Production crosssections of prompt charm mesons are measured with the first data from $pp$ collisions at the LHC at a centreofmass energy of $13\,\mathrm{TeV}$. The data sample corresponds to an integrated luminosity of $4.98 \pm 0.19\,\mathrm{pb}^{1}$ collected by the LHCb experiment. The production crosssections of $D^{0}$, $D^{+}$, $D_{s}^{+}$, and $D^{*+}$ mesons are measured in bins of charm meson transverse momentum, $p_{\mathrm{T}}$, and rapidity, $y$, and cover the range $0 < p_{\mathrm{T}} < 15\,\mathrm{GeV}/c$ and $2.0 < y < 4.5$. The inclusive crosssections for the four mesons, including charge conjugation, within the range of $1 < p_{\mathrm{T}} < 8\,\mathrm{GeV}/c$ are found to be \begin{equation} \sigma(pp \to D^{0} X) = 2072 \pm 2 \pm 124\,\mu\mathrm{b}\\ \sigma(pp \to D^{+} X) = 834 \pm 2 \pm \phantom{1}78\,\mu\mathrm{b}\\ \sigma(pp \to D_{s}^{+} X) = 353 \pm 9 \pm \phantom{1}76\,\mu\mathrm{b}\\ \sigma(pp \to D^{*+} X) = 784 \pm 4 \pm \phantom{1}87\,\mu\mathrm{b} \end{equation} where the uncertainties are due to statistical and systematic uncertainties, respectively.
Distributions for selected $ D^{0} \to K^{} \pi^{+} $ candidates: (left) $ K^{} \pi^{+} $ invariant mass and (right) $\ln{\chi^2_{\rm IP}}$ for a mass window of $\pm\SI{20}{\mevcc}$ around the nominal $ D^{0}$ mass. The sum of the simultaneous likelihood fits in each $ ( p_{\mathrm{T}} , y )$ bin is shown, with components as indicated in the legends. 
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Distributions for selected $ D^{+} \to K^{} \pi^{+} \pi^{+} $ candidates: (left) $ K^{} \pi^{+} \pi^{+} $ invariant mass and (right) $\ln{\chi^2_{\rm IP}}$ for a mass window of $\pm\SI{20}{\mevcc}$ around the nominal $ D^{+}$ mass. The sum of the simultaneous likelihood fits in each $ ( p_{\mathrm{T}} , y )$ bin is shown, with components as indicated in the legends. 
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Distributions for selected $ D_{ s }^{+} \to ( K^{} K^{+} )_{\phi}\pi^{+} $ candidates: (left) $ K^{+} K^{} \pi^{+} $ invariant mass and (right) $\ln{\chi^2_{\rm IP}}$ for a mass window of $\pm\SI{20}{\mevcc}$ around the nominal $ D_{ s }^{+}$ mass. The sum of the simultaneous likelihood fits in each $ ( p_{\mathrm{T}} , y )$ bin is shown, with components as indicated in the legends. 
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Distributions for selected $ D^{*+} \to D^{0} \pi^{+} $ candidates, with $ D^{0} \to K^{} \pi^{+} $ : (left) $\Delta{m} = m( D^{*+} )  m( D^{0} )$ for a mass window of $\pm\SI{20}{\mevcc}$ around the nominal $ D^{0}$ mass and (right) $\ln{\chi^2_{\rm IP}}$ with an additional mass window of $\pm\SI{3}{\mevcc}$ around the nominal $ D^{*+}$ {} $ D^{0}$ mass difference. The sum of the simultaneous likelihood fits in each $ ( p_{\mathrm{T}} , y )$ bin is shown, with components as indicated in the legends. 
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Measurements and predictions for the absolute prompt (top) $ D^{0}$ , and (bottom) $ D^{+}$ crosssections at $\sqrt{s} = \SI{13}{\TeV}$ . Each set of measurements and predictions in a given rapidity bin is offset by a multiplicative factor $10^{m}$, where the factor $m$ is shown on the plots. The boxes indicate the $\pm1\sigma$ uncertainty band on the theory predictions. In cases where this band spans more than two orders of magnitude only its upper edge is indicated. 
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Measurements and predictions for the absolute prompt (top) $ D_{ s }^{+}$ , and (bottom) $ D^{*+}$ crosssections at $\sqrt{s} = \SI{13}{\TeV}$ . Each set of measurements and predictions in a given rapidity bin is offset by a multiplicative factor $10^{m}$, where the factor $m$ is shown on the plots. The boxes indicate the $\pm1\sigma$ uncertainty band on the theory predictions. In cases where this band spans more than two orders of magnitude only its upper edge is indicated. 
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Measurements and predictions of the prompt $ D^{0}$ , $ D^{+}$ , $ D_{ s }^{+}$ , and $ D^{*+}$ crosssection ratios. The dashdotted lines indicate the unit ratio for each of the rapidity intervals and the dashed lines indicate a ratio of two. Each set of measurements and predictions in a given rapidity bin is offset by an additive constant $m$, which is shown on the plot. No prediction is available for the $ D_{ s }^{+}$ ratio. 
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Ratios of crosssectiontimesbranchingfraction measurements of (top) $ D^{+}$ , (middle) $ D_{ s }^{+}$ , and (bottom) $ D^{*+}$ mesons with respect to the $ D^{0}$ measurements. The bands indicate the corresponding ratios computed using measurements from $ e^{+} e^{} $ collider experiments [40,41,42]. The ratios are given as a function of $ p_{\mathrm{T}}$ and different symbols indicate different ranges in $ y$ . The notation $\sigma( D \to f )$ is shorthand for $\sigma(D)\times\mathcal{B} ( D \to f )$ . 
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Integrated crosssections (black diamonds), their average (black circle and blue band) and theory predictions (red squares) [1,2] are shown (left) based on the $ D^{0}$ and $ D^{+}$ for $0 < p_{\mathrm{T}} < \SI{8}{\gevc}$ and (right) for measurements based on all four mesons for $1 < p_{\mathrm{T}} < \SI{8}{\gevc}$. The "absolute" predictions are based on calculations of the \SI{13}{\TeV} crosssection, while the "scaled" predictions are based on calculations of the $13$ to \SI{7}{\TeV} ratio multiplied with the LHCb measurement at \SI{7}{\TeV} [16]. 
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Ratios of crosssectiontimesbranchingfraction measurements of (top) $ D^{*+}$ , and (middle) $ D_{ s }^{+}$ mesons with respect to $ D^{+}$ crosssections, and (bottom) $ D_{ s }^{+}$ over $ D^{*+}$ mesons. The bands indicate the corresponding ratios computed using measurements from $ e^{+} e^{} $ collider experiments [40,41,42]. The ratios are given as a function of $ p_{\mathrm{T}}$ and different symbols indicate different ranges in $ y$ . The notation $\sigma( D \to f )$ is shorthand for $\sigma(D)\times\mathcal{B} ( D \to f )$ . 
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Animated gif made out of all figures. 
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Prompt signal yields in the fully selected dataset, summed over all ( $ p_{\mathrm{T}}$ , $ y$ ) bins in which a measurement is made. 
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Systematic uncertainties expressed as fractions of the crosssection measurements, in percent. Uncertainties that are computed binbybin are expressed as ranges giving the minimum to maximum values. Ranges for the correlations between $ p_{\mathrm{T}}$  $ y$ bins and between modes are also given, expressed in percent. 
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Prompt charm production crosssections in the kinematic ranges given. The computation of the extrapolation factors is described in the text. The first uncertainty on the crosssection is statistical, and the second is systematic and includes the contribution from the extrapolation factor. No extrapolation factor is given for $ D^{+} _{( s )}$ as a measurement is available in every bin of the integrated phase space. 
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Ratios of integrated crosssectiontimesbranchingfraction measurements in the kinematic range $1 < p_{\mathrm{T}} < \SI{8}{\gevc}$ and $2 < y < 4.5$. The first uncertainty on the ratio is statistical and the second is systematic. The notation $\sigma( D \to f )$ is shorthand for $\sigma(D)\times\mathcal{B} ( D \to f )$ . 
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Supplementary material full pdf 
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This ZIP file contains supplemetary material for the publication LHCbPAPER2014041. The files are: supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.jpg, *.eps : The figures in various formats 
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Created on 11 December 2018.Citation count from INSPIRE on 18 December 2018.