Optimisation of selection criteria of $t$-channel single-top-quark events at $\sqrt s$ = 13 TeV for studies of anomalous couplings in the $Wtb$ vertex.

The top-quark is the heaviest known fundamental particle and probing its couplings with the other fundamental particles may open a window to physics beyond the Standard Model. Single top-quark production provides a unique way to study the coupling between the top-quark, the W-boson and the b-quark, since it involves the $Wtb$ vertex in both production and decay. The $Wtb$ vertex structure has been explored through the measurement of top-quark and W-boson polarisation observables using $t$-channel single top-quark events produced in proton-proton collisions during LHC Run I. The most recent limits on anomalous couplings in the $Wtb$ vertex from the ATLAS and CMS experiments are reviewed. Comprehensive studies of the $t$-channel selection requirements have been performed using Monte Carlo samples of signal and background events produced at $\sqrt{s}$ = 13 TeV and normalised to an integrated luminosity of 36.1 ${\rm pb}^{-1}$ . Starting from events containing one isolated lepton, large missing transverse momentum and exactly two jets, one being b-tagged, stringent selection requirements are proposed to discriminate $t$-channel single-top events from the background contributions. These selection requirements have been designed on the basis of an statistical optimisation and regardless of kinematic properties of the top decay products that could potentially bias early measurements of top-quark polarisation in the Run II.