# Measurements of prompt charm production cross-sections in $pp$ collisions at $\sqrt{s}$ = 13 TeV

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## Abstract

Production cross-sections of prompt charm mesons are measured with the first data from $pp$ collisions at the LHC at a centre-of-mass 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 cross-sections 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 cross-sections for the four mesons, including charge conjugation, within the range of $1 < p_{\mathrm{T}} < 8 \mathrm{GeV}/c$ are found to be $$\sigma(pp \to D^{0} X) = 2072 \pm 2 \pm 124 \mu\mathrm{b}\\ \sigma(pp \to D^{+} X) = 834 \pm 2 \pm \phantom{1}78 \mu\mathrm{b}\\ \sigma(pp \to D_{s}^{+} X) = 353 \pm 9 \pm \phantom{1}76 \mu\mathrm{b}\\ \sigma(pp \to D^{*+} X) = 784 \pm 4 \pm \phantom{1}87 \mu\mathrm{b}$$ where the uncertainties are due to statistical and systematic uncertainties, respectively.

## Figures and captions

 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. Fig1a.pdf [60 KiB] HiDef png [361 KiB] Thumbnail [191 KiB] *.C file Fig1b.pdf [65 KiB] HiDef png [345 KiB] Thumbnail [187 KiB] *.C file 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. Fig2a.pdf [60 KiB] HiDef png [355 KiB] Thumbnail [189 KiB] *.C file Fig2b.pdf [65 KiB] HiDef png [344 KiB] Thumbnail [185 KiB] *.C file 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. Fig3a.pdf [61 KiB] HiDef png [332 KiB] Thumbnail [181 KiB] *.C file Fig3b.pdf [65 KiB] HiDef png [329 KiB] Thumbnail [181 KiB] *.C file 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. Fig4a.pdf [80 KiB] HiDef png [372 KiB] Thumbnail [198 KiB] *.C file Fig4b.pdf [65 KiB] HiDef png [363 KiB] Thumbnail [193 KiB] *.C file Measurements and predictions for the absolute prompt (top) $D^{0}$ , and (bottom) $D^{+}$ cross-sections 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. Fig5a.pdf [242 KiB] HiDef png [264 KiB] Thumbnail [178 KiB] *.C file Fig5b.pdf [243 KiB] HiDef png [269 KiB] Thumbnail [181 KiB] *.C file Measurements and predictions for the absolute prompt (top) $D_{ s }^{+}$ , and (bottom) $D^{*+}$ cross-sections 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. Fig6a.pdf [234 KiB] HiDef png [164 KiB] Thumbnail [126 KiB] *.C file Fig6b.pdf [239 KiB] HiDef png [219 KiB] Thumbnail [151 KiB] *.C file Measurements and predictions of the prompt $D^{0}$ , $D^{+}$ , $D_{ s }^{+}$ , and $D^{*+}$ cross-section ratios. The dash-dotted 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. Fig7a.pdf [172 KiB] HiDef png [374 KiB] Thumbnail [330 KiB] *.C file Fig7b.pdf [171 KiB] HiDef png [323 KiB] Thumbnail [298 KiB] *.C file Fig7c.pdf [167 KiB] HiDef png [180 KiB] Thumbnail [111 KiB] *.C file Fig7d.pdf [200 KiB] HiDef png [314 KiB] Thumbnail [279 KiB] *.C file Ratios of cross-section-times-branching-fraction 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 $\sigma(D)\times\mathcal{B} ( D \to f )$ . Fig8a.pdf [236 KiB] HiDef png [257 KiB] Thumbnail [182 KiB] *.C file Fig8b.pdf [236 KiB] HiDef png [273 KiB] Thumbnail [205 KiB] *.C file Fig8c.pdf [236 KiB] HiDef png [278 KiB] Thumbnail [198 KiB] *.C file Integrated cross-sections (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} cross-section, 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]. Fig9a.pdf [225 KiB] HiDef png [240 KiB] Thumbnail [223 KiB] *.C file Fig9b.pdf [225 KiB] HiDef png [165 KiB] Thumbnail [154 KiB] *.C file Ratios of cross-section-times-branching-fraction measurements of (top) $D^{*+}$ , and (middle) $D_{ s }^{+}$ mesons with respect to $D^{+}$ cross-sections, 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 $\sigma(D)\times\mathcal{B} ( D \to f )$ . Fig10a.pdf [236 KiB] HiDef png [280 KiB] Thumbnail [202 KiB] *.C file Fig10b.pdf [236 KiB] HiDef png [274 KiB] Thumbnail [204 KiB] *.C file Fig10c.pdf [236 KiB] HiDef png [281 KiB] Thumbnail [199 KiB] *.C file Animated gif made out of all figures. PAPER-2015-041.gif Thumbnail

## Tables and captions

 Prompt signal yields in the fully selected dataset, summed over all ( $p_{\mathrm{T}}$ , $y$ ) bins in which a measurement is made. Table_1.pdf [51 KiB] HiDef png [95 KiB] Thumbnail [40 KiB] tex code Systematic uncertainties expressed as fractions of the cross-section measurements, in percent. Uncertainties that are computed bin-by-bin 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. Table_2.pdf [47 KiB] HiDef png [79 KiB] Thumbnail [35 KiB] tex code Prompt charm production cross-sections in the kinematic ranges given. The computation of the extrapolation factors is described in the text. The first uncertainty on the cross-section 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. Table_3.pdf [60 KiB] HiDef png [101 KiB] Thumbnail [51 KiB] tex code Ratios of integrated cross-section-times-branching-fraction 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 $\sigma(D)\times\mathcal{B} ( D \to f )$ . [Error creating the table]

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [564 KiB] This ZIP file contains supplemetary material for the publication LHCb-PAPER-2014-041. The files are: supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.jpg, *.eps : The figures in various formats Fig1a-S.pdf [270 KiB] HiDef png [131 KiB] Thumbnail [92 KiB] *C file Fig1b-S.pdf [273 KiB] HiDef png [144 KiB] Thumbnail [98 KiB] *C file Fig2a-S.pdf [269 KiB] HiDef png [137 KiB] Thumbnail [96 KiB] *C file Fig2b-S.pdf [268 KiB] HiDef png [138 KiB] Thumbnail [95 KiB] *C file Fig3a-S.pdf [167 KiB] HiDef png [66 KiB] Thumbnail [38 KiB] *C file Fig3b-S.pdf [167 KiB] HiDef png [65 KiB] Thumbnail [37 KiB] *C file Fig4a-S.pdf [166 KiB] HiDef png [65 KiB] Thumbnail [34 KiB] *C file Fig4b-S.pdf [165 KiB] HiDef png [64 KiB] Thumbnail [33 KiB] *C file

Created on 11 July 2020.