- Email: [email protected]
Measurement of F2cc¯ at HERA
Nuclear Physics B (Proc. Suppl.) 191 (2009) 163–172 www.elsevierphysics.com
Measurement of F2c¯c at HERA K. Lipkaa (on behalf of the H1 and ZEUS collaborations) a
Deutsches Elektronen Synchrotron Notkestrasse, 85, D-22607 Hamburg, Germany Recent results on the extraction of the charm contribution, F2c¯c , to the inclusive proton structure function F2 in deep inelastic ep scattering at HERA are presented. Different methods of charm tagging and measurements of the charm fragmentation function are shown. The issues related to the extrapolation of the visible cross sections to the full phase space are discussed.
1. Introduction Results on the charm contribution to the proton structure function, F2c , at HERA have been published by the H1 and the ZEUS collaborations [1–3]. The data have shown clear evidence that the dynamics of charm production in ep scattering is dominated by the photon gluon fusion proc cess. In this framework the process e+ p → c¯ is sensitive to the gluon density in the proton [4] and allows its universality to be tested. Several charm tagging methods are used at HERA. Charm quarks are either tagged by reconstructing charmed hadrons e.g. D ∗± , D± and D0 mesons, or by making use of the long lifetime and large mass of heavy quarks. F2c¯c is extracted extrapolating the measured cross sections in the phase space of the analysis to the full phase space using the appropriate theory model. When using the lifetime information, the charm and the beauty contributions to the proton structure are extracted simultaneously. The presented analyses partially cover the data from the HERA-II running period, yielding significant integrated luminosity. Therefore, more precise tests of perturbative QCD (pQCD) become possible. 2. Models of charm production The description of open heavy flavour production in electron proton collisions is based on perturbative QCD. In leading order (LO), the photon gluon fusion process (γg → QQ) is the dominant 0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.03.123
contribution [1]. This treatment has been extended to next-to-leading order (NLO) for which calculations in several schemes are available [5– 9]. All approaches assume the scale introduced by the heavy quark mass to be hard enough to apply pQCD and to guarantee the validity of the factorisation theorem. In the analyses presented here the “massive approach” is adopted, i.e. a fixed order calculation with massive quarks and assuming three active flavours in the proton. The momentum densities of the three light quarks and the gluon in the proton are evolved by the DGLAP equation [10]. The heavy quarks are assumed to be produced only at the perturbative level [5] via photon gluon fusion. Based on the NLO calculations of order α2s in the coefficient functions [5] programs for different applications were developed in the fixedflavour-number-scheme (FFNS). The Riemersma program [6] is used for the calculation of inclusive quantities of heavy quark production, like F2c (x, Q2 ), while the HVQDIS program [7,11] allows the calculation of exclusive quantities by providing the four-momenta of the outgoing partons. Both programs are based on the same calculation and use the same input like PDFs, charm mass and factorisation and renormalisation scales. The MRST2004FF and CTEQ5F3 (ZEUS-S-FF) parton densities, mc =1.43 (1.5) GeV and μr = μf = Q2 + 4m2c are used in the H1 (ZEUS) analyses presented here. The data presented here are also compared to the RAPGAP [12] and CAS-
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CADE [13] Monte-Carlo simulations. Both are based on leading order matrix element calculations with the higher order corrections implemented via parton showers. Parton evolution according to the DGLAP equations is used in the RAPGAP simulation. CASCADE implies intrinsic kt factorisation and parton evolution according to the CCFM [14] equations. 3. Extraction of F2c¯c using the reconstruction of charmed hadrons The contribution of charm to the proton structure function can be determined using the measured cross section of charm-tagged events. In the following measurements based on the reconstruction of charmed mesons are presented. The experimental value of F2c¯c is determined by: c¯ c F2,exp =
exp σvis c¯ c · F2,th . th σvis
(1)
exp th (σvis ) denotes the measured (preHere σvis dicted) meson cross section in the visible phase c¯ c corresponds to space of the analysis and F2,th the model prediction for F2c¯c in the full phase space. The visible phase space accessible by the detectors H1 and ZEUS via reconstruction of charmed mesons covers only about 30% of the full phase space. Therefore the determination of F2c¯c strongly depends on the model used for the extrapolation. In the following, HVQDIS and CASCADE are used as extrapolation models. The extrapolation uncertainties within a single model are estimated by the variation of the input parameters like parton densities, charm quark mass and the renormalisation/factorisation scales as well as by the variation of the charm fragmentation model.
3.1. Cross section measurements In the following, the charm tagging method via reconstruction of decays of charmed hadrons is illustrated using the D ∗± mesons. The data were collected with the H1 detector, corresponding to an integrated luminosity L=345 pb−1 . D∗ are reconstructed in decays D ∗ → D0 + πslow → K + π + πslow . The signal is extracted using the mass difference technique from
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Figure 1. Invariant mass difference of Kππ and Kπ combinations of D∗ candidates. the fit to the Δm distribution of the D ∗ candidates (Δm=mKππ − mKπ ). In Fig. 1 the Δm distribution is shown for the D ∗ candidates and the wrong charge background. The doubledifferential cross sections of D ∗ production as
Figure 2. Double-differential D ∗ cross sections as a function of the pseudo-rapidity η in bins of the transverse momentum pT . The hatched (shaded) area corresponds to the HVQDIS prediction using the CTEQ5F3 (MRST2004FF3) parton densities. The widths of the bands corresponds to the variation of model parameters.
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function of the meson kinematics measured by H1 collaboration are shown in Fig. 2 [15]. The measurements are compared to the NLO calculations using the CTEQ5F3 and MRST2004FF3 parton densities, respectively. Overall the NLO calculation describes the distributions well, however, it seems to underestimate the cross section in the forward region at low pT (D∗ ). The dif-
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Figure 3. Differential cross section of D 0 -meson production as a function of the meson kinematics, as measured by the ZEUS experiment. The data are compared to the HVQDIS prediction (shaded band) using the ZEUS-S-FF parton densities. The expected beauty contribution is represented by the dotted line. ferential cross sections of D ± and D0 -mesons are shown in Fig. 3 and Fig. 4 in comparison to the HVQDIS calculation. The data are collected with the ZEUS experiment corresponding to the integrated luminosity of 135 pb−1 [16]. The DIS kinematic region 5
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Figure 5. Cross section of D ∗ meson production as a function of Q2 as measured by the H1 experiment. The data are compared to the Monte-Carlo simulations RAPGAP using the CTEQ6L (upper solid line) and CTEQ65m (lower solid line) parton densities and CASCADE (dotted line).
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energy of a D ∗ -associated jet was required to fulfil ET > 9 GeV. Thereby the charm production phase space far above the threshold is probed. The data are fitted by the NLO massive calculation FMNR [20], using the Kartvelishvili [21] fragmentation function defined by a single parameter α.
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Figure 6. Differential cross section of D ∗ meson production as function of Q2 as measured by the ZEUS experiment. The data are compared to the NLO calculation HVQDIS (shaded band). 3.2. Charm Fragmentation The charm fragmentation function was measured by the H1 and ZEUS experiments using inclusive D∗± meson production in both photoproduction and DIS. A fragmentation observable z is measured, which determines the fractional energy of the charm quark carried by the produced meson. Experimentally, the charm quark energy is approximated by the energy of the D ∗ -containing jet or the D ∗ -containing event hemisphere, which is defined in the photon-proton rest frame. The charm fragmentation function has been measured in D ∗ photoproduction with the ZEUS detector using data corresponding to an integrated luminosity of 120 pb−1 [19]. The mea(E+p ) ∗ sured fragmentation observable z = (E+p|||| )D is jet shown in Fig. 7. The energy E and the longitudinal momentum relative to the jet axis p|| approximate the kinematics of the charm quark. The
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The charm fragmentation function was measured in DIS by the H1 experiment, using data corresponding to an integrated luminosity of 47 pb− 1 [22]. The energy of the charm quark was approximated by the jet associated to the D ∗ meson or by the event hemisphere containing a D∗ . The presence of a D ∗ -associated jet with ET > 3 GeV in the photon-proton rest frame was required, probing the kinematic region significantly above the production threshold. The normalised cross sections are measured as a function of two fragmentation-sensitive observables, zjet and zhem . The data are found to be consistent with the ZEUS measurement and with the prediction of the RAPGAP Monte-Carlo using the fragmentation parameters for heavy quarks ob-
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3.3. Extraction of F2c¯c The contribution of charm events F2c¯c to the proton structure function F2 is determined according to Eq. 1 in bins of Q2 and y using a certain extrapolation model. The double-differential cross section of D ∗ meson production as measured by the H1 experiment is shown in Fig. 9.
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tained from e+ e− annihilation experiments. This result is consistent with the hypothesis of fragmentation universality between ep and e+ e− collisions. The hemisphere method is also used to study the charm fragmentation close to the kinematical threshold. This region is defined by the absence of jet with ET > 3 GeV. The result is shown in Fig. 8: the fragmentation parameter extracted for the QCD models in this sample is significantly different from those obtained from the sample above threshold. Thus, the measurements
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Figure 9. Double differential D ∗ cross sections compared to the HVQDIS calculation. The solid line corresponds to the central value of the prediction. The charm quark mass has been varied from mc = 1.3 GeV to mc = 1.6 GeV, the renormalisation and factorisation scales have been varied simultaneously 0.5μ < μr = μf < 2μ. The light shaded band represents the full theory uncertainty, obtained from the variations of the charm mass, renormalisation and factorisation scales and the fragmentation model. The dark shaded band shows the theory uncertainty alone from the variations in the fragmentation model. Predicted visible differential cross sections are calculated using the HVQDIS program after
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full phase space, estimated by using CASCADE and HVQDIS, are shown in Fig. 10. Overall only small differences are observed. However at high x and low Q2 , the two models differ almost by a factor of 2. The origin of these differences is probably not related to the different parton evolution schemes but rather to the hadronisation models which is currently under investigation. The measurement of F2c¯c in the kinematical region 5
Extrapolation Factor Ratio CASCADE/HVQDIS
fragmenting the charm quarks in the photonproton centre of mass frame into D ∗ mesons. The Kartvelishvili fragmentation function is used. Following the line of the experimental observation [22], an sˆ-dependent charm fragmentation function is used: close to threshold (small sˆ) a harder fragmentation parameter is chosen than at large sˆ. 3
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The extraction of F2c¯c according to Equation 1 is faced with the problem that the measurement covers only about 20% to 60% of the total phase space for charm production, with the lowest acceptance at large x in the low Q2 region. Thus the extrapolation depends significantly on the used model. To investigate this model dependence F2c exp is determined using both the NLO DGLAP calculation HVQDIS and the LO MonteCarlo simulation CASCADE. Both models give a reasonable description of the differential cross sections in both the event kinematics and the kinematics of the D ∗ meson. The ratios of the extrapolation factors from the visible range to the
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Figure 11. The charm contribution, F2c¯c , to the proton structure function using HVQDIS for the extrapolation. The measurements are compared to the NLO FFNS prediction using the CTEQ5F3 (upper line) and MRST2004FF3 (lower line) parton densities. The extrapolation uncertainty, estimated by variation of the renormalisation and factorisation scales and the fragmentation parameters as well as by a variation of parton densities, is shown by the lighter shaded band. The uncertainty alone due to variation of PDFs is shown by the dark band.
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4. Charm Lifetime Tag
Muons
Another method used at HERA to tag charm events relies on the vertex information. Long lifetimes of the b- and c- flavoured hadrons lead to the displacement of tracks from the primary vertex. Measurement of such track displacements is used for simultaneous c- and b-tagging. The production of charm quarks in DIS has been measured at the ZEUS experiment using semi-leptonic decays into muons: c(¯ c) → μ± ν(¯ ν )q [23]. The data correspond to an integrated luminosity of 125 pb−1 . Charm cross sections have been measured for Q2 >20 GeV2 . The muon impact parameter, the muon transverse momentum with respect to the associated jet axis and the missing momentum have been used as discriminating variables to distinguish the b- and cquarks from the light flavour background.
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of the data to the predicted charm, beauty and uds cross sections the contribution of the specific flavour is determined. The single differential cross sections as functions of the muon kinematics are shown in Fig. 13 and Fig. 14 compared to the HVQDIS calculation.
Figure 13. Single differential cross section of muons from b- and c- semi-leptonic decays as function of the muon pseudo-rapidity. The cross sections of beauty (lower data points) and charm (upper data points) are compared to the NLO prediction (shaded band).
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Figure 12. The muon transverse momentum wrt. the associated jet axis as measured in semileptonic decays by the ZEUS experiment. The data are compared to the RAPGAP Monte-Carlo (light solid line). The prediction for the charm contribution is shown by the dark solid line. The contribution from b-quarks is indicated by the shaded area. The light flavour (uds) background is depicted by the dashed line. In Fig. 12 the inclusive distribution of the muon transverse momentum with respect to the associated jet axis, prel T,μ , is shown. From comparison
The contribution of charm and beauty events to the inclusive proton structure function as determined from the semi-muonic decays is shown in Fig. 15. The HVQDIS calculation was used for the extrapolation. The parton density sets ZEUS-S-FF and CTEQ5F3, the charm mass mc =1.5±0.2 GeV and the renormalisa tion/factorisation scales μf = μr = Q2 + 4m2c are used. The phenomenological Peterson [24] fragmentation function, defined by a single parameter =0.055, was used. In a similar way, the inclusive charm and beauty reduced cross sections are measured at the H1 experiment in the kinematic region of 5
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with help of the H1 central vertex detector. The most important of these observables are the transverse displacement of tracks from the primary vertex and the reconstructed position of the secondary vertex in the transverse plane. The charm and beauty reduced cross sections are presented in Fig. 16.
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Figure 15. The charm contribution to the proton structure function extracted from the semimuonic events. The data are compared to the NLO FFNS prediction (solid line) using the ZEUS-S-FF parton density functions. Dashdotted lines correspond to the variation of c- and b-quark masses.
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Figure 16. The reduced charm cross section as a function of x in different Q2 bins. The inner error bars represent the statistical and the outer error bars represent the statistical and systematic uncertainties added in quadrature. The data are compared to different QCD predictions. The measurements are compared with two recent NLO QCD predictions based on the variable flavour number scheme (VFNS) from CTEQ [26] and MSTW [27] as well as with prediction based on the CCFM parton evolution. The predictions provide a reasonable description of the present data. In Fig. 17 F2c¯c , extracted from the reduced cross section after small corrections for FLc¯c , is compared to the NLO and NNLO models from the MSTW group [28]. While the NLO prediction by the MSTW group seems to overestimate
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F2c¯c , the NNLO one is in much better agreement with the data. 5. Summary The recent measurements of the charm contribution F2c¯c to the inclusive structure function at HERA are approaching the final precision. The distinction power of the measurements with respect to the recent developments of the QCD models in NLO and NNLO has significantly increased. The harvest of the current F2c¯c measurements at HERA is shown in Fig. 18. Together, the H1 and ZEUS experiments collected data amounting to an integrated luminosity of about 600 pb−1 . Both experiments are working on further improvements in both, statistical and sys-
tematic uncertainties of the measurement. Different charm tagging methods show consistent results and will be combined taking into account proper correlations between the data points and the measurement methods. The results of both collaborations will be combined, thereby the imrovement in precision is expected. The extrapolation problems has to be studied further to reduce the theory uncertainty. The charm fragmentation function close to the production threshold has to be studied in more details. Taking into account the contribution of charm events to F2 in the global PDF fits will put an important constrain on the gluon distribution, which is of the crucial issues for the physics at the LHC.
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Measurement of F2c¯c at HERA K. Lipkaa (on behalf of the H1 and ZEUS collaborations) a
Deutsches Elektronen Synchrotron Notkestrasse, 85, D-22607 Hamburg, Germany Recent results on the extraction of the charm contribution, F2c¯c , to the inclusive proton structure function F2 in deep inelastic ep scattering at HERA are presented. Different methods of charm tagging and measurements of the charm fragmentation function are shown. The issues related to the extrapolation of the visible cross sections to the full phase space are discussed.
1. Introduction Results on the charm contribution to the proton structure function, F2c , at HERA have been published by the H1 and the ZEUS collaborations [1–3]. The data have shown clear evidence that the dynamics of charm production in ep scattering is dominated by the photon gluon fusion proc cess. In this framework the process e+ p → c¯ is sensitive to the gluon density in the proton [4] and allows its universality to be tested. Several charm tagging methods are used at HERA. Charm quarks are either tagged by reconstructing charmed hadrons e.g. D ∗± , D± and D0 mesons, or by making use of the long lifetime and large mass of heavy quarks. F2c¯c is extracted extrapolating the measured cross sections in the phase space of the analysis to the full phase space using the appropriate theory model. When using the lifetime information, the charm and the beauty contributions to the proton structure are extracted simultaneously. The presented analyses partially cover the data from the HERA-II running period, yielding significant integrated luminosity. Therefore, more precise tests of perturbative QCD (pQCD) become possible. 2. Models of charm production The description of open heavy flavour production in electron proton collisions is based on perturbative QCD. In leading order (LO), the photon gluon fusion process (γg → QQ) is the dominant 0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.03.123
contribution [1]. This treatment has been extended to next-to-leading order (NLO) for which calculations in several schemes are available [5– 9]. All approaches assume the scale introduced by the heavy quark mass to be hard enough to apply pQCD and to guarantee the validity of the factorisation theorem. In the analyses presented here the “massive approach” is adopted, i.e. a fixed order calculation with massive quarks and assuming three active flavours in the proton. The momentum densities of the three light quarks and the gluon in the proton are evolved by the DGLAP equation [10]. The heavy quarks are assumed to be produced only at the perturbative level [5] via photon gluon fusion. Based on the NLO calculations of order α2s in the coefficient functions [5] programs for different applications were developed in the fixedflavour-number-scheme (FFNS). The Riemersma program [6] is used for the calculation of inclusive quantities of heavy quark production, like F2c (x, Q2 ), while the HVQDIS program [7,11] allows the calculation of exclusive quantities by providing the four-momenta of the outgoing partons. Both programs are based on the same calculation and use the same input like PDFs, charm mass and factorisation and renormalisation scales. The MRST2004FF and CTEQ5F3 (ZEUS-S-FF) parton densities, mc =1.43 (1.5) GeV and μr = μf = Q2 + 4m2c are used in the H1 (ZEUS) analyses presented here. The data presented here are also compared to the RAPGAP [12] and CAS-
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CADE [13] Monte-Carlo simulations. Both are based on leading order matrix element calculations with the higher order corrections implemented via parton showers. Parton evolution according to the DGLAP equations is used in the RAPGAP simulation. CASCADE implies intrinsic kt factorisation and parton evolution according to the CCFM [14] equations. 3. Extraction of F2c¯c using the reconstruction of charmed hadrons The contribution of charm to the proton structure function can be determined using the measured cross section of charm-tagged events. In the following measurements based on the reconstruction of charmed mesons are presented. The experimental value of F2c¯c is determined by: c¯ c F2,exp =
exp σvis c¯ c · F2,th . th σvis
(1)
exp th (σvis ) denotes the measured (preHere σvis dicted) meson cross section in the visible phase c¯ c corresponds to space of the analysis and F2,th the model prediction for F2c¯c in the full phase space. The visible phase space accessible by the detectors H1 and ZEUS via reconstruction of charmed mesons covers only about 30% of the full phase space. Therefore the determination of F2c¯c strongly depends on the model used for the extrapolation. In the following, HVQDIS and CASCADE are used as extrapolation models. The extrapolation uncertainties within a single model are estimated by the variation of the input parameters like parton densities, charm quark mass and the renormalisation/factorisation scales as well as by the variation of the charm fragmentation model.
3.1. Cross section measurements In the following, the charm tagging method via reconstruction of decays of charmed hadrons is illustrated using the D ∗± mesons. The data were collected with the H1 detector, corresponding to an integrated luminosity L=345 pb−1 . D∗ are reconstructed in decays D ∗ → D0 + πslow → K + π + πslow . The signal is extracted using the mass difference technique from
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Figure 1. Invariant mass difference of Kππ and Kπ combinations of D∗ candidates. the fit to the Δm distribution of the D ∗ candidates (Δm=mKππ − mKπ ). In Fig. 1 the Δm distribution is shown for the D ∗ candidates and the wrong charge background. The doubledifferential cross sections of D ∗ production as
Figure 2. Double-differential D ∗ cross sections as a function of the pseudo-rapidity η in bins of the transverse momentum pT . The hatched (shaded) area corresponds to the HVQDIS prediction using the CTEQ5F3 (MRST2004FF3) parton densities. The widths of the bands corresponds to the variation of model parameters.
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function of the meson kinematics measured by H1 collaboration are shown in Fig. 2 [15]. The measurements are compared to the NLO calculations using the CTEQ5F3 and MRST2004FF3 parton densities, respectively. Overall the NLO calculation describes the distributions well, however, it seems to underestimate the cross section in the forward region at low pT (D∗ ). The dif-
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Figure 4. Differential cross section of D ± -meson production as a function of the meson kinematics, as measured by the ZEUS experiment. The data are compared to the HVQDIS prediction (shaded band) using the ZEUS-S-FF parton densities. The expected beauty contribution is represented by the dotted line.
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Figure 3. Differential cross section of D 0 -meson production as a function of the meson kinematics, as measured by the ZEUS experiment. The data are compared to the HVQDIS prediction (shaded band) using the ZEUS-S-FF parton densities. The expected beauty contribution is represented by the dotted line. ferential cross sections of D ± and D0 -mesons are shown in Fig. 3 and Fig. 4 in comparison to the HVQDIS calculation. The data are collected with the ZEUS experiment corresponding to the integrated luminosity of 135 pb−1 [16]. The DIS kinematic region 5
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Figure 5. Cross section of D ∗ meson production as a function of Q2 as measured by the H1 experiment. The data are compared to the Monte-Carlo simulations RAPGAP using the CTEQ6L (upper solid line) and CTEQ65m (lower solid line) parton densities and CASCADE (dotted line).
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energy of a D ∗ -associated jet was required to fulfil ET > 9 GeV. Thereby the charm production phase space far above the threshold is probed. The data are fitted by the NLO massive calculation FMNR [20], using the Kartvelishvili [21] fragmentation function defined by a single parameter α.
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Figure 6. Differential cross section of D ∗ meson production as function of Q2 as measured by the ZEUS experiment. The data are compared to the NLO calculation HVQDIS (shaded band). 3.2. Charm Fragmentation The charm fragmentation function was measured by the H1 and ZEUS experiments using inclusive D∗± meson production in both photoproduction and DIS. A fragmentation observable z is measured, which determines the fractional energy of the charm quark carried by the produced meson. Experimentally, the charm quark energy is approximated by the energy of the D ∗ -containing jet or the D ∗ -containing event hemisphere, which is defined in the photon-proton rest frame. The charm fragmentation function has been measured in D ∗ photoproduction with the ZEUS detector using data corresponding to an integrated luminosity of 120 pb−1 [19]. The mea(E+p ) ∗ sured fragmentation observable z = (E+p|||| )D is jet shown in Fig. 7. The energy E and the longitudinal momentum relative to the jet axis p|| approximate the kinematics of the charm quark. The
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The charm fragmentation function was measured in DIS by the H1 experiment, using data corresponding to an integrated luminosity of 47 pb− 1 [22]. The energy of the charm quark was approximated by the jet associated to the D ∗ meson or by the event hemisphere containing a D∗ . The presence of a D ∗ -associated jet with ET > 3 GeV in the photon-proton rest frame was required, probing the kinematic region significantly above the production threshold. The normalised cross sections are measured as a function of two fragmentation-sensitive observables, zjet and zhem . The data are found to be consistent with the ZEUS measurement and with the prediction of the RAPGAP Monte-Carlo using the fragmentation parameters for heavy quarks ob-
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3.3. Extraction of F2c¯c The contribution of charm events F2c¯c to the proton structure function F2 is determined according to Eq. 1 in bins of Q2 and y using a certain extrapolation model. The double-differential cross section of D ∗ meson production as measured by the H1 experiment is shown in Fig. 9.
Q d σ/dQ dy [nb GeV ]
tained from e+ e− annihilation experiments. This result is consistent with the hypothesis of fragmentation universality between ep and e+ e− collisions. The hemisphere method is also used to study the charm fragmentation close to the kinematical threshold. This region is defined by the absence of jet with ET > 3 GeV. The result is shown in Fig. 8: the fragmentation parameter extracted for the QCD models in this sample is significantly different from those obtained from the sample above threshold. Thus, the measurements
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Figure 9. Double differential D ∗ cross sections compared to the HVQDIS calculation. The solid line corresponds to the central value of the prediction. The charm quark mass has been varied from mc = 1.3 GeV to mc = 1.6 GeV, the renormalisation and factorisation scales have been varied simultaneously 0.5μ < μr = μf < 2μ. The light shaded band represents the full theory uncertainty, obtained from the variations of the charm mass, renormalisation and factorisation scales and the fragmentation model. The dark shaded band shows the theory uncertainty alone from the variations in the fragmentation model. Predicted visible differential cross sections are calculated using the HVQDIS program after
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full phase space, estimated by using CASCADE and HVQDIS, are shown in Fig. 10. Overall only small differences are observed. However at high x and low Q2 , the two models differ almost by a factor of 2. The origin of these differences is probably not related to the different parton evolution schemes but rather to the hadronisation models which is currently under investigation. The measurement of F2c¯c in the kinematical region 5
Extrapolation Factor Ratio CASCADE/HVQDIS
fragmenting the charm quarks in the photonproton centre of mass frame into D ∗ mesons. The Kartvelishvili fragmentation function is used. Following the line of the experimental observation [22], an sˆ-dependent charm fragmentation function is used: close to threshold (small sˆ) a harder fragmentation parameter is chosen than at large sˆ. 3
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The extraction of F2c¯c according to Equation 1 is faced with the problem that the measurement covers only about 20% to 60% of the total phase space for charm production, with the lowest acceptance at large x in the low Q2 region. Thus the extrapolation depends significantly on the used model. To investigate this model dependence F2c exp is determined using both the NLO DGLAP calculation HVQDIS and the LO MonteCarlo simulation CASCADE. Both models give a reasonable description of the differential cross sections in both the event kinematics and the kinematics of the D ∗ meson. The ratios of the extrapolation factors from the visible range to the
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Figure 11. The charm contribution, F2c¯c , to the proton structure function using HVQDIS for the extrapolation. The measurements are compared to the NLO FFNS prediction using the CTEQ5F3 (upper line) and MRST2004FF3 (lower line) parton densities. The extrapolation uncertainty, estimated by variation of the renormalisation and factorisation scales and the fragmentation parameters as well as by a variation of parton densities, is shown by the lighter shaded band. The uncertainty alone due to variation of PDFs is shown by the dark band.
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4. Charm Lifetime Tag
Muons
Another method used at HERA to tag charm events relies on the vertex information. Long lifetimes of the b- and c- flavoured hadrons lead to the displacement of tracks from the primary vertex. Measurement of such track displacements is used for simultaneous c- and b-tagging. The production of charm quarks in DIS has been measured at the ZEUS experiment using semi-leptonic decays into muons: c(¯ c) → μ± ν(¯ ν )q [23]. The data correspond to an integrated luminosity of 125 pb−1 . Charm cross sections have been measured for Q2 >20 GeV2 . The muon impact parameter, the muon transverse momentum with respect to the associated jet axis and the missing momentum have been used as discriminating variables to distinguish the b- and cquarks from the light flavour background.
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of the data to the predicted charm, beauty and uds cross sections the contribution of the specific flavour is determined. The single differential cross sections as functions of the muon kinematics are shown in Fig. 13 and Fig. 14 compared to the HVQDIS calculation.
Figure 13. Single differential cross section of muons from b- and c- semi-leptonic decays as function of the muon pseudo-rapidity. The cross sections of beauty (lower data points) and charm (upper data points) are compared to the NLO prediction (shaded band).
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Figure 12. The muon transverse momentum wrt. the associated jet axis as measured in semileptonic decays by the ZEUS experiment. The data are compared to the RAPGAP Monte-Carlo (light solid line). The prediction for the charm contribution is shown by the dark solid line. The contribution from b-quarks is indicated by the shaded area. The light flavour (uds) background is depicted by the dashed line. In Fig. 12 the inclusive distribution of the muon transverse momentum with respect to the associated jet axis, prel T,μ , is shown. From comparison
The contribution of charm and beauty events to the inclusive proton structure function as determined from the semi-muonic decays is shown in Fig. 15. The HVQDIS calculation was used for the extrapolation. The parton density sets ZEUS-S-FF and CTEQ5F3, the charm mass mc =1.5±0.2 GeV and the renormalisa tion/factorisation scales μf = μr = Q2 + 4m2c are used. The phenomenological Peterson [24] fragmentation function, defined by a single parameter =0.055, was used. In a similar way, the inclusive charm and beauty reduced cross sections are measured at the H1 experiment in the kinematic region of 5
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with help of the H1 central vertex detector. The most important of these observables are the transverse displacement of tracks from the primary vertex and the reconstructed position of the secondary vertex in the transverse plane. The charm and beauty reduced cross sections are presented in Fig. 16.
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Figure 16. The reduced charm cross section as a function of x in different Q2 bins. The inner error bars represent the statistical and the outer error bars represent the statistical and systematic uncertainties added in quadrature. The data are compared to different QCD predictions. The measurements are compared with two recent NLO QCD predictions based on the variable flavour number scheme (VFNS) from CTEQ [26] and MSTW [27] as well as with prediction based on the CCFM parton evolution. The predictions provide a reasonable description of the present data. In Fig. 17 F2c¯c , extracted from the reduced cross section after small corrections for FLc¯c , is compared to the NLO and NNLO models from the MSTW group [28]. While the NLO prediction by the MSTW group seems to overestimate
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Figure 18. F2c¯c measurements at HERA as a function of x for different values of Q2 compared to different QCD predictions.
F2c¯c , the NNLO one is in much better agreement with the data. 5. Summary The recent measurements of the charm contribution F2c¯c to the inclusive structure function at HERA are approaching the final precision. The distinction power of the measurements with respect to the recent developments of the QCD models in NLO and NNLO has significantly increased. The harvest of the current F2c¯c measurements at HERA is shown in Fig. 18. Together, the H1 and ZEUS experiments collected data amounting to an integrated luminosity of about 600 pb−1 . Both experiments are working on further improvements in both, statistical and sys-
tematic uncertainties of the measurement. Different charm tagging methods show consistent results and will be combined taking into account proper correlations between the data points and the measurement methods. The results of both collaborations will be combined, thereby the imrovement in precision is expected. The extrapolation problems has to be studied further to reduce the theory uncertainty. The charm fragmentation function close to the production threshold has to be studied in more details. Taking into account the contribution of charm events to F2 in the global PDF fits will put an important constrain on the gluon distribution, which is of the crucial issues for the physics at the LHC.
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