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

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 \begin{equation*} \sigma(pp \to D^{0} X) = 2460 \pm \phantom{1}3 \pm 130\,\mu\mathrm{b} \end{equation*} \begin{equation*} \sigma(pp \to D^{+} X) = 1000 \pm \phantom{1}3 \pm 110\,\mu\mathrm{b} \end{equation*} \begin{equation*} \sigma(pp \to D_{s}^{+} X) = 460 \pm 13 \pm 100\,\mu\mathrm{b} \end{equation*} \begin{equation*} \sigma(pp \to D^{*+} X) = 880 \pm \phantom{1}5 \pm 140\,\mu\mathrm{b} \end{equation*} where the uncertainties are due to statistical and systematic uncertainties, respectively.