Search for a W$^\prime$ boson decaying to a top and a bottom quark at $\sqrt{s}=13~\mathrm{TeV}$

A search is performed for a W$^\prime$ boson decaying to a top and a bottom quark in proton-proton collisions at a center-of-mass energy of $13~\mathrm{TeV}$. The analyzed data have been collected by the CMS Collaboration between 2016 and 2018 and correspond to an integrated luminosity of $137~\mathrm{fb}^{-1}$. Deep neural network algorithms are used to identify the jets initiated by the b quark and also the jets containing the decay products of the top quark when the W boson from the top quark decays hadronically. No excess above the estimated standard model background is observed and upper limits on the production cross section of W$^\prime$ bosons are set. Both left- and right-handed W$^\prime$ bosons with masses below $3.4~\mathrm{TeV}$ are excluded at $95\%$ confidence level. These results are the best limits to date on W$^\prime$ bosons decaying to a top and a bottom quark in the all-handronic final state.