UvA-DARE ( Digital Academic Repository ) Measurement of charm fragmentation fractions in photoproduction at HERA

The production of D0, D∗+, D+, D+ s and Λ + c charm hadrons and their antiparticles in ep scattering at HERA has been studied with the ZEUS detector, using a total integrated luminosity of 372 pb. The fractions of charm quarks hadronising into a particular charm hadron were derived. In addition, the ratio of neutral to charged D-meson production rates, the fraction of charged D mesons produced in a vector state, and the stangenesssuppression factor have been determined. The measurements have been performed in the photoproduction regime. The charm hadrons were reconstructed in the range of transverse momentum pT > 3.8 GeV and pseudorapidity |η| < 1.6. The charm fragmentation fractions are compared to previous results from HERA and from e+e− experiments. The data support the hypothesis that fragmentation is independent of the production process.


Introduction
The fragmentation fractions of charm quarks into specific charm hadrons cannot be predicted by Quantum Chromodynamics (QCD) and have to be measured. It is usually assumed that they are universal, i.e. the same for charm quarks produced in e + e − annihilation, in ep collisions and also in pp or other hadronic collisions, even though the charm production mechanisms are not the same: in e + e − collisions, cc pairs are produced dominantly by QED pair production, whereas in ep collisions, the main production mechanism is the QCD boson-gluon fusion process γg → cc. The fragmentation universality can be tested by measuring the fragmentation fractions at HERA and comparing the results with those obtained with e + e − collisions. Additionally, the values of the fragmentation fractions are crucial parameters used in comparisons of perturbative QCD (pQCD) calculations with measurements of charm production at HERA and elsewhere.

JHEP09(2013)058
The analysis was performed with data taken from 2004 to 2007, when HERA collided electrons or positrons with energy E e = 27.5 GeV and protons with energy E p = 920 GeV. The corresponding total integrated luminosity was 372 ± 7 pb −1 .
A detailed description of the ZEUS detector can be found elsewhere [18]. A brief outline of the components that are most relevant for this analysis is given below.
In the kinematic range of the analysis, charged particles were tracked in the central tracking detector (CTD) [19][20][21] and the microvertex detector (MVD) [22]. 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 2 region 15 • < θ < 164 • . The MVD silicon tracker consisted of a barrel (BMVD) and a forward (FMVD) section. The BMVD contained three layers and provided polar-angle coverage for tracks from 30 • to 150 • . The four-layer FMVD extended the polarangle coverage in the forward region to 7 • . After alignment, the single-hit resolution of the MVD was 24 µm. The transverse distance of closest approach (DCA) of tracks to the nominal vertex in XY was measured to have a resolution, averaged over the azimuthal angle, of (46 ⊕ 122/p T ) µm, with p T in GeV. 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. 1 For all studied charm hadrons, the charge conjugated states are implied throughout the paper. 2 The ZEUS coordinate system is a right-handed Cartesian system, with the Z axis pointing in the nominal proton beam direction, referred to as the "forward direction", and the X axis pointing left towards the centre of HERA. The coordinate origin is at the centre of the CTD. The pseudorapidity is defined as η = − ln tan θ 2 , where the polar angle, θ, is measured with respect to the Z axis.

JHEP09(2013)058
The high-resolution uranium-scintillator calorimeter (CAL) [23][24][25][26] consisted of three parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters. Each part was subdivided transversely into towers and longitudinally into one electromagnetic section (EMC) and either one (in RCAL) or two (in BCAL and FCAL) hadronic sections (HAC). The smallest subdivision of the calorimeter was called a cell. The CAL energy resolutions, as measured under test-beam conditions, were σ(E)/E = 0.18/ √ E for electrons and σ(E)/E = 0.35/ √ E for hadrons, with E in GeV. The luminosity was measured using the Bethe-Heitler reaction ep → eγp by a luminosity detector which consisted of independent lead-scintillator calorimeter [27][28][29] and magnetic-spectrometer [30] systems. The fractional systematic uncertainty on the measured luminosity was 1.9 %.

Monte Carlo simulation
Monte Carlo (MC) simulations were used in the analysis for modelling signal and background processes and to correct the data for acceptance effects. MC samples of charm and beauty photoproduction events were produced with the Pythia 6.416 event generator [31]. The generation of events, based on leading-order matrix elements, includes direct photon processes, in which the photon couples as a point-like object in the hard scatter, and resolved photon processes, where the photon acts as a source of partons, one of which participates in the hard scattering process. Initial-and final-state parton showering is added to simulate higher-order processes. The CTEQ5L [32] and GRV LO [33] parametrisations were used for the parton distribution functions of the proton and photon, respectively. The charm (beauty) quark masses were set to 1.5 (4.75) GeV. Events for all processes were generated in proportion to the predicted MC cross sections. The Lund string model [34] as implemented in Jetset [31] was used for hadronisation in Pythia. The Bowler modification [35] of the Lund symmetric fragmentation function [36] was used for the longitudinal component of the charm-and beauty-quark fragmentation. The generated events were passed through a full simulation of the detector using Geant 3.21 [37] and processed with the same reconstruction program as used for the data.
To ensure a good description of the data, a reweighting was applied to the transverse momentum, p T (D, D * , Λ c ), and pseudorapidity, η(D, D * , Λ c ), distributions of the Pythia MC samples. The reweighting factors were tuned using a large D * + sample. The factors deviate by no more than ±15% from unity. The effect of the reweighting on the measured fragmentation fractions was small; the reweighting uncertainty was included in the systematic uncertainty.

Event selection
A three-level trigger system [38] was used to select events online. The first-and second-level trigger used CAL and CTD data to select ep collisions and to reject beam-gas events. At the third level, the full event information was available. The sample used in this analysis JHEP09(2013)058 was mainly selected by third-level triggers where at least one reconstructed charm-hadron candidate was required. A dijet trigger was used in addition to increase the efficiency.
Photoproduction events were selected by requiring that no scattered electron with energy of greater than 5 GeV be identified in the CAL [39]. The photon-proton centreof-mass energy, W , was reconstructed using the Jacquet-Blondel [40] estimator of W , Here E i and θ i denote the energy and polar angle of the i th energy-flow object (EFO) [41], respectively, and the sum i runs over all final-state energyflow objects built from CTD-MVD tracks and energy clusters measured in the CAL. After correcting for detector effects, the most important of which were energy losses in inactive material in front of the CAL and particle interactions in the beam pipe [39,42], events were selected in the interval 130 < W JB < 300 GeV. The lower limit was set by the trigger requirements, while the upper limit was imposed to suppress remaining DIS events with an unidentified low-energy scattered electron in the CAL [39].

Reconstruction of charm hadrons
The production yields of D 0 , D * + , D + , D + s and Λ + c charm hadrons were measured in the range of transverse momentum p T (D, D * , Λ c ) > 3.8 GeV and the range of pseudorapidity |η(D, D * , Λ c )| < 1.6. The p T cut was imposed by trigger requirements and the η cut ensured a good acceptance in the CTD-MVD detector system. Charm hadrons were reconstructed using CTD-MVD tracks. Combinations of good tracks were used to form charm-hadron candidates, as detailed in the following sections. To ensure good momentum resolution, each track was required to reach at least the third superlayer of the CTD. The combinatorial background was significantly reduced by requiring p T (D, D * )/E θ>10 • T > 0.2 and p T (Λ c )/E θ>10 • T > 0.25 for charm mesons and baryons, respectively. The transverse energy was calculated as E θ>10 • T = Σ i,θ i >10 • (E i sin θ i ), where the sum runs over all energy deposits in the CAL with polar angles θ i above 10 • . A further background reduction was achieved by applying cuts on the minimal transverse momenta of the charm-hadron decay products. The large combinatorial background for the D 0 , D + and D + s mesons was additionally suppressed by secondary-decay vertex cuts (see section 5.1).

Reconstruction of
The D 0 mesons were reconstructed using the decay mode D 0 → K − π + . In each event, tracks with opposite charges and p T > 0.8 GeV were combined in pairs to form D 0 candidates. The nominal kaon and pion masses were assumed in turn for each track and the invariant mass of the pair, M (Kπ), was calculated. The kaon and pion tracks, measured precisely in the CTD-MVD detector system, were used to reconstruct the decay point of the D 0 meson. The relatively long lifetime of the D 0 meson resulted in a secondary vertex that is often well separated from the primary interaction point. This property was exploited to improve the signal-to-background ratio. The decay-length significance, S l , was used as a discriminating variable. It is defined as S l = l/σ l , where l is the decay length in the transverse plane and σ l is the uncertainty JHEP09(2013)058 associated with this distance. The decay length is the distance in the transverse plane between the point of creation and decay vertex of the meson and is given by where p D T is the transverse momentum vector and S XY is the two-dimensional position vector of the reconstructed decay vertex projected onto the XY plane. The vector B XY points to the fitted geometrical centre of the beam-spot which is taken as the origin of the D meson. The centre of the elliptical beam-spot was determined using the average primary-vertex position for groups of a few thousand events. The vector B XY was corrected for each event for the small difference in angle between the beam direction and the Z direction, using the Z position of the primary vertex of the event. The widths of the beam spot were 88 µm (80 µm) and 24 µm (22 µm) in the X and Y directions, respectively, for the e + p (e − p) data. The decay-length error, σ l , was determined by folding the width of the beam-spot with the covariance matrix of the decay vertex after both were projected onto the D-meson momentum vector.
A cut S l > 1 was applied. In addition, the χ 2 of the vertex fit was required to be less than 15; this quality cut was applied for all secondary D-meson decay-vertex fits in this paper.
For the selected D 0 candidates, a search was performed for a track that could be a "soft" pion, π s , from a D * + → D 0 π + s decay. The soft pion was required to have p T > 0.2 GeV and a charge opposite to that of the particle taken as a kaon. The corresponding D 0 candidate was assigned to the class of candidates "with ∆M tag" if the mass difference, ∆M = M (Kππ s ) − M (Kπ), was in the range 0.143 < ∆M < 0.148 GeV. All remaining D 0 candidates were assigned to the class of candidates "without ∆M tag".
For D 0 candidates with ∆M tag, the kaon and pion mass assignment was fixed according to the charge of the tracks. For D 0 candidates without ∆M tag, two mass assignments were assumed for each Kπ pair, yielding two entries into the mass distribution: the true value, corresponding to the signal, and a wrong value, distributed over a broad range. To remove this background, the mass distribution, obtained for D 0 candidates with ∆M tag and assigning the wrong masses to the kaon and pion tracks, was subtracted from the M (Kπ) distribution for all D 0 candidates without ∆M tag. The subtracted mass distribution was normalised to the ratio of numbers of D 0 mesons without and with ∆M tag obtained from the fit described below. Reflections from D 0 → K − K + and D 0 → π − π + decays were seen as two small bumps below and above the signal peak, respectively, of the D 0 → K − π + decay. They were subtracted using the simulated reflection shapes and normalised to the D 0 → K − π + signal according to the normalisation ratios observed in the simulation and using the PDG values of the respective branching ratios [43]. Figure 1 shows the M (Kπ) distribution for D 0 candidates with and without ∆M tag obtained after the subtractions described above. Clear signals are seen at the nominal value of the D 0 mass in both distributions. The distributions were fitted simultaneously, assuming the same shape for the signals in both distributions. To describe the shape, a modified Gaussian function was used:

JHEP09(2013)058
The free parameters A, B and D were assumed to be independent for the two M (Kπ) distributions. The numbers of D 0 mesons yielded by the fit were N tag (D 0 ) = 7281±104 and N untag (D 0 ) = 27787 ± 680 for selections with and without ∆M tag, respectively. The mass value obtained from the fit 3 was 1865.4 ± 0.3 MeV for the D 0 tagged and 1865.1 ± 0.4 MeV for the D 0 untagged samples, compared to the PDG value of 1864.83 ± 0.14 MeV [43].

Reconstruction of additional
The D * + → D 0 π + s decays with p T (D * + ) > 3.8 GeV and |η(D * + )| < 1.6 can be considered as a sum of two subsamples: decays with the D 0 having p T (D 0 ) > 3.8 GeV and |η(D 0 )| < 1.6, and decays with the D 0 outside that kinematic range. The former sample is represented by D 0 mesons reconstructed with ∆M tag, as discussed in the previous section. The latter sample of additional D * + mesons was obtained using the same D 0 → K − π + decay channel and the selection described below.
In each event, tracks with opposite charges and p T > 0.4 GeV were combined in pairs to form D 0 candidates. To calculate the invariant mass, M (Kπ), kaon and pion masses were assumed in turn for each track. Only D 0 candidates which satisfy 1.81 < M (Kπ) < 1.92 GeV were kept. Moreover, the D 0 candidates were required to have p T (D 0 ) < 3.8 GeV or |η(D 0 )| > 1.6. Any additional track with p T > 0.2 GeV and a charge opposite to that of the kaon track was assigned the pion mass and combined with the D 0 candidate to form a D * + candidate with invariant mass M (Kππ s ). The D * + candidate was required to satisfy the cuts p T (D * + ) > 3.8 GeV and |η(D * + )| < 1.6. 2)) describing the signal and a function of the form A · (∆M − m π ) B · e −C·∆M , describing the non-resonant background, was used to fit the data. Here m π is the pion mass and A, B and C are free parameters of the fit. The fitted mass value 3 for the ∆M signal is 145.51 ± 0.01 MeV, compared to the PDG value of 145.42 ± 0.01 MeV [43]. The number of reconstructed additional D * + mesons determined from the fit was N add (D * + ) = 2139 ± 59.
The combinatorial background was estimated also from the mass-difference distribution for wrong-charge combinations, in which both tracks forming the D 0 candidate had the same charge and the third track had the opposite charge. The number of reconstructed additional D * + mesons was determined by subtracting the wrong-charge ∆M distribution after normalising it to the distribution of D * + candidates with the appropriate charges in the range 0.151 < ∆M < 0.167 GeV. The subtraction was performed in the signal range 0.143 < ∆M < 0.148 GeV. The results obtained using the subtraction procedure instead of the fit were used to estimate the systematic uncertainty of the signal extraction.

Reconstruction of D
The D + mesons were reconstructed using the decay mode D + → K − π + π + . In each event, two tracks with the same charge and p T > 0.5 GeV and a third track with the opposite JHEP09(2013)058 charge and p T > 0.7 GeV were combined to form D + candidates. The pion mass was assigned to the two tracks with the same charge, the kaon mass was assigned to the third track, and the candidate invariant mass, M (Kππ), was calculated. To suppress background from D * + decays, combinations with M (Kππ) − M (Kπ) < 0.15 GeV were removed. The background from D + s → φπ + with φ → K + K − was suppressed by requiring that the invariant mass of any two tracks with opposite charges from D + candidates was not within ±8 MeV of the φ mass [43] when the kaon mass was assigned to both tracks. To suppress combinatorial background, a cut on the decay-length significance for D + candidates was applied of S l > 3. Figure 3 shows the M (Kππ) distribution for the D + candidates after all cuts. A clear signal is seen at the nominal value of the D + mass. The sum of two Gaussian functions with the same peak position was used to describe the signal:  An exponential function describing the non-resonant background was used. Reflections caused by wrong mass assignments for the decay products of D + s and Λ + c decaying to three charged particles were added to the fit function using the simulated reflection shapes normalised to the measured D + s and Λ + c production rates. They give rise to a small increase of the background in the signal region. The number of reconstructed D + mesons yielded by the fit was N (D + ) = 18917 ± 324. The fitted mass 3 of the D + was 1869.0 ± 0.2 MeV, compared to the PDG value of 1869.62 ± 0.15 MeV [43].  and combined in pairs to form φ candidates. The φ candidate was kept if its invariant mass, M (KK), was within ±8 MeV of the φ mass [43]. Any additional track with p T > 0.5 GeV was assigned the pion mass and combined with the φ candidate to form a D + s candidate with invariant mass M (KKπ). The cut on the decay-length significance for D + s candidates was S l > 0. Figure 4 shows the M (KKπ) distribution for the D + s candidates after all cuts. A clear signal is seen at the nominal D + s mass. There is also a smaller signal around the nominal D + mass as expected from the decay D + → φπ + with φ → K + K − . The mass distribution was fitted by the sum of two modified Gaussian functions (eq. (5.2)) describing the signals and an exponential function describing the non-resonant background. To reduce the number of free fit parameters in the fit, the ratio of the widths of the D + and D + s signals

JHEP09(2013)058
was fixed to the value observed in the MC simulation. Reflections arising from wrong mass assignments for the decay products of D + and Λ + c decays to three charged particles were added to the fit function using the simulated reflection shapes normalised to the measured D + and Λ + c production rates. The number of reconstructed D + s mesons yielded by the fit was N (D + s ) = 2802 ± 141. The fitted mass 3 of the D + s was 1968.0 ± 0.5 MeV, compared to the PDG value of 1968.49 ± 0.32 MeV [43].

Reconstruction of Λ
c baryons were reconstructed using the decay mode Λ + c → K − pπ + . In each event, two same-charge tracks and a third track with opposite charge were combined to form Λ + c candidates. Due to the large difference between the proton and pion masses and the high Λ + c momentum, the proton momentum is typically larger than that of the pion. Therefore, the proton (pion) mass was assigned to the track of the same-charge pair with the larger (smaller) momentum. The kaon mass was assigned to the third track and the invariant mass, M (Kpπ), was calculated. Only candidates with p T (K) > 0.5 GeV, p T (p) > 1.3 GeV and p T (π) > 0.5 GeV were kept. Reflections from D + and D + s decays to three charged particles were subtracted from the M (Kpπ) spectrum using the simulated reflection shapes normalised to the measured D + and D + s production rates. Figure 5 shows the M (Kpπ) distribution for the Λ + c candidates after all cuts, obtained after the reflection subtraction. A clear signal is seen at the nominal Λ + c mass. The sum of a modified Gaussian function (eq. (5.2)) describing the signal and a background function parametrised as where A, B and C are free parameters, was fitted to the mass distribution. The width parameter of the modified Gaussian was fixed to σ = 10 MeV. This value corresponds to the width determined in the MC, multiplied by a factor 1.11. The uncertainty of this number is taken into account in the systematics variations. The factor 1.11 corrects for the difference of the observed width of the D + → K − π + π + signal between data and simulation. The number of reconstructed Λ + c baryons yielded by the fit was N (Λ + c ) = 7682±964. The fitted mass 3 of the Λ + c was 2290±1.8 MeV, compared to the PDG value of 2286.46±0.14 MeV [43].

Charm-hadron production cross sections
The cross sections for the production of the various charm hadrons were determined, but the fragmentation fractions involve only ratios, in which common normalisation uncertainties cancel. The fraction of charm quarks hadronising as a particular charm hadron, f (c → D, D * , Λ c ), is given by the ratio of the production cross section for the hadron to the sum of the production cross sections for all charm ground states. The charm-hadron cross sections were determined for the process ep → e(D, D * , Λ c )X in the kinematic region Q 2 < 1 GeV 2 , 130 < W < 300 GeV, p T (D, D * , Λ c ) > 3. The cross section for a given charm hadron was calculated from where N data (D,D * ,Λc) denotes the number of reconstructed charm hadrons in the data, A the acceptance for this charm hadron, L the integrated luminosity and B the branching ratio or the product of the branching ratios [43] for the decay channels used in the reconstruction. The Pythia MC sample of charm photoproduction (see section 3) was used to evaluate the acceptance. The contributions from beauty-hadron decays were subtracted using the prediction from Pythia. For this purpose, the branching ratios of beauty-quark decays to the charmed hadrons were corrected in the MC, using the correction factors [1] based on the values measured at LEP [44,45]. Finally, the number of reconstructed charm hadrons JHEP09(2013)058 from beauty, N b,MC D,D * ,Λc , in the MC, normalised to the data luminosity and multiplied by a scale factor, s b , was subtracted from the data (eq. (6.1)). The scale factor was chosen as s b = 1.5 ± 0.5, an average value which was estimated from ZEUS measurements [46][47][48] of beauty photoproduction.

Systematic uncertainties
The systematic uncertainties were determined by changing the analysis procedure or by varying parameter values within their estimated uncertainties. The following systematic uncertainty sources were considered: • {δ 1 } the uncertainty of the beauty subtraction (see section 6) was determined by varying the scale factor s b for the Pythia MC prediction by ±0.5 from the nominal value s b = 1.5. This was done to account for the range of the Pythia beauty-prediction scale factors extracted in various analyses [46][47][48]. In addition the branching ratios of b quarks to charm hadrons were varied by their uncertainties [44,45]; • {δ 2 } the uncertainty in the rate of the charm-strange baryons (see section 8.2) was determined by varying the normalisation factor for the Λ + c production cross section by its estimated uncertainty [1] of ±0.05 from the nominal value 1.14; • {δ 3 } the uncertainties related to the signal extraction procedures (see sections 5.1-5.5) were obtained by the following (independent) variations: for the D 0 signals with and without ∆M tag: the background parametrisation was changed: for the region M (Kπ) < 1.92 GeV a linear term C ·[M (Kπ)−1.92] was added to the argument of the exponential function; the transition point for the parametrisation was moved from 1.92 GeV to 1.84 GeV. The fit range was narrowed by 50 MeV on both sides;

JHEP09(2013)058
for the additional D * + signal: the M (Kπ) mass window for the selected D 0 candidates was narrowed by 5.5 MeV on both sides. The range used for the fit of the ∆M distribution was narrowed by 1 MeV (left) and 5 MeV (right); The wrong-charge subtraction procedure was used instead of the fit; the range used for the normalisation of the wrong-charge background was narrowed by 1 MeV (left) and 5 MeV (right); the signal range used for the wrong-charge subtraction was narrowed or broadened by 1 MeV on both sides; for the D + signal: a modified Gaussian was used as an alternative parametrisation for the signal; the background parametrisation was changed to a parabola. The fit range was narrowed by 50 MeV on both sides; for the D + s signal: the background parametrisation was changed to a parabola. The fit range was narrowed by 50 MeV (left) and 30 MeV (right); for the Λ + c signal: the background parametrisation was changed to a cubic polynomial. The fit range was narrowed by 30 MeV on both sides. The width parameter σ of the modified Gaussian (eq. (5.2)) was varied by ±10% from its nominal value, a conservative estimate of its uncertainty. Further cross checks were performed: the width of the modified Gaussian was used as a free fit parameter; the mass of the Λ + c was fixed to the PDG value [43]. The resulting signal-yield changes from these two variations were negligible.
The uncertainties arising from the various reflections in the mass spectra (see section 5) were evaluated by varying the size of each reflection conservatively by ±20%.
The largest contribution to the signal extraction procedures was the change of the background parametrisation; • {δ 4 } the model dependence of the acceptance corrections was estimated by varying the reweighting of the MC kinematic distributions (see section 3) until clear discrepancies became visible between the shapes observed in the data and in the MC; • {δ 5 } the uncertainty of the trigger efficiency was evaluated by comparing the fitted signal yields taken with independent triggers. This uncertainty largely cancels in the fragmentation fractions; • {δ 6 } the overestimate of the track-finding efficiency in the MC relative to that in the data was estimated to be at most 2%. This leads to a possible underestimation of the production cross sections for the charm hadrons with two (three) decay tracks by a factor 1.02 2 (1.02 3 ) which was taken into account for the systematics of the fragmentation fractions; • {δ 7 } the uncertainty of the CAL simulation was determined by varying the simulation: the CAL energy scale was changed by ±2% and the CAL energy resolution by ±20% of its value; • {δ 8 } the uncertainty related to the S l cut was determined by changing the value of the cut to S l > 4 for D + and by omitting the S l cut for D 0 and D + s . Contributions from the different systematic uncertainties were calculated and added in quadrature separately for positive and negative variations. The total and individual systematic uncertainties δ 1 to δ 8 for the charm fragmentation fractions are summarised in table 1.

JHEP09(2013)058
The largest systematic uncertainties are related to the signal-extraction procedures.

Equivalent phase-space treatment
To compare the inclusive D + and D 0 cross sections with each other and with the inclusive D * + cross section, it is necessary to take into account that in the D * decay only a fraction of the parent D * momentum is transferred to the daughter D meson. For such a comparison, the "equivalent" D + and D 0 cross sections, σ eq (D + ) and σ eq (D 0 ), were defined [1] as the cross section for D + and D 0 production including the contributions from D * decay, plus the contribution from additional D * mesons (see section 5.2). The cross section for D + and D 0 production is σ(D + ) and σ tag (D 0 ) + σ untag (D 0 ), respectively. The contributions from additional D * mesons are, for the D + meson, and for the D 0 meson σ add (D 0 ) = σ add (D * + )B D * + →D 0 π + + σ add (D * 0 ), noting that D * 0 decays always to D 0 [43]. The cross-section σ add (D * 0 ) is not measured and is determined as where R u/d is the ratio of neutral to charged D-meson production rates. It is given by the ratio of the sum of D * 0 and direct D 0 production to the sum of D * + and direct D + production cross sections. It can be written as [1] .

JHEP09(2013)058
Combining everything produces the following expressions for σ eq (D + ) and σ eq (D 0 ): which together with eq. (8.1) gives The observable R u/d was measured in the kinematic region Q 2 < 1 GeV 2 , 130 < W < 300 GeV, p T (D) > 3.8 GeV and |η(D)| < 1.6. The value obtained from eq. (8.2) is where the last uncertainty arises from the uncertainties of the branching ratios used. The result is in agreement with the previous measurement [1] and slightly above but still compatible with R u/d = 1, expected from isospin invariance in the kinematic range of this measurement.
Monte Carlo studies performed for the previous ZEUS measurement [1] showed that this equivalent phase-space treatment for the non-strange D and D * mesons minimises differences between the fragmentation fractions measured in the accepted p T (D, D * , Λ c ) and η(D, D * , Λ c ) kinematic region and those in the full phase space. The extrapolation factors using the Pythia MC with either the Peterson or Bowler fragmentation function were generally close to unity to within a few percent [1].

Charm fragmentation fractions
For the determination of the fragmentation fractions of the D 0 , D + , D + s and Λ + c charm ground states, the total cross section for charmed hadron production is needed. In this cross section, the production cross sections of the charm-strange baryons Ξ + c , Ξ 0 c and Ω 0 c must also be included. Since these charm-strange baryons do not decay into Λ + c , a correction is needed. The production rates for these baryons are expected to be much lower than that of the Λ + c due to strangeness suppression. The relative rates for the ground states of the charm-strange baryons were estimated from the non-charm sector following the LEP procedure [49]. The total rate for the three charm-strange baryons relative to the Λ + c state is expected to be about 14% [1]. Therefore the Λ + c production cross section was scaled by the factor 1.14.
The fragmentation fractions for the measured charm ground states and for D * + are given by The charm fragmentation fractions, measured in the kinematic region Q 2 < 1 GeV 2 , 130 < W < 300 GeV, p T (D, D * , Λ c ) > 3. c Λ → f (c Figure 6. Fractions of charm quarks hadronising as a particular charm hadron. The photoproduction measurements presented in this paper are shown (first column) and compared to previous HERA results in photoproduction (second column), DIS (third and fourth column) and to e + e − data (last column), with statistical, systematic and branching-ratio uncertainties added in quadrature.
values [43]. The measurements are compared to previous HERA results [1][2][3][4] and to the combined fragmentation fractions for charm production in e + e − annihilations compiled previously [16] and updated [17,50] with the 2010 branching-ratio values [51]. This comparison is also shown in figure 6. The obtained precision of the fragmentation fractions is competitive with measurements in e + e − collisions. All data from ep and e + e − collisions are in agreement with each other. This demonstrates that the fragmentation fractions of charm quarks are independent of the production process and supports the hypothesis of universality of heavy-quark fragmentation.
Using a data set with an integrated luminosity of 372 pb −1 , the fractions of charm quarks hadronising as D 0 , D * + , D + , D + s and Λ + c hadrons have been determined. In addition, the ratio of neutral to charged D-meson production rates, the fraction of charged D mesons produced in a vector state, and the strangeness-suppression factor have been determined.
The precision of the fragmentation fractions obtained is competitive with measurements in e + e − collisions. All data from ep and e + e − collisions are in agreement with each other. This demonstrates that the fragmentation fractions of charm quarks are independent of the production process and supports the hypothesis of the universality of heavy-quark fragmentation.