Measurement of Charm and Beauty Photoproduction at HERA using D ∗ µ Correlations

A measurement of charm and beauty photoproduction at the electron proton collider HERA is presented based on the simultaneous detection of a D * ± meson and a muon. The correlation between the D * meson and the muon serves to separate the charm and beauty contributions and the analysis provides comparable sensitivity to both. The total and differential experimental cross sections are compared to LO and NLO QCD calculations. The measured charm cross section is in good agreement with QCD predictions including higher order effects while the beauty cross section is higher.


Introduction
At the electron proton collider HERA, heavy quarks are predominantly produced via photon-gluon fusion, γ g → cc or bb, where the photon is emitted from the incoming lepton and the gluon from the proton. The production cross sections are largest for photoproduction, i.e., for photons with virtuality Q 2 0. The light quarks u, d and s are produced much more copiously than c and b, and beauty production is suppressed by a factor of approximately 200 compared to charm. Charm and beauty measurements performed at HERA so far relied on the tagging of only one heavy quark in each event. While the charm measurements [1][2][3][4][5][6][7][8][9][10][11] were mostly based on the reconstruction of D mesons, the beauty measurements [12][13][14][15][16][17] used semi-leptonic decays or lifetime signatures or both. Here an analysis is presented, where in a large fraction of events both heavy quarks are tagged using a D * ± meson and a E-mail address: eperez@hep.saclay.cea.fr (E. Perez). 1 Also at Physics Department, National Technical University, Zografou Campus, GR-15773 Athens, Greece. 2 Also at Rechenzentrum, Universität Wuppertal, Wuppertal, Germany. 3 Also at University of P.J. Šafárik, Košice, Slovak Republic. 4 Also at CERN, Geneva, Switzerland. 5 Also at Max-Planck-Institut für Physik, München, Germany. 6 Also at Comenius University, Bratislava, Slovak Republic. 7 15 Supported by the Swiss National Science Foundation. 16 Supported by CONACYT, México, grant 400073-F. 17 Partially Supported by Russian Foundation for Basic Research, grant No. 00- 15-96584. muon as signatures. The correlations between the direction of the muon with respect to the D * ± and their electric charges are used to separate charm and beauty contributions. Total cross sections are measured separately for the processes ep → eccX → eD * µX and ep → ebbX → eD * µX in the visible kinematic region, while differential cross sections are derived for combined samples of cc and bb events. The measurements, which are based on an integrated luminosity of L = 89 pb −1 , are compared to leading order (LO) and next-to-leading order (NLO) perturbative QCD (pQCD) calculations. This measurement extends to significantly lower centre-of-mass energies of the bb system than previous measurements of beauty cross sections at HERA. The simultaneous detection of the D * meson and the muon makes possible new tests of higher order QCD effects. For instance, in the photon-gluon rest frame the angle between the heavy quarks is 180 • at leading order, but at next-to-leading order it can differ significantly from this value due to hard gluon radiation. Furthermore, the D * µ pair is expected to be sensitive to a possible transverse momentum k t of the gluons entering the quark pair production process.

Separation of charm and beauty
The separation of charm and beauty contributions exploits the charge and azimuthal angle 18 correlations of the D * meson and the muon. The azimuthal angle difference Φ between the D * and the muon and their respective electric charges Q(D * ) and Q(µ) are used to define four 'correlation regions' I-IV. For Q(D * ) = Q(µ) regions I and II cover Φ < 90 • and Φ > 90 • , respectively. Regions III and IV are defined correspondingly for Q(D * ) = Q(µ).
The four regions are populated differently by charm and beauty events as is illustrated in Fig. 1. Neglecting any transverse momenta of the photon and the gluon, the fusion process γ g → cc or bb leads to a back-toback configuration of the two heavy quarks. Approximating the directions of the D * ± meson and the muon Fig. 1. Definition of the correlation regions in terms of Φ and the relative charges of the D * meson and the muon. The sketches illustrate these correlations in cc and bb quark decays to D * µ. The numbers represent the relative distribution over the four correlation regions of charm and beauty events that satisfy the cuts given in Section 4.1, as obtained from the PYTHIA simulation without detector effects.
with those of the quark and antiquark and selecting opposite charges, cc pairs populate correlation region IV. In contrast, beauty events populate regions II, III and IV, depending on whether the muon originates from the same b quark as the D * or from the oppositeb. If the muon originates from the same b quark as the D * meson, the events lie in region III. For muons coming from theb opposite to the D * meson, the direct decay populates region II, while the cascade process b →c → µ populates region IV. Region IV hence receives contributions from both cc and bb events and region I stays empty.
The azimuthal angle correlations are smeared by fragmentation and semileptonic decay processes and by higher order QCD effects such as gluon radiation and any initial transverse momentum of the gluon. Processes such as heavy quark decays via τ leptons conserve the charge correlation, which is not the case for B 0 -B 0 mixing and, e.g., the decays b → cW − ; W − →cs. According to the PYTHIA Monte Carlo simulation [18], which takes into account these smearing effects, the relative population of the four regions is as given by the numbers in Fig. 1. These numbers apply in the analysed kinematic region defined in Section 4.1 and do not include detector effects. Since the population of the four correlation regions is very different for bb and cc, it can be used for the separation of these two components.

QCD Calculations and Monte Carlo simulations
The Monte Carlo simulations PYTHIA [18] and CASCADE [19] are used for the description of the signal and background distributions in the separation of charm and beauty, for the determination of efficiencies and acceptances and for systematic studies. Their Table 1 Fragmentation fractions [27,28] used in the QCD calculations of the cross sections. The b → c → µ fraction also contains the b → ccs decay and the τ contributions predictions are also compared with the measured cross sections. In PYTHIA and CASCADE leading order matrix elements which take into account the mass of the heavy quark are implemented and parton showers in the initial and final state are included to approximate higher orders (LO-ME+PS). The parton evolution in PYTHIA uses the DGLAP equations [20]. In addition to the direct process, a resolved photon component is generated in PYTHIA where the photon fluctuates into a hadronic state acting as a source of partons, one of which participates in the hard interaction. This component is dominated by heavy flavour excitation processes [21], where the heavy quark is a constituent of the resolved photon. In the PYTHIA calculation of heavy flavour excitation, in which quark masses are neglected, the contribution of excitation to the total charm cross section in the analysed kinematic region is found to be 41%, while it is 23% for beauty. In comparison to this component the contribution of the resolved component due to light quarks or gluons in the photon can be neglected in the present analysis, as can the heavy flavour component of the proton. CASCADE contains an implementation of the CCFM [22] evolution equation for the initial state parton shower. The γ g → cc or bb process is implemented using off-shell matrix elements convoluted with k t unintegrated proton parton distributions. PYTHIA and CASCADE use the JETSET program as implemented in PYTHIA for the hadronisation (via the Peterson fragmentation function [23]) and for the decay of beauty and charm quarks. In order to correct for detector effects, the generated events are passed through a detailed simulation of the detector response based on the GEANT program [24] and the same reconstruction software as used for the data.
The measured cross sections are also compared with NLO pQCD calculations in the massive scheme [25] using the program FMNR [26]. These calcula-tions are expected to give reliable results in the kinematic region considered here, where the transverse momentum of the heavy quark is of the same order of magnitude as its mass. The calculations are available for both the direct and resolved photon processes. However, in contrast to the PYTHIA program, heavy flavour excitation is not explicitly included in the resolved part of the FMNR program. The contributions of the resolved light quark and gluon components are found to be small in FMNR (< 3% for charm and < 6% for beauty in the analysed kinematic region) and are neglected.
The original FMNR program is extended to include the effects of the hadronisation of c and b quarks and their semileptonic decays in order to make comparisons with the measured cross sections in the experimentally accessible kinematical region. The heavy quark is 'hadronised' by rescaling the three momentum of the quark using the Peterson fragmentation function. For the decay into muons the momentum spectrum is implemented as obtained from JETSET. In the case of beauty quarks, the direct decays of bflavoured hadrons into muons are taken into account as are the decays via a charm quark, b → c → µ. When the D * meson and the muon originate from the same quark, the angular and momentum correlations are implemented as in JETSET. The measured fragmentation fractions [27,28] for c and b quarks given in Table 1 are used for the calculation of the cross sections. The important parameters of the pQCD programs used in this analysis are summarised in Table 2.

Data analysis
The data were collected with the H1 detector [32,33] at HERA during the years 1997 to 2000 and correspond to an integrated luminosity of L = 89 pb −1 . The largest part of the luminosity (80%) was collected at a centre-of-mass energy of √ s ≈ 320 GeV, the beam energies being 27.6 GeV and 920 GeV for electrons 19 and protons, respectively. The remaining 20% of the luminosity was taken at √ s ≈ 300 GeV (proton energy 820 GeV). 19 HERA has been operated with electron and positron beams.
These periods will not be distinguished in this analysis. Table 2 Parameters used in the Monte Carlo and NLO programs. The FMNR calculations are performed in the MS scheme using the default values of Λ QCD for the parton density functions. µ r and µ f denote the renormalisation and factorisation scales, p 2 T qq the average of the squares of the transverse momenta of the two heavy quarks, m q the heavy quark masses,ŝ the centre-of-mass energy squared, Q 2 T the transverse momentum squared of the heavy quark system, p T q the transverse momentum of a heavy quark and q the Peterson fragmentation parameters [29]. For

Event selection
A detailed account of this analysis can be found in [34]. Events with at least one reconstructed D * and at least one muon are selected; multiple D * or muon combinations are treated as separate events. The D * is reconstructed via the decay channel 20 D * + → D 0 π + s → K − π + π + s (branching ratio (2.59 ± 0.06)% [28]), where π s refers to the low momentum π in the decay. The decay particles of the D * meson are reconstructed in the central tracking detector (20 • θ 160 • ) without particle identification. Muons are identified by reconstructing track segments in the instrumented iron return yoke of the solenoidal magnet. These are linked to tracks in the central tracking detector. In order to ensure good detector acceptance, cuts on the transverse momentum p T with respect to the proton direction and the pseudorapidity η = − ln tan(θ/2) are applied for the D * meson and the muon in the laboratory frame (see Table 3).
Photoproduction events are selected by demanding the absence of any signals for the scattered electron, restricting the accepted range of negative fourmomentum transfer squared Q 2 to be below 1 GeV 2 . A cut on the inelasticity 0.05 < y < 0.75 is applied, where y = P · q/P · k (q, k and P are the four vectors of the exchanged photon, incoming electron and proton, respectively). The variable y is reconstructed from 20 Charge conjugate states are always implicitly included. Table 3 The D * selection cuts and definition of the visible kinematic region Visible kinematic region p T (D * ) > 1.5 GeV |η(D * )| < 1.5 p(µ) > 2 GeV |η(µ)| < 1.735 0.05 < y < 0.75 Q 2 < 1 GeV 2 the measured hadronic final state using the Jacquet-Blondel method [35]. The events are triggered by fast signals from the central tracking and muon detectors. The analysed 'visible' kinematic region of the measurement is defined in Table 3.

Fit procedure
The D * yield is measured using the M technique [36], where M = m Kππ s − m Kπ is the difference of the invariant masses of the Kππ s and the Kπ systems. Fig. 2(a) shows the M distribution for the selected D * µ sample separately for the 'right' (K − π + π + s ) and 'wrong' (K − π − π + s ) charge combinations. The wrong charge distribution is normalised to the right charge distribution in the range 0.155 M 0.1685 GeV. The number of signal events is extracted from a fit to the M distribution using a Gaussian function for the signal and a parameterisation of the background. 21 The parameters of the background function are determined from right and normalised wrong charge combinations. The result of this fit for the total signal is also shown in Fig. 2(a).
The total number of D * µ events obtained from the fit is N D * µ = 151 ± 22. This number still contains a contribution from 'fake muons', i.e., from hadrons misidentified as muons and muons from the decay of light mesons. The relative contribution of the fake muon background is about 37% in charm initiated events, according the PYTHIA Monte Carlo simulation. In beauty initiated events this relative fake contribution is lower, about 5%, due to the larger fraction of real muons which fulfill the kinematic requirements of the analysis. It has been checked that the simulation of fake muons reproduces reasonably the data.
In Fig. 2(b)-(e), the M distributions of the selected D * µ events are shown separately for the four correlation regions defined in Section 2. Clear peaks due to D * mesons are observed in regions II-IV, whereas region I shows little or no signal, consistent with the expectation.
The charm and beauty contributions in the data are determined by performing a simultaneous likelihood fit of the M distributions in the four correlation regions. In the following, this fit will be referred to as a 'two-dimensional fit', in order to distinguish the results from the separate one-dimensional fits of M in each correlation region.
In this two-dimensional fit, in addition to the D * µ contribution from bb and cc, the fake muon background and the combinatorial background under the M peaks have to be considered. The position and width of the M peak corresponding to the D * signal as well as the parameters describing the shape of the combinatorial background are fixed to the values obtained from the one-dimensional M fit to the total sample ( Fig. 2(a)). The normalisation of the combinatorial background is fitted using right and wrong charge combinations in each region separately. The relative distributions of signal events from charm and beauty between the correlation re- 21 The functional form used is c 1 where c i are fit parameters. gions as well as the fractions of fake muon background in each region predicted by the PYTHIA Monte Carlo simulations are used as input for the fit. In total there are six free fit parameters, the total numbers of D * µ events from bb and cc quark pairs, N b and N c , and four parameters for the combinatorial background, one in each correlation region.

Results
The result of the two-dimensional fit is shown together with the data in Fig. 2(b)-(e). The data are described well and the quality of the fit is good (χ 2 = 145.5 for 154 d.o.f.). In Fig. 3, the numbers of D * signal events from the two-dimensional fit in the four correlation regions are compared to the results of onedimensional fits of the M distributions performed in each correlation region separately. The agreement is very good. The distribution of the contributing processes as obtained from the two-dimensional fit is also shown in Fig. 3. The following event numbers and errors are obtained for the charm and beauty contributions from the two-dimensional fit:

Total cross section
The number of b and c events are used to compute the total cross sections in the kinematic region defined in Table 3. The efficiencies and acceptances are derived from the Monte Carlo simulations. Values of σ c vis ep → eD * µX = 250 ± 57(stat.) ± 40(syst.) pb, and of σ b vis (ep → eD * µX) = 206 ± 53(stat.) ± 35(syst.) pb, are obtained for charm and beauty production, respectively. The measured cross sections are similar due to the definition of the visible kinematic region, which requires in particular a high momentum muon, suppressing central charm production. The results are compared with the pQCD predictions in Table 4, where error estimates due to the uncertainty of the quark masses and the scales are given for the NLO calculations. In order to assess the influence of mass effects in the extraction of gluon densities used in the  calculations, the default CTEQ5M sets have been replaced by the CTEQ5F sets [30]. The results are found to be compatible. The uncertainties for PYTHIA and CASCADE are found to be of similar size as those of the NLO calculations. The measured cross section for charm production agrees well with the LO-ME+PS models (PYTHIA and CASCADE) and the NLO prediction (FMNR). The measured beauty cross section exceeds the calculated cross sections. In other recent measurements of the beauty cross section in photoproduction at HERA [12,15], based on the selection of high transverse momentum jets, ratios of measurement and FMNR based calculations between 1 and 3 are found. Note that the present analysis extends down to the production threshold for bb, while the jet measurements have a threshold which is approximately 5 GeV higher in the bb centre-of-mass system.
The systematic uncertainties of the cross section measurement are evaluated by varying the Monte Carlo simulations. The dominant experimental errors come from the uncertainties in the track reconstruction efficiency (13%), the trigger efficiency (5%) and Table 4 Measured D * µ cross sections for charm and beauty production in the kinematic region defined in Table 3. For the data the statistical and the systematic errors are given. The LO-ME+PS predictions (PYTHIA, CASCADE) and NLO calculations (FMNR) are also shown. The uncertainties of the FMNR results are obtained by varying the renormalisation and the factorisation scales simultaneously by factors of 0.5 and 2. The uncertainty due to a variation of the quark masses m c by ±0.2 GeV and m b by ±0.25 GeV is added quadratically. The last column shows the ratios of the measurement to the prediction 4.0 the width of the M signal (3%). Smaller contributions are due to uncertainties in the determination of the background due to misidentified muons 22 (1%; 1.5%) and in the fragmentation fractions (1%; 1.5%). Model uncertainties are estimated using the CAS-CADE Monte Carlo generator instead of PYTHIA (3.5%) and either taking into account or omitting the resolved component in PYTHIA (3%; 5%). Taking into account the uncertainties due to the contribution of D * reflections (5%), the muon identification, the luminosity measurement and the D * decay branching ratios, the total systematic errors for the charm and beauty cross sections are estimated to be 16% and 17%, respectively.

Differential cross sections for charm and beauty
Differential cross sections for D * µ production in the visible kinematic region are evaluated as functions of variables characterising the D * meson, the muon and the D * µ system. In this section results are presented for the complete data set, which contains the contributions from charm and beauty (Figs. 4 and 5).
In order to compute the differential cross sections for the data, the numbers of events in bins of the chosen variable are determined by a fit to the M distribution in each bin, as described in Section 4.2. Here, no attempt is made to separate charm and beauty contributions. A correction for 'fake muons' is applied according to the Monte Carlo simulation. Since the fake muon fraction is different for charm and beauty, it is computed using the b fraction of 45% given by the measured cross sections (Table 4).
The data are shown with the results of the PYTHIA and CASCADE Monte Carlo models and the LO and NLO FMNR calculations. In the theoretical models, the beauty and charm contributions are combined according to the measured total visible cross sections (Table 4) and normalised to the sum of these cross sections, in order to facilitate a shape comparison. The error bands for the FMNR prediction are computed as for the total cross section (see caption of Table 4). The measured differential cross sections are similarly normalised, which has 22 Where two numbers are given the first applies to charm and the second to beauty. the advantage that the systematic errors largely cancel and are negligible compared to the statistical errors. Fig. 4 shows the differential cross sections as a function of the transverse momentum and pseudorapidity of the D * meson and the muon separately. Overall the QCD models describe the shapes of the measured distributions quite well, although there is a tendency for the measured p T (D * ) and p T (µ) distributions to be softer than the calculations. A slight discrepancy is also present in the differential cross section as a function of the pseudorapidity of the muon (Fig. 4(c)) which shows a central dip due to the large muon momentum required.
Quantities derived from a combined measurement of the D * and muon are shown in Fig. 5. In Fig. 5(a) and (c), the differential cross sections as a function of p T (D * µ), which is defined as p T (D * µ) = | p T (D * ) + p T (µ)|, and Φ are compared with the LO and NLO FMNR predictions. The data show the expected deviations from the LO calculations due to higher order effects: the observed p T (D * µ) distribution is flatter and the Φ peak around 180 • is broader than the LO computation. The data are in good agreement with the NLO calculation. In Fig. 5(b) and (d), the same differential cross sections for p T (D * µ) and Φ are compared with PYTHIA and CASCADE which also give a good description of the data. Although different approaches are used in PYTHIA and CASCADE to compute the evolution of the partons from the proton and the hard interaction, the differences between the two simulations are smaller than the experimental errors.  The data (points) are compared with the prediction of the NLO calculation FMNR and the LO-ME+PS QCD models PYTHIA and CASCADE. A beauty fraction of 45% as obtained from the measured cross sections is used in the calculations. The error bands for FMNR are obtained as described in Table 4. The PYTHIA b quark contribution is indicated separately. The experimental systematic uncertainties for the normalised distributions are negligible compared to the statistical errors.

Results for a charm dominated 'quark-antiquark tag' sample
The cross sections in the previous section refer to the complete data set including events from region III in which both D * and muon originate from the same b quark. Since this leads to a dilution of the correlation of quantities characterising the quark pair and the measured D * µ pair, results for a smaller sample are given here, where both the heavy quark and the antiquark are tagged by either a D * or a muon ('quark antiquark tag'). This is possible in correlation region IV ( Φ > 90 • and Q(D * ) = Q(µ)). This region (see Fig. 1) is dominated by cc pairs: the bb contribution is 18% according to the two-dimensional fit. Due to migrations from correlation region III, approximately half of the bb contribution is due to b → D * µ events in which the D * µ pair comes from the same b quark (according to the PYTHIA simulation). A visible cross section of σ 2q = 263 ± 48 ± 36 pb is measured 24 after 24 The index '2q' is used for the cross sections in this section to distinguish them from those in the previous section.  Table 4. A beauty fraction of 45% as obtained from the measured cross sections is used in the calculations. The subtracting this fraction, while 264 +148 −50 pb is expected from the FMNR calculations.
In this data sample, the correlation of kinematic quantities reconstructed using the D * meson and the muon to those of the quark pairs is good for x g and y(D * µ), while it is weaker for p T (D * µ). Here x g is the fraction of the proton energy carried by the gluon in the hard interaction, which is approximated by Fig. 6. Normalised differential D * µ cross sections for a 'quark antiquark tag', charm dominated sample (approximately 10% bb quark contamination), where the D * and the µ originate from different quarks. The data and predictions of the LO and NLO calculation FMNR and of the Monte Carlo generators PYTHIA and CASCADE are shown. The error bands for FMNR are obtained as described in Table 4. In (c) the resolved excitation component of PYTHIA is indicated separately. The experimental systematic uncertainties for the normalised distributions are negligible compared to the statistical errors.
x obs g = (M(D * µ)) 2 /ys. The normalised differential cross section for x obs g (D * µ) is shown in Fig. 6(a). All QCD calculations (FMNR to LO and NLO, PYTHIA and CASCADE) give a reasonable description of the data. Fig. 6(b) and (c) show the p T (D * µ) andŷ(D * µ) distributions of the D * µ pair, respectively, with the same model calculations. The LO FMNR prediction for p T (D * µ) is again too soft, as observed for the total sample (Fig. 5(a)), while the NLO FMNR prediction fits the data well. Although this sample should be sensitive to any transverse momentum of the incoming gluon, the differences between PYTHIA (collinear factorisation) and CASCADE (k t factorisation) are small in the kinematic region studied.

Conclusion
A measurement of cc and bb photoproduction cross sections using the H1 detector at HERA has been presented. For the majority of events both heavy quarks are tagged using a D * meson and a muon as signatures. The separation of the charm and beauty contributions is possible due to the different correlations between the charges and angles between the D * meson and the muon. The measured total cross section for charm in the visible kinematic region is in agreement with the NLO QCD prediction, while the beauty cross section is higher than predicted. The kinematic region of the latter is characterised by lower bb centre-of-mass energies than in most previous analyses, which require high momentum jets. Comparisons of the shapes of the measured differential distributions with QCD calculations including higher order effects show general agreement. Effects beyond the LO approximation are directly observed. In the kinematic region studied, effects due to k t factorisation, as implemented in CASCADE, are found to be small compared to the experimental errors.