Measurement of $ D^{*\pm}$ production in deep inelastic scattering at HERA

The production of $D^{*\pm}$ mesons in deep inelastic $ep$ scattering has been measured for exchanged photon virtualities $ 5<Q^2<1000 \gev^2 $, using an integrated luminosity of 363 pb$^{-1}$ with the ZEUS detector at HERA. Differential cross sections have been measured and compared to next-to-leading-order QCD calculations. The cross-sections are used to extract the charm contribution to the proton structure functions, expressed in terms of the reduced charm cross section, $\sigma_{\rm red}^{c\bar{c}}$. Theoretical calculations based on fits to inclusive HERA data are compared to the results.

h now at Rockefeller University, New York, NY 10065, USA i now at DESY group FS-CFEL-1 j now at Institute of High Energy Physics, Beijing, China k now at DESY group FEB, Hamburg, Germany l also at Moscow State University, Russia m now at University of Liverpool, United Kingdom n now at CERN, Geneva, Switzerland o also affiliated with University College London, UK p now at Goldman Sachs, London, UK q also at Institute of Theoretical and Experimental Physics, Moscow, Russia r also at FPACS, AGH-UST, Cracow, Poland s partially supported by Warsaw University, Poland t supported by the Alexander von Humboldt Foundation u now at Istituto Nazionale di Fisica Nucleare (INFN), Pisa, Italy v now at Haase Energie Technik AG, Neumünster, Germany w now at Department of Physics, University of Bonn, Germany x also affiliated with DESY, Germany y also at University of Tokyo, Japan z now at Kobe University, Japan † deceased aa supported by DESY, Germany ab member of National Technical University of Ukraine, Kyiv Polytechnic Institute, Kyiv, Ukraine ac member of National Technical University of Ukraine, Kyiv, Ukraine ad now at DESY ATLAS group ae member of National University of Kyiv -Mohyla Academy, Kyiv, Ukraine af Alexander von Humboldt Professor; also at DESY and University of Oxford ag STFC Advanced Fellow ah now at LNF, Frascati, Italy ai This material was based on work supported by the National Science Foundation, while working at the Foundation.aj also at Max Planck Institute for Physics, Munich, Germany, External Scientific Member VI ak now at Tokyo Metropolitan University, Japan al now at Nihon Institute of Medical Science, Japan am now at Osaka University, Osaka, Japan an also at Lódź University, Poland ao member of Lódź University, Poland ap now at Department of Physics, Stockholm University, Stockholm, Sweden

Introduction
The measurement of charm production in deep inelastic ep scattering (DIS) is a powerful tool to study quantum chromodynamics (QCD) and the proton structure.In leading-order QCD, charm production occurs through the boson-gluon fusion (BGF) process γ * g → cc, which is directly sensitive to the gluon content of the proton.Different approaches to the calculation of the heavy-quark contribution to the proton structure functions are currently used in global analyses of parton density functions (PDFs) [1][2][3][4].Comparisons to measurements of charm production in DIS provide direct tests of these approaches [5].It has also been shown recently that a combined analysis of charm production and inclusive DIS data can provide a competitive determination of the charm-quark mass [5][6][7].
The D * + mesons1 were reconstructed through the decay D * + → D 0 π + with D 0 → K − π + .Differential cross sections are presented as a function of Q 2 , y, the Bjorken-x variable, and of the fraction of the exchanged-photon energy transferred to the D * + meson in the proton rest frame, z D * ≡ (P • p D * )/(P • q), as well as of the D * + pseudorapidity, η D * , and the transverse momentum, p D * T , in the laboratory frame 2 .Double-differential cross sections in Q 2 and y are presented and used to extract the charm contribution to the proton structure functions in the form of the reduced charm cross section, σ cc red .Previous measurements and theoretical calculations are compared to the results.

Experimental set-up
The measurement was based on e ± p collisions collected with the ZEUS detector at HERA in the period 2004-2007 with an electron3 beam energy, E e , of 27.5 GeV and a proton beam energy, E p , of 920 GeV, corresponding to a centre-of-mass energy √ s = 318 GeV.
The corresponding integrated luminosity, L = 363 ± 7 pb −1 , is four times larger than that used for the previous ZEUS measurement [11].
A detailed description of the ZEUS detector can be found elsewhere [21].In the kinematic range of the analysis, charged particles were tracked in the central tracking detector (CTD) [22] and in the microvertex detector (MVD) [23].These components operated in a magnetic field of 1.43 T provided by a thin superconducting solenoid.The CTD consisted of 72 cylindrical drift chamber layers, organised in nine superlayers covering the polar-angle region 15 • < θ < 164 • .The MVD consisted of a barrel (BMVD) and a forward (FMVD) section with three cylindrical layers and four vertical planes of single-sided silicon strip sensors in the BMVD and FMVD respectively.The BMVD provided polar-angle coverage for tracks crossing the three layers from 30 • to 150 • .The FMVD extended the polar-angle coverage in the forward region down to 7 • .For CTD-MVD tracks that pass through all nine CTD superlayers, the momentum resolution was σ(p T )/p T = 0.0029p T ⊕ 0.0081 ⊕ 0.0012/p T , with p T in GeV.
The high-resolution uranium-scintillator calorimeter (CAL) [24] consisted of three parts: the forward, the barrel, and the rear (RCAL) calorimeters.Under test-beam conditions, the CAL single-particle relative energy resolutions were σ(E)/E = 0.18/ √ E for electrons and σ(E)/E = 0.35/ √ E for hadrons, with E in GeV.The energy of electrons hitting the RCAL was corrected for the presence of dead material using the rear presampler detector [25] and the small angle rear tracking detector (SRTD) [26].
The luminosity was measured using the Bethe-Heitler reaction ep → eγp by a luminosity detector which consisted of two independent systems: a lead-scintillator calorimeter [27] and a magnetic spectrometer [28].

QCD calculations
Cross sections for heavy-quark production in DIS were calculated at next-to-leading order (NLO), i.e.O(α 2 s ), in the fixed-flavour-number scheme (FFNS), in which only light flavours and gluons are present as partons in the proton and heavy quarks are produced in the hard interaction [29].The program Hvqdis [30,31] was used to compute singleand double-differential D * + cross sections.
The parameters used as input to Hvqdis are listed below, together with the variations used to evaluate the uncertainty on the theoretical prediction: • charm-quark pole mass: m c = 1.50 ± 0.15 GeV; • renormalisation (µ R ) and factorisation (µ , varied independently up and down by a factor two; • strong coupling constant in the three-flavour FFNS: α nf=3 s (M Z ) = 0.105 ± 0.002; • the PDFs and their uncertainties, taken from a FFNS variant [5] of the HERAPDF1.0fit [32].The central PDF set was obtained from a fit performed using the same values of m c , µ R , µ F and α s as used in the Hvqdis program.For each variation of these parameters in Hvqdis, a different PDF set was used, in which the parameters were varied consistently.
The NLO calculation provided differential cross sections for charm quarks.The fragmentation model described in a previous publication [5] was used to compare to the measured D * + cross sections.This model is based on the fragmentation function of Kartvelishvili et al. [33], controlled by the parameter α K , to describe the fraction of the charm momentum transferred to the D * + mesons.It also implements a transverse fragmentation component by assigning to the D * + meson a transverse momentum, k T , with respect to the charmquark direction.The uncertainty on the fragmentation model was estimated by varying α K and the average k T according to the original prescription [5].The fraction of charm quarks hadronising into D * + mesons was set to f (c → D * + ) = 0.2287 ± 0.0056 [34].
For the inclusive cross section, theoretical predictions were also obtained in the generalisedmass variable-flavour-number scheme (GM-VFNS).In this scheme, charm quarks are treated as massive particles for Q 2 ≤ m 2 c and as massless partons for Q 2 ≫ m 2 c , interpolating in the intermediate region [35][36][37].The calculation was performed using the Roberts-Thorne (RT) "standard" [38,39] variant of the GM-VFNS at NLO, corresponding to O(α 2 s ) for the Q 2 ≤ m 2 c part and to O(α s ) for the Q 2 ≫ m 2 c part.PDFs obtained from the HERAPDF1.5[40] fit to inclusive HERA data were used.The central prediction was obtained for m c = 1.5 GeV.To evaluate the theoretical uncertainty, the calculation was repeated varying the PDF set and its parameters according to the systematic variations associated with the HERAPDF1.5fit.The dominant source of uncertainty was the charm-quark mass, which was varied in the range 1.35 < m c < 1.65 GeV.

Monte Carlo samples
Monte Carlo (MC) samples were used to calculate the experimental acceptance and to estimate the background contamination.MC samples of charm and beauty DIS events were generated using Rapgap 3.00 [41].The main sample consisted of events generated according to the LO BGF process.Radiative QED corrections to the BGF process were included through Heracles 4.6 [42].Additional Rapgap samples were generated for diffractive charm production and for the resolved-photon processes gg → cc and cg → cg, in which one of the incoming partons originates from the exchanged photon.Charm photoproduction was simulated using Pythia 6.2 [43].
Both Rapgap and Pythia use parton showers to simulate higher-order QCD effects and use the Pythia/Jetset hadronisation model [43].All samples were generated using the CTEQ5L [44] proton PDFs and, for resolved-photon processes, the GRV-G LO [45] photon PDFs.The diffractive samples were generated using the "H1 fit 2" [46] diffractive PDFs.The heavy-quark masses were set to m c = 1.5 GeV and m b = 4.75 GeV.Masses, widths and lifetimes of charmed mesons were taken from PDG2010 [47].
The MC samples correspond to about four times the luminosity of the data and were passed through a full simulation of the ZEUS detector based on Geant 3.21 [48].They were then subjected to the same trigger criteria and reconstructed with the same programs as used for the data.

Event selection and signal extraction 5.1 DIS event selection
A three-level trigger system was used to select DIS events online [21,49,50] by requiring electromagnetic energy deposits in the CAL at the first level and applying loose DIS selection criteria at the second and third levels.
Offline, the hadronic system was reconstructed using energy-flow objects (EFOs) [51] which combine tracking and calorimeter information.The electron was identified using a neural-network algorithm [52].The kinematical variables Q 2 , y, and x were reconstructed using the Σ method [53].The variable z D * was reconstructed according to , where y JB is the inelasticity reconstructed with the Jacquet-Blondel method [54] and E D * and p D * Z are the D * + energy and longitudinal momentum, respectively.
The following criteria were applied to select DIS events [55]: • E e ′ > 10 GeV, where E e ′ is the energy of the scattered electron; • y e < 0.7, y JB > 0.02, where y e is the inelasticity reconstructed from the scattered electron; • 40 < E −P Z < 70 GeV, where E −P Z is the global difference of energy and longitudinal momentum, obtained by summing the electron and the hadronic final state, which is expected to be 2E e = 55 GeV for fully contained events; • the Z position of the primary vertex, Z vtx , was required to be in the range |Z vtx | < 30 cm; • the impact point of the scattered electron on the RCAL was required to lie outside a square region around the beam-pipe hole: |X e | > 15 cm or |Y e | > 15 cm; , where Q 2 is reconstructed with the Σ method.

Selection of D * + candidates and signal extraction
The D * + mesons were identified using the decay channel D * + → D 0 π + s with the subsequent decay D 0 → K − π + , where π + s refers to a low-momentum ("slow") pion accompanying the D 0 .
Tracks from the D * + decay products were required to have at least one hit in the MVD or in the inner superlayer of the CTD and to reach at least the third superlayer.Tracks with opposite charge and with transverse momentum p K,π T > 0.4 GeV were combined in pairs to form D 0 candidates.The track parameters were improved by fitting the two tracks to a common vertex.Pairs incompatible with coming from the same decay were removed by requiring a distance of closest approach of the two tracks of less than 1 mm, and the χ 2 of the two-track vertex fit smaller than 20 for one degree of freedom.The tracks were alternately assigned the kaon and pion mass and the invariant mass of the pair, M(Kπ), was calculated.Each additional track, with charge opposite to that of the kaon track and a transverse momentum p πs T > 0.12 GeV, was assigned the pion mass and combined with the D 0 candidate to form a D * + candidate.The π s track was then fitted to the primary vertex of the event, obtained exploiting the other tracks reconstructed in the event and the constraint from the average position of the interaction point [8].The mass difference ∆M ≡ M(Kππ s ) − M(Kπ) was used to extract the D * + signal.The D * + candidates were required to have 1.80 < M(Kπ) < 1.92 GeV, 143.2 < ∆M < 147.7 MeV, 1.5 < p D * T < 20 GeV and |η D * | < 1.5.The distribution of M(Kπ) for D * + candidates, without the requirement on M(Kπ), is shown in Fig. 1.Also shown is the distribution of wrong-sign (WS) candidates, obtained by combining two tracks with the same charge.The WS distribution provides an estimate of combinatorial backgrounds.A clear peak at the D 0 mass is visible in the correct-sign (CS) distribution.The excess of CS candidates at masses below the D 0 peak is due to partly-reconstructed D 0 decays, mostly The distribution of ∆M for D * + candidates, without the requirement on ∆M, is shown in Fig. 2. A clear D * + peak is seen.The D * + signal was extracted by subtracting the background estimate from the number of candidates in the signal window 143.2 < ∆M < 147.7 MeV.The background estimate was obtained by fitting simultaneously the CS and WS distributions to the parametrisation where A, B, C, D are free parameters of the fit [56] and ζ = ∆M − m π + .The fit was performed in the region ∆M < 168 MeV.The region with a possible signal contribution, 140 < ∆M < 150 MeV, was removed from the fit to the CS distribution.The parameter D, which represents the normalisation of the CS background with respect to the WS distribution, is slightly larger than unity, D = 1.021 ± 0.005.This is consistent with the MC estimation of the additional combinatorial background component in the CS distribution due to real D 0 → Kπ decays associated with a random track to form a CS D * + candidate.The total signal is N D * ± data = 12893 ± 185.The amount of signal lost due to the tails of the D 0 mass peak leaking outside the M(Kπ) window was estimated by enlarging the mass window to 1.7 < M(Kπ) < 2.0 GeV.The fraction of additional D * + found within the enlarged window was 13%, including the contribution from partly reconstructed D 0 .This fraction, as well as its dependence on p D * T and η D * and on the width of the M(Kπ) window, was found to be well reproduced by MC.The signal in the tails of the D * + peak outside the ∆M window was estimated similarly, enlarging the signal window to 140 < ∆M < 150 MeV.The fraction of additional D * + was 6% on average, with a dependence on the transverse momentum of the slow pion, due to the momentum and angular resolution degrading at low p π S T .This effect is not completely reproduced by the MC.An acceptance correction [55] dependent on p πs T was then applied, ranging from ≈ 10% at p πs T = 0.12 GeV to ≈ 1% at large p πs T .

Cross-section extraction
The differential cross sections, dσ vis /dξ, for producing a D * + in the "visible" phase space 1.5 < p D * T < 20 GeV, |η D * | < 1.5, 5 < Q 2 < 1000 GeV 2 and 0.02 < y < 0.7 was obtained as where N D * data is the signal extracted in a bin of a given variable ξ, N D * γp is the photoproduction background, ∆ξ is the bin size, A is the acceptance, BR = B(D * + → D 0 π + ) × B(D 0 → K − π + ) = 0.0263 ± 0.0004 [57] is the branching ratio, L is the integrated luminosity and C r is the QED radiative correction.
The background from charm photoproduction (Q 2 < 1.5 GeV 2 ) was evaluated using the photoproduction MC sample, normalised to the luminosity using the cross sections previously measured by ZEUS [58].
The acceptance, A, was calculated as the ratio between the number of reconstructed and generated D * + in the bin, using a signal MC based on a mix of charm and beauty production.The beauty MC was normalised to 1.6 times the cross section given by Rapgap, consistent with ZEUS measurements [18,[59][60][61].The charm MC contained nondiffractive and diffractive components, summed according to the relative cross sections as given by Rapgap.The normalisation of the charm MC was adjusted such that the sum of all the MC components reproduced the number of D * + mesons in the data.Resolvedphoton processes were not included.They were only used for systematic checks.The η D * and p D * T distributions of the charm MC were reweighted [55] to improve the agreement with data, with the p D * T weights dependent on Q 2 .The acceptance as determined by the MC was corrected to account for imperfections in the simulation of the trigger and track-reconstruction efficiencies.One of the main sources of track-reconstruction inefficiency for charged pions and kaons were hadronic interactions in the material between the interaction point and the CTD.This effect was studied using special tracks from ep → eρ 0 with ρ 0 → π + π − events, reconstructed from MVD hit information alone [62].For these tracks, an extension into the CTD was searched for.In addition, the p T dependence of the tracking efficiency was studied by exploiting the isotropic angular distribution of pions from K 0 S decays.The studies showed that the MC slightly underestimated the effect of nuclear interactions.For central pions with p T ≈ 1 GeV, the track-reconstruction inefficiency due to hadronic interactions was measured to be (7 ± 1)% while the MC predicted 5%.The track-efficiency correction was applied as a function of η and p T of each track.For p T > 1.5 GeV, no correction was necessary.
The acceptance ranges from A ≈ 10% in the lowest p D * T and Q 2 bins to A ≈ 45% in the highest p D * T and Q 2 bins.Fig. 3 shows y and z D * .The sum of the different MC samples is compared to the data.The agreement is satisfactory.
The cross sections were corrected to the QED Born level, using a running coupling constant α em (Q 2 ), such that they can be compared directly to the QCD predictions from the Hvqdis program.The radiative corrections were obtained as C r = σ Born vis /σ rad vis , where σ Born vis is the Rapgap cross section with the QED corrections turned off but keeping α em running and σ rad vis is the Rapgap cross section with the full QED corrections, as in the standard MC samples.

Systematic uncertainties
The experimental systematic uncertainties are listed below [55], with their typical effect on the measured cross sections is given in parenthesis: δ 1 energy-scale uncertainty on the hadronic system of ±2% (±1%, up to ±10% at low y); All the systematic uncertainties, except the overall normalisations δ 18 and δ 19 , were added in quadrature to the statistical uncertainties to obtain the total error bars in the figures.

Results
Single-and double-differential cross sections have been measured in the phase space 5 < Q 2 < 1000 GeV 2 ; 0.02 < y < 0. T and is almost constant in η D * .The NLO calculations based on Hvqdis and the Rapgap MC implementing the leading-order BGF process are compared to the data.As the Rapgap MC is based on leading-order matrix elements, it is not expected to estimate the normalisation correctly.Therefore the Rapgap prediction was normalised to the data, scaling it by 1.1, to allow a direct comparison of the shapes.The data are well described by the NLO calculation and by Rapgap with the exception of the shape in z D * , which is not well reproduced by the NLO calculation, suggesting possible imperfections in the fragmentation model.Differential cross sections in Q 2 , y and x are reported in Tables 4-6 and in Fig. 5.The results are reasonably well described by the NLO calculation.The MC predictions reproduce the shapes of the data, except for the high-Q 2 tail, where the MC prediction is too high, and for dσ/dy, where the prediction is too low at low y and too high at large y.These imperfections in the MC are to be expected in the absence of higher-order terms in Rapgap.
Visible cross sections in two-dimensional bins of Q 2 and y, σ vis , are given in Table 7.The corresponding bin-averaged double-differential cross sections are shown in Figs. 6  and 7.The values of the individual systematic uncertainties on the double-differential cross sections are given in Table 8.Measurements performed in the same phase space by the H1 Collaboration [16,17], which are the most precise previous measurement of D * + production in DIS, are compared to the present results.The two data sets are in agreement and have similar precision.The double-differential cross sections are well described by the NLO calculation.
In a previous ZEUS measurement [11], a possible excess in the D * + yield in e − p collisions was observed with respect to e + p collisions.The ratio of observed rates, increasing with Q 2 , was r e − p /r e + p = 1.67 ± 0.21(stat.)for 40 < Q 2 < 1000 GeV 2 .The measurement was based on a luminosity of 17 (65) pb −1 of e − p (e + p) collisions.The present measurement is based on an independent data set, consisting of 187 (174) pb −1 of e − p (e + p) collisions.Fig. 8 shows the cross-section ratio as a function of Q 2 .Only statistical uncertainties are shown since systematic effects mostly cancel in the ratio.No deviation from unity is observed, confirming the original interpretation of the e − p excess as a statistical fluctuation.

Charm reduced cross sections
The reduced cross section for charm, σ cc red , and the charm contribution to the proton structure functions, F cc 2 and F cc L , are defined as: where The Hvqdis program was used to extrapolate the measured visible D * + cross sections in bins of y and Q 2 , σ vis , to the full phase space: where σ beauty vis is the beauty contribution as predicted by the Rapgap MC, normalised as discussed in Section 6, and σ cc red, Hvqdis , σ vis, Hvqdis are the charm reduced and the visible D * + cross sections, respectively, as given by Hvqdis.The reference values of x and Q 2 were chosen close to the average x and Q 2 of the bins.The kinematic acceptance of the visible phase space, defined as A ps = σ vis /(σ cc • 2 f (c → D * + )), where σ cc is the charm production total cross section in the y and Q 2 bin, ranges from 17% to 64%, depending on the bin.
Following the method used in the previously published combination of ZEUS and H1 results [5], the Hvqdis and fragmentation variations described in Section 3 were used to determine the theoretical uncertainty on the extraction of σ cc red .The scales µ R and µ F were varied simultaneously rather than independently as in the theoretical uncertainty for the differential cross sections.An additional uncertainty originates from the subtracted beauty component that was varied by ±50%.The theoretical uncertainties due the extrapolation on σ cc red (x, Q 2 ) are given in Table 9.The experimental part of the uncertainties on σ cc red (x, Q 2 ) is defined as the quadratic sum of the statistical and the experimental systematic uncertainties described in Section 7.
The results are reported in Table 10 and are shown in Fig. 9.The combined result based on previous H1 and ZEUS charm measurements [5] and a recent ZEUS measurement with D + mesons [9], not included in the combined results, are also shown.All three measurements are in good agreement.The D * measurement has a precision close to that of the combined result in some parts of the phase space.The GM-VFNS calculation, based on the HERAPDF1.5parton-density fit to inclusive HERA data, is compared to the present measurement and shown in Fig. 10.The uncertainty on the prediction is dominated by the charm-quark mass.The prediction is in good agreement with the data.

Conclusions
Differential cross sections for the production of D * ± mesons in DIS have been measured with the ZEUS detector in the kinematic range 5 < Q 2 < 1000 GeV 2 ; 0.02 < y < 0.7; 1.5 < p D * T < 20 GeV; |η D * | < 1.5, using data from an integrated luminosity of 363 pb −1 .The new data represents one of the most precise measurements of charm production in DIS obtained to date.The data are reasonably well described by NLO QCD calculations and are in agreement with previously published results.
The measurements have been used to extract the reduced cross sections for charm σ cc red .A GM-VFNS calculation based on a PDF fit to inclusive DIS HERA data agrees well with the results.This demonstrates a consistent description of charm and inclusive data within the NLO QCD framework.

1.08
Table 6: Differential cross section of D * ± production in x.See Table 1 for other details.

Table 8:
Individual systematical uncertainties as defined in Section 7 for the double-differential cross sections in bins of Q 2 and y.The uncertainty δ 8 and δ 10 are not reported as δ 8 is constant (+2 %) and δ 10 was found to be negligible.The overall normalisation uncertanties δ 18 = ±1.9% and δ 19 = ±1.5% are also not listed.Table 9: Breakdown of the theoretical uncertainty on σ cc red (x, Q 2 ), showing the uncertainty from the variation of charm mass (δ mc ), of the renormalisation and factorisation scales (δ µ ), of α S (δ αs ), of the fragmentation function (δ α K ), of the transverse fragmentation (δ k T ), and of the expected beauty component (δ b ).The upper (lower) value gives the effect of a positive (negative) variation of the parameter.

Q
under contract No. 05 H09PDF D supported by the Science and Technology Facilities Council, UK E supported by HIR and UMRG grants from Universiti Malaya, and an ERGS grant from the Malaysian Ministry for Higher Education F supported by the US National Science Foundation.Any opinion, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.G supported by the Polish Ministry of Science and Higher Education as a scientific project No. DPN/N188/DESY/2009 H supported by the Polish Ministry of Science and Higher Education and its grants for Scientific Research I supported by the German Federal Ministry for Education and Research (BMBF), under contract No. 05h09GUF, and the SFB 676 of the Deutsche Forschungsgemeinschaft (DFG) J supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and its grants for Scientific Research K supported by the Korean Ministry of Education and Korea Science and Engineering Foundation L supported by FNRS and its associated funds (IISN and FRIA) and by an Inter-University Attraction Poles Programme subsidised by the Belgian Federal Science Policy Office M supported by the Spanish Ministry of Education and Science through funds provided by CICYT N supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) O partially supported by the German Federal Ministry for Education and Research (BMBF) P supported by RF Presidential grant N 3920.2012.2 for the Leading Scientific Schools and by the Russian Ministry of Education and Science through its grant for Scientific Research on High Energy Physics Q supported by the Netherlands Foundation for Research on Matter (FOM) R supported by the Israel Science Foundation V a now at University of Salerno, Italy b now at Queen Mary University of London, United Kingdom c also funded by Max Planck Institute for Physics, Munich, Germany d also Senior Alexander von Humboldt Research Fellow at Hamburg University, Institute of Experimental Physics, Hamburg, Germany e also at Cracow University of Technology, Faculty of Physics, Mathematics and Applied Computer Science, Poland f supported by the research grant No. 1 P03B 04529 (2005-2008) g partially supported by the Polish National Science Centre projects DEC-2011/01/B/ST2/03643 and DEC-2011/03/B/ST2/00220

δ 2 2 3 + Bζ + Cζ 1 2
electron energy-scale uncertainty of ±1%[63] (±1%, up to ±7% at low y); δ 3 alignment uncertainty on the electron impact point on the RCAL, estimated by varying the cut on the electron position in the MC by ±2 mm separately for the X e and Y e coordinates[63] (±7% at low Q 2 and low y, negligible at large Q 2 ); δ 4 uncertainty on the position of the electron impact point on the RCAL due to imperfections in the simulation of the shower shape and of the detector resolution, estimated by loosening the cut on the electron position by 1 cm (|X e | > 14 cm or |Y e | > 14 cm) both in data and in MC (up to ±10% at low y and low Q 2 , negligible at large Q 2 ); δ 5 uncertainty on the background shape in ∆M, estimated by replacing the function f cs (ζ) by f ′ cs (ζ) = Aζ (+0.3%); δ 6 a further uncertainty on the background shape, evaluated by reducing the fit range from ∆M < 168 MeV to ∆M < 165 MeV (+0.5%); δ 7 uncertainty on the amount of signal outside the ∆M window, evaluated by varying the p π S T -dependent correction by its uncertainty (±1.5%, up to ±3% at low p T ); δ 8 uncertainty on the amount of signal outside the M(Kπ) window, estimated by comparing data and MC in an enlarged mass range (+2%); δ 9 uncertainty on the track-efficiency, evaluated by varying the track efficiency correction applied to MC by the associated uncertainty (±2%); δ 10 uncertainty on the trigger efficiency, evaluated using independent triggers (±0.5%); δ 11 statistical uncertainty on the calculation of the acceptance (±1%); δ 12 uncertainty on the normalisation of the beauty MC of ±50% to cover the range allowed by ZEUS measurements [59, 61] (±0.3%); δ 13 uncertainty on the normalisation of the photoproduction MC of ±100% (up to ±3% at high y, but negligible elsewhere); δ 14 uncertainty on the normalisation of the diffractive charm MC of ±50% to cover the range allowed by data-MC comparison and by previous ZEUS results [64] (up to ±4.5% at low y, but negligible elsewhere); δ 15 uncertainty due to the resolved-photon component, evaluated by adding the resolvedphoton samples to the charm MC normalised according to the generator cross section (+2%); δ 16 uncertainty on the MC reweighting as a function of p D * T and Q 2 , which was varied by ±50% (±2%); δ 17 uncertainty on the MC reweighting as a function of η D * which was replaced by a MC reweighting as a function of y (from −2% to +3%, depending on y); δ 18 uncertainty on the integrated luminosity of ±1.9%; δ 19 uncertainty on the branching ratio BR of ±1.5%.

Figure 5 :
Figure 5: Differential D * ± cross sections as a function of (a) Q 2 , (b) y and (c) x.Other details as in Fig. 4.

Figure 8 : 1 HERAFigure 9 : 1 Figure 10 :
Figure 8:Ratio of e − p to e + p visible D * ± cross sections as a function of Q 2 .Only statistical uncertainties are shown.Bin boundaries are as in Table4.

Table 2 :
Differential cross section of D * ± production in η D *. See Table1for other details.

Table 3 :
Differential cross section of D * ± production in z D * .See Table1for other details.

Table 4 :
Differential cross section of D * ± production in Q 2 .See Table1for other details.

Table 5 :
Differential cross section of D * ± production in y.See Table1for other details.

Table 7 :
Visible cross sections, σ vis , for D * ± production in bins of Q 2 and y.The second but last column reports the estimated contribution from beauty decays, based on the Rapgap beauty MC rescaled to ZEUS data.See Table1for other details.

Table 10 :
The reduced cross-section σ cc red (x, Q 2 ) with statistical, systematic and theoretical uncertainties.The last column shows the kinematical acceptance.