Search for the production of four top quarks in the single-lepton and opposite-sign dilepton final states in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search for the standard model production of four top quarks (pp $\to$ $\mathrm{t\bar{t}t\bar{t}}$) is reported using single-lepton plus jets and opposite-sign dilepton plus jets signatures. Proton-proton collisions are recorded with the CMS detector at the LHC at a center-of-mass energy of 13 TeV in a sample corresponding to an integrated luminosity of 35.8 fb$^{-1}$. A multivariate analysis exploiting global event and jet properties is used to discriminate $\mathrm{t\bar{t}t\bar{t}}$ from $\mathrm{t\bar{t}}$ production. No significant deviation is observed from the predicted background. An upper limit is set on the cross section for $\mathrm{t\bar{t}t\bar{t}}$ production in the standard model of 48 fb at 95% confidence level. When combined with a previous measurement by the CMS experiment from an analysis of other final states, the observed signal significance is 1.4 standard deviations, and the combined cross section measurement is 13 $^{+11}_{-9}$ fb. The result is also interpreted in the framework of effective field theory.