Extraction of CKM matrix elements in single top quark $t$-channel events in proton-proton collisions at $\sqrt{s} = 13$ TeV

This note presents a model-independent extraction of the modulus of the Cabibbo Kobayashi Maskawa matrix elements $\mathrm{V_{\mathrm{tb}}}$, $\mathrm{V_{\mathrm{td}}}$, and $\mathrm{V_{\mathrm{ts}}}$ using an event sample enriched in single top quark $t$-channel events. The analysis uses proton-proton collisions data from the LHC collected during 2016 by the CMS experiment at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{\mathrm{-1}}$. Processes directly sensitive to the matrix elements $\mathrm{V_{\mathrm{tb}}}$, $\mathrm{V_{\mathrm{td}}}$, and $\mathrm{V_{\mathrm{ts}}}$ are considered in both the production and decay vertices of the top quark in single top quark $t$-channel production, as well as in the background processes containing top quarks. Final states are investigated where a muon or electron stems from the leptonic decay chain of the top quark, and two or three jets are selected, one or two of which are identified as coming from the hadronisation of a b quark. The event sample is divided into categories according to the number of jets. Multivariate classifier variables are built in each category in order to discriminate between signal and other standard model processes, and a simultaneous maximum-likelihood fit to data is performed on all categories. The measured value of $\mathrm{|V_{\mathrm{tb}}|}$ is 1.00 $\pm$ 0.03, where the uncertainty includes both statistical and systematic uncertainties, and the upper limit derived on $\mathrm{|V_{\mathrm{ts}}|^2}+\mathrm{|V_{\mathrm{td}}|^2}$ is 0.17 at 95$\%$ confidence level.