NLO calculation and somewhat underestimated by the FO NLO calculation. 4.4. Visible Cross Section The visible cross section c$i’ (e+e-+ efe-D*+X) is calculated separately in the acceptance range [Eq. (l)] for the three considered decay modes. The weighted average over all of the considered decay modes using the dominating statistical uncertainties for weighting is D*’ (e+e- --+ e+e-D*‘X) ovis
J. H@,
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B (Proc.
Suppl.)
35
126 (2004)
_ -
25
_ 1
78
PDF: GRV and AFG m, = 1.5GeV, %=Q2=m$ and 2% .-*.- Default setup: GRV, rn, = 1.5 GeV, h=w=q
- a
30
172-l
FO NLO (Massive approach) PDF: GRS m, = 1.2 GeV and 1.8 GeV h=29 for direct, and m,J2 for resolved Default setup: GRS, mc = 1.5 GeV, &$=@.=I+
20 NLO
i
QCD
m
RES NLO (Massless approach) PDF: GUV and AFG m, = 1.5 GeV, !+3+JZ=m/2 and 29 -.--. Default setup: GRV, m, = 1.5 GeV, h=Q.=m,
m
FO NLO (Massive approach) PDF: GRS D,, = 1.2 GeV and 1.8 GeV
-1
10
i I,,
2
,
3
I
4
*
I,
I
5
6
I
15
lo
I,
I
7
8
,
I,
I,
9
I
Figure 3. Differential cross section da/dpg*+ for the inclusive D*+ production. The points show the combined differential cross sections from the three decay modes under studies. The error bars correspond to the total uncertainties. The shaded bands represent the theoretical uncertainties of these calculations.
= 23.39 f 1.64,t,t f 1.52,,,t pb The cross section theoretically FO NLO calculation [lo] is ffvisD*+(e”e-
-+ e+e-D*+X)
.
predicted
= 17.3::::
pb
t
*I
10 11 12 #+ [GeVk]
by the
7 (2)
and is consistent with this measurement within the given uncertainties. 4.5. Total Cross Section The total cross section for the reaction e+e- -+ e+e-cF can be calculated knowing the ratio
of the total D*+ cross section to the visible cross section in the acceptance range for di-
Y
OO
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,””””””””’
! 0.5
-3
, 1
Figure 4. Differential cross section do/d(qD*+j the inclusive D*+ production.
i
1.5 lJID’+l
for
rect/resolved processes. It describes the extrapolation of the measured cross section to the total phase space available. Separate Monte Carlo samples are used to estimate R&r and R,,, for direct and single-resolved processes. This yields Rdir = 12.74&0.45,t,t and Rres = 18.62*0.80,t,t. 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 m, = 1.3 GeV/c2 and m, = l.7GeV/c2 yields relative errors on Rdir of HO% and on R,,, of +43% and -19%, respectively. In the single-resolved case an additional uncertainty enters R,,, by the choice of the parton density functions describing the resolved photon. Alternatively to the default choice the GRVLO parametrization [16] was used to calculate R l-es. This yields a relative deviation of 12% and is added in quadrature to the other systematic uncertainties on R,,,. The following values are
J H@, A. Nguc/Nucleur
Physics B (Proc. Suppl.) 126 (2004) 172-178
177 ALEPH
therefore obtained: Rdir = 12.7& 1.3 ,
R,,, = l&6+;:’
.
Finally the total cross section for the reaction e+e- + e+e-cF at e+e- centre-of-mass energies ,/ii = (183-209) GeV, corresponding to the luminosity weighted average of 197 GeV, is calculated to be
a(e+e-
+ e+e-cC)(Gj=lg7GeV
731 k 74stat f 47s,t:;;;xtr
= pb
I 0
-+ e+e-cZ)(Ajc197GeV
1087f &at
40
60
80
100
,,,,I,
120
140
I,,,,..,
160
180 200 & [G&J
.
Alternatively, the total cross section is determined by means of the NLO calculation referenced in the previous section.The value Rtot = 22.2+16.0 . -7,3 1s extracted from [lo]. The large uncertainty of Rtot again is mainly due to the uncertainty of the charm quark mass chosen in the range from m, = 1.2GeV/c2 to m, = 1.8 GeV/c2. This results in a total cross section a(e+e-
l,,t,II,,I,,,I,
20
Figure 5. The total cross section for charm production a(e+e- -+ efe-cc) versus the centre-ofmass energy & of the ese- system. The measurement of this analysis is shown as a square. The band represents the NLO QCD calculation [l]. The results obtained by L3 and OPAL using D*$ are represented in [18] and [17], respectively. The L3 measurements using lepton tag can be found in [19]. The values for TASSO, TPC/&, JADE, AMY, and VENUS are taken from [20].
=
f 70systt-;;;extr pb .
The measured total cross section [Eq. (3)] is shown in Fig. 5 in comparison to the NLO QCD prediction of Drees et al. [l] and to results from other experiments [17-201. Within the uncertainties, this NLO QCD prediction is in good agreement with our measurement and others [21]. 5. CONCLUSIONS The fractions of the main contributing processes, direct and single-resolved, were determined using the event variable $*‘/W,i, to be Tdir = (62.6f4.2)% and T,,~ = 1 -r&r = (37.4f 4.2)%, within the acceptance. The differential were cross sections da/dpf’+ and da/d)qD*+] measured and compared to theoretical predictions. While the data show a slightly harder spectrum in the pF** distribution compared to calculations, the almost flat distribution of da/d/qD**) which is predicted by the NLO calculations for the visible D*+ region is in agreement with the Overall, the measurements of measurement.
da/d$*+ and da/d]qD’+ ) were slightly underestimated by the FO NLO calculation with m, = 1.5 GeV/c2 and overestimated by the RES NLO calculation. For the i$egrated visible D*+ cross section a value of a,, = 23.39 + 1.64,t,t 4: 1.52,,,$ pb 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 is dominated by theoretical uncertainties due to the charm quark mass and the parton density function used for the resolved photon. REFERENCES 1. M. Drees et. al., Phys. Lett. B 306 (1993) 371. 2. T. Sjijstrand, Comput. Phys. Commun. 82 (1994) 74. 3. G. A. Schuler and T. Sjostrand, Z. Phys. C 68 (1995) 607. 4. C. Peterson et. al., Phys. Rev. D 27 (1983)
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105. 5. ALEPH Collaboration, Nucl. Instrum. Meth. A 294 (1990) 121; Nucl. Instrum. Meth. A379 (1996) 121. 6. ALEPH Collaboration, Nucl. Instrum. Meth. A 360 (1995) 481. 7. ALEPH Collaboration,CERN-EP-2003-002 8. Particle.Data Group, Phys. J. C 15 (2000) 1. 9. L3 Collaboration, Phys. Lett. B 503 (2001) 10. 10. S. Frixione, M. Kramer, and E. Laenen, Nucl. Phys. B 571 (2000) 169. 11. J. Binnewies, B.A. Kniehl and G. Kramer, Phys. Rev. D 58 (1998) 014014; D 53 (1996) 6110. 12. M. Gliick, E. Reya, and I. Schienbein, Phys. Rev. D 60 (1999) 54019. 13. M. Gliick, E. Reya, and A. Vogt, Phys. Rev. D 46 (1992) 1973. 14. ALEPH Collaboration, Eur. Phys. J. C 16 (2000) 597. 15. P. Aurenche, J.P. Guillet, and M. Fontannaz, Z. Phys. C 64 (1994) 621. 16. M. Gliick, E. Reya, and A. Vogt, Phys. Rev. D 45 (1992) 3986. 17. OPAL Collaboration, Eur. Phys. J. C 16 (2000) 579. 18. L3 Collaboration, CERN-EP/2002-012. 19. L3 Collaboration, Phys. Lett. B 453 (1999) 83. 20. G. Altarelli,
T. SjSstrand and F. Zwirner, CERN 96-01 (1996). 21. A. Bijhrer and M. Krawczyk, Summary of PHOTON2001, hep-ph/0203231.
SUPPLEMENTS Nuclear Physics B (Proc. Suppl.) 126 (2004) 172-178
ELSEVIER
Measurement
of the inclusive D** production
www.cJhevierphysics.com
in yy collisions at LEP
J. Hel?, A. Ngac” “Fachbereich Physik, University 57068 Siegen, Germany
of Siegen,
collisions is measured with the ALEPH detector at The inclusive production of D** mesons in two-photon e+e- centre-of-mass energies from 183 GeV to 209 GeV. A total of 360 i 27 D*’ meson events are observed from an integrated luminosity of 699 pb-‘. Cont$>tions from direct and single-resolved processes are separated of the D** to the visible invariant mass Wyis of the event. using the ratio of the transverse momentum p, Differential cross sections of D** production as functions of pf** and the pseudorapidity (qD** ( are measured to next-to-leading order in the range 2GeV/c < pt*** < 12 GeV/c and IqD**/ < 1.5. They are compared The extrapolation of the integrated visible D** cross section to the (NLO) perturbative QCD calculations. total charm cross section, based on the Pythia Monte Carlo program, yields u(e+e-+ efe-cF)(fi))=leiGev = 731 i 74,tat k 47,,,t + 157,,t, pb.
1. INTRODUCTION Heavy flavour production in two-photon events at LEP 2 centre-of-mass energies is dominated by charm production processes in which both of the photons couple directly to the charm quark (direct processes) or in which one photon couples directly and the other appears resolved (singleresolved processes) [l]. These two contributions are of the same order of magnitude within the Because the singleexperimental acceptance. resolved process is dominated by yg 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 (doubleresolved processes) are suppressed by more than two orders of magnitude compared to the total cross section [l]. 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 yy sample is first selected, then examined for its charm content via reconstruction of D*” mesons in their 0920-5632/s - see front matter doi:10.1016/j.nuc1p1~ysbps.2003.11.029
0 2004 Published
by Elsevier
B.\!
decay to Don+. Throughout this note chargeconjugated particles and their decays are implicitly included.
2. MONTE
CARLO
SIMULATIONS
In order to simulate the process e+e- + e+e-yy -+ e+e-cc -+ e+e-D**X, the leadingorder (LO) PYTHIA 6.121 Monte Carlo [2] is used. Events are generated at e+e- centre-ofmass energies ranging from 183 GeV to 209 GeV 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 m, is chosen to be 1.5 GeV/c2 and the parameter &CD is set to 0.291GeV/c2 . The yy invariant mass W,, is required to be at least 3.875 GeV/c2, which is the DD threshold. In order to ensure that both photons are quasi-real, the maximum squared four-momentum transfer is limited to 4.5GeV/c2. In the singleSF&X resolved process, the SaS-1D [3] parametrization is used for the partonic distribution of the resolved photon. The Peterson et al. parametrization [4] is adopted as the fragmentation function of the charm quark with the nonperturbative parameter ec = 0.031. The background process
J H&
A. Nguc/Ndear
Physics B (Proc. Suppl.) 126 (2004) 172-178
e+e- + e+e- yy --+ e+e-bb is simulated using PYTHIA 6.121 with W,, being required to be at least 10.5GeV/c2, which is the BB threshold. The b quark mass is set to 4.5 GeV/c2. Again the Peterson et al. parametrization is adopted with cb = 0.0035. The background processes e+e- -+ qq, e+e- -+ ~+r-, e+e- + e+e-r+rand e+e- -+ W+W- have been simulated using appropriate Monte Carlo generators. 3. DATA The ALEPH detector and its performance have been described in detail elsewhere [5,6]. Charged tracks and neutral calorimeter energy as defined by the ALEPH energy flow package [6] are used in this analysis. 3.1. Selection of yy 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 .C = 699pb-‘. Usual cuts on multiplicity, reconstructed invariant mass and transverse momentum are applied to select yy events. The selection retains a sample of 4.9 million events. Monte Carlo studies of possible background sources predict a yy purity of 98.8%. For more detaiIs see [7]. 3.2. Reconstruction of D*+ Mesons Charm quarks are detected using reconstructed D*+ mesons which decay via D*+ -+ D”rrTt, with the Do being identified in three decay modes, (1) K-r+, (2) Ke~+7r0, and (3) K-@n-r+. For tracks that fulfill certain quality conditions the measured specific energy loss dE/dx is used to identify K* and 7r* candidates. The x0 candidates are formed from pairs of photons found in ECAL with an energy of at least 250 MeV each and an invariant mass within 85MeV/c2 of the nominal no mass. The energy resolution could be improved by refitting the energies of the photons under a 7~~mass constraint. The Do candidates are formed from appropriate combinations of identified kaons and pions according to three considered decay modes. The Do candidate is retained if it has an invariant mass within 20 MeV/c2, 65 MeV/c2, and 20 MeV/c2 of
173
the nominal Do mass for decay mode (l), (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 Do are fitted to a common vertex and the confidence level of this fit is required to be greater than 0.2%. The combination of each Do with one of the remaining 7r.f 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 Pt and the pseudorapidity 77= - ln(tan(0/2)) of the D*+: 2GeV/c
< $‘+
< 12GeV/c,
]~o*~] < 1.5
.(l)
Figure 1 shows the mass difference Am = mDI+ 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 an appropriate parametrization. In order to exclude systematic binning effects an unbinned maximum likelihood fit is performed. The width a of the Gaussian describing the peak is fixed to 0.5MeV/c2, as determined in Monte Carlo. As the result a total of 360.0&27.0,t,t D*+ events are observed in the signal region for all three D*+ decay modes together. Among the possible background processes, only the contribution from yy -+ b6 -+ D**X is found to be sizeable. This contribution is estimated to be 20.5 f l.6,tat D*+ events. After subtraction of this background, a total of 339.5 f 27.0,tat D*+ events are found in the data sample analyzed. 4. CROSS
SECTION
MEASUREMENTS
4.1. Relative Fractions of Direct and Single-resolved Contributions As mentioned in the introduction, open charm production in yy collisions is dominated by contributions from direct and single-resolved processes. In the direct case the CS:pair makes up the final state of the yy system (in LO) whereas in the single-resolved case the partons of the resolved photon (photon residue) in addition to the
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Direct : (62.6 +_4.2)% Single-resolved : (37.4 + 4.2)%
80 60 40 20 n L “0.13
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0.15 0.16 0.17 0.18 Am = m,*+ - mDO [GeV/c’]
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Figure 1. Mass difference of reconstructed D*’ and Do candidates for all considered Do decay modes together. The points show data, the error bars represent statistical uncertainties, and the solid curve indicates the result of an unbinned maximum likelihood fit.
CE pair make up the final state. The transverse momentum pp* of the D*+ is correlated with the invariant mass of the CEsystem and the total visible invariant mass l&is is in turn correlated with the invariant mass of the total yy system. The ratio Py*+/Wvi, should therefore be distributed at higher values for the direct case compared to the distribution of single-resolved events. Figure 2 shows the distribution of Pp*+JW+, in data for all events found in the signal region of the mass-difference spectrum. Combinatorial background has been subtracted using events of the upper sideband 0.16 GeV/c2 < Am < 0.2 GeV/c2 of the mass-difference spectrum. Background from b6 production has also been subtracted. The relative fractions 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 f 4.2)% and a single-resolved contribution of T,,, = 1 - r&r = (37.4 f 4.2)X.
0
0.1
0.2
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0.4
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FNvis
Figure 2. Pp*‘JWvis distribution for reconstructed D*+ events. The points with error bars show data. The relative contributions from direct (shaded histogram) and single-resolved (open histogram) processes are extracted by means of a fit.
4.2. 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 D*+ Pt F and the second as a function of pseudorapidity ]Q~*+). Both are restricted to the range defined in Eq. (1). The former is measured in three py*’ bins: [2-31, [3-51, [S-12] GeV/c, and the latter in three ]qD*+] bins: [O-0.5], [0.5-1.01, [l.O-1.51. All considered D*+ decay modes were treated separately. The efficiencies are determined separately for direct and single-resolved processes. The total efficiency is a weighted combination using the fractions as determined in Section 4.1. The resulting cross sections for the different D*+ decay modes are consistent with each other for all bins in p,D*+ as well as in [qD*+ 1, taking into account the statistical uncertainties. 4.3.
Systematic Errors on Differential Cross Sections The study of systematic errors was performed separately for each pF*’ and ]qD*’ ] bin and for each of the considered D*+ decay modes. Therefore ranges for the size of the particular uncer-
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tainties are given. The systematic error introduced by the event selection was studied by varying the cuts within the resolution obtained from the Monte Carlo detector simulation. This yields an uncertainty of 0.6%-6.4%. The selection of pion and kaon candidates depends essentially on the dE/dx measurement. The uncertainty of the dE/dx calibration changes the efficiency by 0.5%-5.8%. The uncertainty due to the accepted mass range used to classify Do candidates was found to be negligible. In order to estimate the error introduced by the method for extracting the number of D*+ events (Section 3.2) the parameters of the fitted Gaussian were varied about its values as obtained in Monte Carlo. The resulting relative error on the efficiencies was 0.8%-2.1%. The present analysis assumes the fractions rdir/res to be constant over the considered kinematic range. Monte Carlo studies have been performed with varied fractions and an uncertainty in the cross section of 0.3%-3.4% is estimated. The statistical error of bb background subtraction and the uncertainties of the total cross section a(e’e- -+ e+e-bb) 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. Relative errors on the branching ratios given in [8] are used to estimate the corresponding uncertainties. Similarly the relative uncertainties in the efficiencies due to finite statistics in the Monte Carlo samples, 0.5%-2.3%, are taken into account. 43.1. Comparison to Theory Figures 3 and 4 show the measured dg/dpF*+ and da/dlqD*+ 1 in comparison to two different NLO perturbative QCD calculations, the fixedorder (FO) NLO (also known as massive approach) [lo] and the resummed (RES) NLO (massless approach) [ll]. In both cases, the charm quark mass m, is set to 1.5GeV/c2, the renormalization scale pn and the factorization
175
scale j.LF are chosen such that & = 4& ti rn$ 5 m,2 + pt (c12, where 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 [12] in the FO NLO calculation, whereas the RES NLO uses GRV-HO [13]. The fragmentation of the charm quark to the D*+ is modelled by the fragmentation function suggested by Peterson et al. [4], with E, = 0.035 in the case of FO NLO. The RES NLO calculation uses Ed = 0.185, which was determined by using nonperturbative fragmentation functions fitted [ll] to ALEPH measurements of inclusive D*+ production in e+eannihilation [14]. The results of the two NLO QCD calculations are represented by the dashed lines (for RES NLO) and solid lines (FO NLO) in both Fig. 3 and Fig. 4. In order to estimate the theoretical 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 [15] ansatz as an alternative for parton density function and varying the renormalization and factorization scales. The resulting theoretical uncertainties are indicated by the bands around the corresponding default values in Figs. 3 and 4. Altogether, the measurement of dcr/d#*‘+ seems to favour a harder py*+ spectrum than predicted. The RES NLO calculation clearly overestimates the measurement in the low p,““’ region, while the FO NLO calculation slightly underestimates it in the pp” > 3.0GeVjc region. The measured da/dlqD*+I is consistent with the almost flat distribution predicted by both NLO calculations, but the measurement of do/dJqD*+J is again overestimated by the RES NLO calculation and somewhat underestimated by the FO NLO calculation. 4.4. Visible Cross Section The visible cross section c$i’ (e+e-+ efe-D*+X) is calculated separately in the acceptance range [Eq. (l)] for the three considered decay modes. The weighted average over all of the considered decay modes using the dominating statistical uncertainties for weighting is D*’ (e+e- --+ e+e-D*‘X) ovis
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PDF: GRV and AFG m, = 1.5GeV, %=Q2=m$ and 2% .-*.- Default setup: GRV, rn, = 1.5 GeV, h=w=q
- a
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FO NLO (Massive approach) PDF: GRS m, = 1.2 GeV and 1.8 GeV h=29 for direct, and m,J2 for resolved Default setup: GRS, mc = 1.5 GeV, &$=@.=I+
20 NLO
i
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m
RES NLO (Massless approach) PDF: GUV and AFG m, = 1.5 GeV, !+3+JZ=m/2 and 29 -.--. Default setup: GRV, m, = 1.5 GeV, h=Q.=m,
m
FO NLO (Massive approach) PDF: GRS D,, = 1.2 GeV and 1.8 GeV
-1
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i I,,
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I
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I,
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I
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lo
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I
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Figure 3. Differential cross section da/dpg*+ for the inclusive D*+ production. The points show the combined differential cross sections from the three decay modes under studies. The error bars correspond to the total uncertainties. The shaded bands represent the theoretical uncertainties of these calculations.
= 23.39 f 1.64,t,t f 1.52,,,t pb The cross section theoretically FO NLO calculation [lo] is ffvisD*+(e”e-
-+ e+e-D*+X)
.
predicted
= 17.3::::
pb
t
*I
10 11 12 #+ [GeVk]
by the
7 (2)
and is consistent with this measurement within the given uncertainties. 4.5. Total Cross Section The total cross section for the reaction e+e- -+ e+e-cF can be calculated knowing the ratio
of the total D*+ cross section to the visible cross section in the acceptance range for di-
Y
OO
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,””””””””’
! 0.5
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Figure 4. Differential cross section do/d(qD*+j the inclusive D*+ production.
i
1.5 lJID’+l
for
rect/resolved processes. It describes the extrapolation of the measured cross section to the total phase space available. Separate Monte Carlo samples are used to estimate R&r and R,,, for direct and single-resolved processes. This yields Rdir = 12.74&0.45,t,t and Rres = 18.62*0.80,t,t. 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 m, = 1.3 GeV/c2 and m, = l.7GeV/c2 yields relative errors on Rdir of HO% and on R,,, of +43% and -19%, respectively. In the single-resolved case an additional uncertainty enters R,,, by the choice of the parton density functions describing the resolved photon. Alternatively to the default choice the GRVLO parametrization [16] was used to calculate R l-es. This yields a relative deviation of 12% and is added in quadrature to the other systematic uncertainties on R,,,. The following values are
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177 ALEPH
therefore obtained: Rdir = 12.7& 1.3 ,
R,,, = l&6+;:’
.
Finally the total cross section for the reaction e+e- + e+e-cF at e+e- centre-of-mass energies ,/ii = (183-209) GeV, corresponding to the luminosity weighted average of 197 GeV, is calculated to be
a(e+e-
+ e+e-cC)(Gj=lg7GeV
731 k 74stat f 47s,t:;;;xtr
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I 0
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1087f &at
40
60
80
100
,,,,I,
120
140
I,,,,..,
160
180 200 & [G&J
.
Alternatively, the total cross section is determined by means of the NLO calculation referenced in the previous section.The value Rtot = 22.2+16.0 . -7,3 1s extracted from [lo]. The large uncertainty of Rtot again is mainly due to the uncertainty of the charm quark mass chosen in the range from m, = 1.2GeV/c2 to m, = 1.8 GeV/c2. This results in a total cross section a(e+e-
l,,t,II,,I,,,I,
20
Figure 5. The total cross section for charm production a(e+e- -+ efe-cc) versus the centre-ofmass energy & of the ese- system. The measurement of this analysis is shown as a square. The band represents the NLO QCD calculation [l]. The results obtained by L3 and OPAL using D*$ are represented in [18] and [17], respectively. The L3 measurements using lepton tag can be found in [19]. The values for TASSO, TPC/&, JADE, AMY, and VENUS are taken from [20].
=
f 70systt-;;;extr pb .
The measured total cross section [Eq. (3)] is shown in Fig. 5 in comparison to the NLO QCD prediction of Drees et al. [l] and to results from other experiments [17-201. Within the uncertainties, this NLO QCD prediction is in good agreement with our measurement and others [21]. 5. CONCLUSIONS The fractions of the main contributing processes, direct and single-resolved, were determined using the event variable $*‘/W,i, to be Tdir = (62.6f4.2)% and T,,~ = 1 -r&r = (37.4f 4.2)%, within the acceptance. The differential were cross sections da/dpf’+ and da/d)qD*+] measured and compared to theoretical predictions. While the data show a slightly harder spectrum in the pF** distribution compared to calculations, the almost flat distribution of da/d/qD**) which is predicted by the NLO calculations for the visible D*+ region is in agreement with the Overall, the measurements of measurement.
da/d$*+ and da/d]qD’+ ) were slightly underestimated by the FO NLO calculation with m, = 1.5 GeV/c2 and overestimated by the RES NLO calculation. For the i$egrated visible D*+ cross section a value of a,, = 23.39 + 1.64,t,t 4: 1.52,,,$ pb 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 is dominated by theoretical uncertainties due to the charm quark mass and the parton density function used for the resolved photon. REFERENCES 1. M. Drees et. al., Phys. Lett. B 306 (1993) 371. 2. T. Sjijstrand, Comput. Phys. Commun. 82 (1994) 74. 3. G. A. Schuler and T. Sjostrand, Z. Phys. C 68 (1995) 607. 4. C. Peterson et. al., Phys. Rev. D 27 (1983)
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