The search for a third-generation leptoquark coupling to a $\tau$ lepton and a b quark through single, pair and nonresonant production at $\sqrt{s}=13~\mathrm{TeV}$

A search is presented for a third-generation leptoquark (LQ) coupling to a $\tau$ lepton and a b quark. Events with $\tau$ leptons plus at least one jet originating from a b quark are considered, targeting the single and pair production of the LQ as well as nonresonant production via $t$-channel LQ exchange. The search is based on proton-proton collision data at a center-of-mass energy of $\sqrt{s}=13~\mathrm{TeV}$ recorded with the CMS detector, corresponding to an integrated luminosity of $137~\mathrm{fb}^{-1}$. Upper limits are set on the LQ production cross section in the LQ mass range 0.5-2.3 TeV. Lower limits at $95\%$ confidence level on the LQ mass are set in the 1.22-1.96 TeV range and for a coupling strength less than 2.5, depending on the LQ model. Upper limits are also set on the coupling strength of such LQs as a function of their mass. For a representative LQ mass of 2 TeV and a coupling strength of 2.5, an excess with a significance of 3.4 standard deviations above the standard model expectation is observed in the data. Consequently, the observed upper limits on the LQ production cross section are about three times larger than expected for this benchmark. $$\textit{This document has been revised with respect to the version dated Jul 9, 2022.}$$