Search for vector-boson resonances decaying to a top quark and bottom quark in the lepton plus jets final state in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search for new charged massive gauge bosons, $W^{\mathrm{\prime }}$, is performed with the ATLAS detector at the LHC. Data were collected in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}$ = 13 TeV and correspond to an integrated luminosity of 36.1 ${\text{fb}}^{-1}$. This analysis searches for $W^{\mathrm{\prime }}$ bosons in the $W^{\mathrm{\prime }}\to t\bar{b}$ decay channel in final states with an electron or muon plus jets. The search covers resonance masses between 0.5 and 5.0 TeV and considers right-handed $W^{\mathrm{\prime }}$ bosons. No significant deviation from the Standard Model (SM) expectation is observed and upper limits are set on the $W^{\mathrm{\prime }}\to t\bar{b}$ cross section times branching ratio and the $W^{\mathrm{\prime }}$ boson effective couplings as a function of the $W^{\mathrm{\prime }}$ boson mass. For right-handed $W^{\mathrm{\prime }}$ bosons with coupling to the SM particles equal to the SM weak coupling constant, masses below 3.15 TeV are excluded at the 95% confidence level. This search is also combined with a previously published ATLAS result for $W^{\mathrm{\prime }}\to t\bar{b}$ in the fully hadronic final state. Using the combined searches, right-handed $W^{\mathrm{\prime }}$ bosons with masses below 3.25 TeV are excluded at the 95% confidence level.