Measurements of charm production and $CP$ violation with the LHCb detector

This thesis presents two measurements made using data collected by the LHCb detector, operating at the Large Hadron Collider accelerator at the CERN particle physics laboratory. The first is a measurement of the production rates of promptly produced $D^{0}$, $D^{+}$, $D_{s}^{+}$, and $D^{*+}$ open charm mesons, using data collected in 2015 at a proton-proton centre-of-mass energy of $\sqrt{s} = 13\,\mathrm{TeV}$. The second is a search for direct $CP$ violation in two three-body decays of the $\Lambda_{c}^{+}$ charm baryon, $pK^{-}K^{+}$ and $p\pi^{-}\pi^{+}$, using data collected in 2011 at $\sqrt{s} = 7\,\mathrm{TeV}$ and in 2012 at $\sqrt{s} = 8\,\mathrm{TeV}$. For each measurement, motivation and context are given from the standpoint of improving the theoretical understanding of the Standard Model and searching for signs of physics that cannot be explained by it, and then the various statistical analysis techniques used to extract physical quantities from the data are explained. The systematic limitations of the method are explored and quantified, and then the results are presented.