Search for W' bosons decaying to a top and a bottom quark in leptonic final states at $\sqrt{s} = 13\mathrm{TeV}$

A search for W' bosons decaying to a top and a bottom quark in final states including electrons or muons is performed with the CMS detector at the LHC. The analyzed data correspond to an integrated luminosity of $138~\mathrm{fb}^{-1}$ of proton-proton collisions at a center-of-mass energy of $13~\mathrm{TeV}$. In general, good agreement with the Standard Model expectation is observed. The largest observed excess is found for a W' boson mass hypothesis of $3.8~\mathrm{TeV}$ with a relative decay width of $1\%$, with a local (global) significance of $2.6$ $(2.0)$ standard deviations. Upper limits on the production cross sections of W' bosons decaying to a top and a bottom quark are set. Left- and right-handed W' bosons with masses below $3.9$ and $4.3~\mathrm{TeV}$ are excluded at $95\%$ confidence level in the approximation that the new particle has negligible decay width. Limits are also set considering decay widths of up to $30\%$ of the W' boson mass. These are the most stringent limits to date on W' bosons decaying to a top and a bottom quark. $$\textit{This document has been revised with respect to the version dated March 23, 2023.}$$