The rate for Higgs ({mathrm{H}} ) bosons production in association with either one ({mathrm{t}} {mathrm{H}} ) or two ({mathrm{t}} {{overline{{{mathrm{t}}}}}} {mathrm{H}} ) top quarks is measured in final states containing multiple electrons, muons, or tau leptons decaying to hadrons and a neutrino, using proton–proton collisions recorded at a center-of-mass energy of 13,text {TeV} by the CMS experiment. The analyzed data correspond to an integrated luminosity of 137,text {fb}^{-1}. The analysis is aimed at events that contain {mathrm{H}} rightarrow {mathrm{W}} {mathrm{W}} , {mathrm{H}} rightarrow {uptau } {uptau } , or {mathrm{H}} rightarrow {mathrm{Z}} {mathrm{Z}} decays and each of the top quark(s) decays either to lepton+jets or all-jet channels. Sensitivity to signal is maximized by including ten signatures in the analysis, depending on the lepton multiplicity. The separation among {mathrm{t}} {mathrm{H}} , {mathrm{t}} {{overline{{{mathrm{t}}}}}} {mathrm{H}} , and the backgrounds is enhanced through machine-learning techniques and matrix-element methods. The measured production rates for the {mathrm{t}} {{overline{{{mathrm{t}}}}}} {mathrm{H}} and {mathrm{t}} {mathrm{H}} signals correspond to 0.92 pm 0.19,text {(stat)} ^{+0.17}_{-0.13},text {(syst)} and 5.7 pm 2.7,text {(stat)} pm 3.0,text {(syst)} of their respective standard model (SM) expectations. The corresponding observed (expected) significance amounts to 4.7 (5.2) standard deviations for {mathrm{t}} {{overline{{{mathrm{t}}}}}} {mathrm{H}} , and to 1.4 (0.3) for {mathrm{t}} {mathrm{H}} production. Assuming that the Higgs boson coupling to the tau lepton is equal in strength to its expectation in the SM, the coupling y_{{mathrm{t}}} of the Higgs boson to the top quark divided by its SM expectation, kappa _{{mathrm{t}}}=y_{{mathrm{t}}}/y_{{mathrm{t}}}^{mathrm {SM}}, is constrained to be within -0.9< kappa _{{mathrm{t}}}< -0.7 or 0.7< kappa _{{mathrm{t}}}< 1.1, at 95% confidence level. This result is the most sensitive measurement of the {mathrm{t}} {{overline{{{mathrm{t}}}}}} {mathrm{H}} production rate to date.
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