Search for single production of vector-like quarks decaying into $Wb$ in $pp$ collisions at $\sqrt{s} =$ 13 TeV with the ATLAS detector

A search for singly-produced vector-like quarks $Q$, where $Q$ can be either a $T$ quark with charge $2/3$ or a $Y$ quark with charge $4/3$, is performed in 3.2 $fb^{-1}$ of proton--proton collision data at a centre-of-mass energy of 13 TeV recorded with the ATLAS detector at the LHC. The analysis targets $Q \to Wb$ decays where the $W$ boson decays leptonically. No significant excess over Standard Model backgrounds is observed and upper limits on the $Q \to Wb$ cross-section times branching ratio are set as a function of the vector-like quark mass. For a $QWb$ coupling strength of $\sqrt{(c_{\mathrm{L}}^{Wb})^2 + (c_{\mathrm{R}}^{Wb})^2 }=1/\sqrt{2}$, the observed (expected) 95 % confidence level lower limit on the $Y$-quark mass is 1.44 TeV (1.45 TeV). The results are also interpreted as limits on the $QWb$ coupling strength and the mixing with the Standard Model sector for a singlet $T$ quark or a $Y$ quark from a $(B,Y)$ doublet. The smallest excluded coupling-strength values are obtained for vector-like quark masses around 1000 GeV; they are as small as $|c_{L}^{Wb}|=0.45$ for a $T$ quark and $\sqrt{(c_{\mathrm{L}}^{Wb})^2 + (c_{\mathrm{R}}^{Wb})^2 }=0.33$ for a $Y$ quark. Within a $(B,Y)$ doublet model, the excluded mixing parameter, $|\sin{\theta_{R}}|$, in this mass region is comparable to the exclusion limits from electroweak precision observables.