# Measurements of prompt charm production cross-sections in $pp$ collisions at $\sqrt{s} = 5$ TeV

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## Abstract

Production cross-sections of prompt charm mesons are measured using data from $pp$ collisions at the LHC at a centre-of-mass energy of $5$TeV. The data sample corresponds to an integrated luminosity of $8.60\pm0.33$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, $p_{\text{T}}$, and rapidity, $y$. They cover the rapidity range $2.0<y<4.5$ and transverse momentum ranges $0 < p_{\text{T}} < 10 \text{GeV}/c$ for $D^0$ and $D^+$ and $1 < p_{\text{T}} < 10 \text{GeV}/c$ for $D_s^+$ and $D^{*+}$ mesons. The inclusive cross-sections for the four mesons, including charge-conjugate states, within the range of $1 < p_{\text{T}} < 8 \text{GeV}/c$ are determined to be \sigma(pp\rightarrow D^0 X) = 1004 \pm 3 \pm 54 \mu\text{b} \sigma(pp\rightarrow D^+ X) = 402 \pm 2 \pm 30 \mu\text{b} \sigma(pp\rightarrow D_s^+ X) = 170 \pm 4 \pm 16 \mu\text{b} \sigma(pp\rightarrow D^{*+} X)= 421 \pm 5 \pm 36 \mu\text{b} where the uncertainties are statistical and systematic, respectively.

## Figures and captions

 Distributions for selected $D ^0 \to K^{-} \pi^{+}$ candidates: (left) $K^{-} \pi^{+}$ invariant mass and (right) $\ln{\left(\chi^2_{\rm IP}\right)}$ 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 [246 KiB] HiDef png [323 KiB] Thumbnail [214 KiB] *.C file Fig1b.pdf [257 KiB] HiDef png [276 KiB] Thumbnail [169 KiB] *.C file Distributions for selected $D ^+ \to K^{-} \pi^{+} \pi^{+}$ candidates: (left) $K^{-} \pi^{+} \pi^{+}$ invariant mass and (right) $\ln{\left(\chi^2_{\rm IP}\right)}$ 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 [246 KiB] HiDef png [296 KiB] Thumbnail [196 KiB] *.C file Fig2b.pdf [256 KiB] HiDef png [261 KiB] Thumbnail [159 KiB] *.C file Distributions for selected $D ^+_ s \to ( K^{-} K^{+} )_{\phi}\pi^{+}$ candidates: (left) $K^{+} K^{-} \pi^{+}$ invariant mass and (right) $\ln{\left(\chi^2_{\rm IP}\right)}$ 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 [244 KiB] HiDef png [308 KiB] Thumbnail [202 KiB] *.C file Fig3b.pdf [255 KiB] HiDef png [271 KiB] Thumbnail [163 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) $\ln{\left(\chi^2_{\rm IP}\right)}$ of the $D ^0$ 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 [243 KiB] HiDef png [327 KiB] Thumbnail [220 KiB] *.C file Fig4b.pdf [256 KiB] HiDef png [286 KiB] Thumbnail [176 KiB] *.C file Measurements and predictions for the absolute prompt (top) $D ^0$ , and (bottom) $D ^+$ cross-sections at $\sqrt{s} = \SI{5}{\TeV}$ . 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, where only the upper edge is shown if the uncertainty exceeds two orders of magnitude. Fig5a.pdf [236 KiB] HiDef png [201 KiB] Thumbnail [141 KiB] *.C file Fig5b.pdf [237 KiB] HiDef png [202 KiB] Thumbnail [140 KiB] *.C file Measurements and predictions for the absolute prompt (top) $D ^+_ s$ , and (bottom) $D ^{*+}$ cross-sections at $\sqrt{s} = \SI{5}{\TeV}$ . 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, where only the upper edge is shown if the uncertainty exceeds two orders of magnitude. Fig6a.pdf [235 KiB] HiDef png [160 KiB] Thumbnail [123 KiB] *.C file Fig6b.pdf [236 KiB] HiDef png [195 KiB] Thumbnail [137 KiB] *.C file Measurements and predictions of the prompt $D ^0$ , $D ^+$ , $D ^+_ s$ , and $D ^{*+}$ cross-section ratios between $\sqrt{s} = 13$ and \SI{5}{\TeV}. Each set of measurements and predictions in a given rapidity bin is offset by an additive constant $m$, which is shown on the plot. Only central values are provided for the GMVFNS predictions. Fig7a.pdf [175 KiB] HiDef png [296 KiB] Thumbnail [230 KiB] *.C file Fig7b.pdf [175 KiB] HiDef png [298 KiB] Thumbnail [231 KiB] *.C file Fig7c.pdf [174 KiB] HiDef png [237 KiB] Thumbnail [203 KiB] *.C file Fig7d.pdf [204 KiB] HiDef png [252 KiB] Thumbnail [205 KiB] *.C file Ratios of the measurements of cross-section times branching fraction 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 [42,43,44]. The ratios are given as a function of $p_{\mathrm{T}}$ integrated over $y$ . The notation $\sigma( D \to f )$ is shorthand for $\sigma(D)\times\mathcal{B} ( D \to f )$ . Fig8a.pdf [227 KiB] HiDef png [165 KiB] Thumbnail [117 KiB] *.C file Fig8b.pdf [227 KiB] HiDef png [188 KiB] Thumbnail [125 KiB] *.C file Fig8c.pdf [227 KiB] HiDef png [175 KiB] Thumbnail [113 KiB] *.C file Ratios of the measurements of cross-section times branching fraction 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 [42,43,44]. The ratios are given as a function of $p_{\mathrm{T}}$ integrated over $y$ . The notation $\sigma( D \to f )$ is shorthand for $\sigma(D)\times\mathcal{B} ( D \to f )$ . Fig9a.pdf [227 KiB] HiDef png [190 KiB] Thumbnail [122 KiB] *.C file Fig9b.pdf [227 KiB] HiDef png [171 KiB] Thumbnail [119 KiB] *.C file Fig9c.pdf [227 KiB] HiDef png [204 KiB] Thumbnail [137 KiB] *.C file Integrated $c \overline c$ 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 $0 < p_{\mathrm{T}} < \SI{8}{ {\mathrm{Ge V /}c}}$ and (right) for measurements based on all four mesons for $1 < p_{\mathrm{T}} < \SI{8}{ {\mathrm{Ge V /}c}}$. Fig10a.pdf [225 KiB] HiDef png [169 KiB] Thumbnail [161 KiB] *.C file Fig10b.pdf [225 KiB] HiDef png [150 KiB] Thumbnail [144 KiB] *.C file Animated gif made out of all figures. PAPER-2016-042.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. Only statistical uncertainties are given. Table_1.pdf [51 KiB] HiDef png [87 KiB] Thumbnail [38 KiB] tex code Fractional systematic uncertainties, 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 [71 KiB] Thumbnail [31 KiB] tex code Prompt { $D$ }-meson production cross-sections in the kinematic ranges given. The computation of the extrapolation factors is described in Ref [22]. The first uncertainty on the cross-section is statistical, and the second is systematic and includes the contribution from the extrapolation factor. A dash indicates that measurements are available in all bins and no extrapolation factor is needed. Integrated numbers in the reduced acceptance $2.5 < y < 4.0$ are quoted as reference for future heavy ion measurements. Table_3.pdf [60 KiB] HiDef png [107 KiB] Thumbnail [53 KiB] tex code Ratios of integrated prompt { $D$ }-meson production cross-sections between measurements at $\sqrt{s} = \SI{13}{\TeV}$ and $\sqrt{s} = \SI{5}{\TeV}$ . The first uncertainty on the ratio is statistical, and the second is systematic. Table_4.pdf [48 KiB] HiDef png [50 KiB] Thumbnail [25 KiB] tex code Ratios of the measurements of cross-section times branching fraction in the kinematic range $1 < p_{\mathrm{T}} < \SI{8}{ {\mathrm{Ge V /}c}}$ 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] Differential production cross-sections, $\text{d}^2\sigma/(\text{d} p_{\mathrm{T}} \text{d}y)$, in $\si{\micro\barn}/(\si{ {\mathrm{Ge V /}c}})$ for prompt $D ^0 + \overline{ D }{} {}^0$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. Table_6.pdf [44 KiB] HiDef png [106 KiB] Thumbnail [45 KiB] tex code Differential production cross-sections, $\text{d}^2\sigma/(\text{d} p_{\mathrm{T}} \text{d}y)$, in $\si{\micro\barn}/(\si{ {\mathrm{Ge V /}c}})$ for prompt $D ^+ + D ^-$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. Table_7.pdf [44 KiB] HiDef png [83 KiB] Thumbnail [45 KiB] tex code Differential production cross-sections, $\text{d}^2\sigma/(\text{d} p_{\mathrm{T}} \text{d}y)$, in $\si{\micro\barn}/(\si{ {\mathrm{Ge V /}c}})$ for prompt $D ^+_ s + D ^-_ s$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. Table_8.pdf [44 KiB] HiDef png [100 KiB] Thumbnail [42 KiB] tex code Differential production cross-sections, $\text{d}^2\sigma/(\text{d} p_{\mathrm{T}} \text{d}y)$, in $\si{\micro\barn}/(\si{ {\mathrm{Ge V /}c}})$ for prompt $D ^{*+} + D ^{*-}$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. Table_9.pdf [44 KiB] HiDef png [99 KiB] Thumbnail [42 KiB] tex code The ratios of differential production cross-sections, $R_{13/5}$, for prompt $D ^0 + \overline{ D }{} {}^0$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. Table_10.pdf [44 KiB] HiDef png [108 KiB] Thumbnail [47 KiB] tex code The ratios of differential production cross-sections, $R_{13/5}$, for prompt $D ^+ + D ^-$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. Table_11.pdf [44 KiB] HiDef png [107 KiB] Thumbnail [47 KiB] tex code The ratios of differential production cross-sections, $R_{13/5}$, for prompt $D ^+_ s + D ^-_ s$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. Table_12.pdf [44 KiB] HiDef png [95 KiB] Thumbnail [42 KiB] tex code The ratios of differential production cross-sections, $R_{13/5}$, for prompt $D ^{*+} + D ^{*-}$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. Table_13.pdf [43 KiB] HiDef png [94 KiB] Thumbnail [41 KiB] tex code The ratios of the measurements of cross-section times branching fraction for prompt $D ^+$ and $D ^0$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. All values are given in percent. Table_14.pdf [44 KiB] HiDef png [107 KiB] Thumbnail [52 KiB] tex code The ratios of the measurements of cross-section times branching fraction for prompt $D ^+_ s$ and $D ^0$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. All values are given in percent. Table_15.pdf [44 KiB] HiDef png [101 KiB] Thumbnail [46 KiB] tex code The ratios of the measurements of cross-section times branching fraction for prompt $D ^{*+}$ and $D ^0$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. All values are given in percent. Table_16.pdf [44 KiB] HiDef png [103 KiB] Thumbnail [49 KiB] tex code The ratios of the measurements of cross-section times branching fraction for prompt $D ^+_ s$ and $D ^+$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. All values are given in percent. Table_17.pdf [44 KiB] HiDef png [100 KiB] Thumbnail [45 KiB] tex code The ratios of the measurements of cross-section times branching fraction for prompt $D ^{*+}$ and $D ^+$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. All values are given in percent. Table_18.pdf [44 KiB] HiDef png [103 KiB] Thumbnail [49 KiB] tex code The ratios of the measurements of cross-section times branching fraction for prompt $D ^+_ s$ and $D ^{*+}$ mesons in bins of $( p_{\mathrm{T}} , y )$ . The first uncertainty is statistical, and the second is the total systematic. All values are given in percent. Table_19.pdf [44 KiB] HiDef png [101 KiB] Thumbnail [48 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [418 KiB] This ZIP file contains supplemetary material for the publication LHCb-PAPER-2016-042. The files are: supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.jpg, *.eps : The figures in various formats Fig1a-S.pdf [234 KiB] HiDef png [155 KiB] Thumbnail [110 KiB] *C file Fig1b-S.pdf [234 KiB] HiDef png [156 KiB] Thumbnail [110 KiB] *C file Fig2a-S.pdf [233 KiB] HiDef png [151 KiB] Thumbnail [106 KiB] *C file Fig2b-S.pdf [233 KiB] HiDef png [147 KiB] Thumbnail [106 KiB] *C file Fig3-S.pdf [193 KiB] HiDef png [103 KiB] Thumbnail [84 KiB] *C file

Created on 20 February 2021.