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A measurement of the W$^+$W$^-$ boson pair production cross section inproton-proton collisions at $\sqrt{s} =$ 13 TeV is presented. The data used inthis study are collected with the CMS detector at the CERN LHC and correspondto an integrated luminosity of 35.9 fb$^{-1}$. The W$^+$W$^-$ candidate eventsare selected by requiring two oppositely charged leptons (electrons or muons).Two methods for reducing background contributions are employed. In the firstone, a sequence of requirements on kinematic quantities is applied allowing ameasurement of the total production cross section: 117.6 $\pm$ 6.8 pb, whichagrees well with the theoretical prediction. Fiducial cross sections are alsoreported for events with zero or one jet, and the change in the zero-jetfiducial cross section with the jet transverse momentum threshold is measured.Normalized differential cross sections are reported within the fiducial region.A second method for suppressing background contributions employs two randomforest classifiers. The analysis based on this method includes a measurement ofthe total production cross section and also a measurement of the normalized jetmultiplicity distribution in W$^+$W$^-$ events. Finally, a dilepton invariantmass distribution is used to probe for physics beyond the standard model in thecontext of an effective field theory, and constraints on the presence ofdimension-6 operators are derived.

W$^+$W$^-$ boson pair production in proton-proton collisions at $\sqrt{s} =$ 13 TeV