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A search is presented for a third-generation leptoquark (LQ) coupledexclusively to a $\tau$ lepton and a b quark. The search is based onproton-proton collision data at a center-of-mass energy of 13 TeV recorded withthe CMS detector, corresponding to an integrated luminosity of 138 fb$^{-1}$.Events with $\tau$ leptons and a varying number of jets originating from bquarks are considered, targeting the single and pair production of LQs, as wellas nonresonant $t$-channel LQ exchange. An excess is observed in the data withrespect to the background expectation in the combined analysis of all searchregions. For a benchmark LQ mass of 2 TeV and an LQ-b-$\tau$ coupling strengthof 2.5, the excess reaches a local significance of up to 2.8 standarddeviations. Upper limits at the 95% confidence level are placed on the LQproduction cross section in the LQ mass range 0.5-2.3 TeV, and up to 3 TeV for$t$-channel LQ exchange. Leptoquarks are excluded below masses of 1.22-1.88 TeVfor different LQ models and varying coupling strengths up to 2.5. The study ofnonresonant $\tau\tau$ production through $t$-channel LQ exchange allows lowerlimits on the LQ mass of up to 2.3 TeV to be obtained.

Search for a third-generation leptoquark coupled to a $\tau$ lepton and  a b quark through single, pair, and nonresonant production in proton-proton  collisions at $\sqrt{s}$ = 13 TeV