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A measurement is presented of differential cross sections for $t$-channelsingle top quark and antiquark production in proton-proton collisions at acentre-of-mass energy of 13 TeV by the CMS experiment at the LHC. From a dataset corresponding to an integrated luminosity of 35.9 fb$^{-1}$, eventscontaining one muon or electron and two or three jets are analysed. The crosssection is measured as a function of the top quark transverse momentum($p_\mathrm{T}$), rapidity, and polarisation angle, the charged lepton$p_\mathrm{T}$ and rapidity, and the $p_\mathrm{T}$ of the W boson from the topquark decay. In addition, the charge ratio is measured differentially as afunction of the top quark, charged lepton, and W boson kinematic observables.The results are found to be in agreement with standard model predictions usingvarious next-to-leading-order event generators and sets of parton distributionfunctions. Additionally, the spin asymmetry, sensitive to the top quarkpolarisation, is determined from the differential distribution of thepolarisation angle at parton level to be 0.440 $\pm$ 0.070, in agreement withthe standard model prediction.

european physical journal. c, particles and fields

Measurement of differential cross sections and charge ratios for  $t$-channel single top quark production in proton-proton collisions at  $\sqrt{s} =$ 13 TeV