Search for nonresonant Higgs boson pair production in the WW$\gamma\gamma$ channel in pp collisions at $\sqrt{s}=13~\mathrm{TeV}$

A search for nonresonant production of Higgs boson pairs in final states with two W bosons and two photons is presented. The search uses data from proton-proton collisions at a center-of-mass energy of $\sqrt{s}=13~\mathrm{TeV}$, recorded with the CMS detector at the LHC between 2016 and 2018, which correspond to an integrated luminosity of ${138\,\mathrm{fb}^{-1}}$. This is the first search performed in this final state by the CMS collaboration. The observed (expected) 95$\%$ confidence level (CL) upper limit on Higgs boson pair production cross-section is evaluated to be $3.0~ (1.6)~\mathrm{pb}$, corresponding to about 97 (53) times the standard model prediction. Scans of modified SM and purely beyond SM (BSM) coupling parameters in an effective field theory framework result in an observed (expected) constraint on the Higgs boson self-coupling strength of -25.8 (-14.4) to 24.1 (18.3) times its SM value, and a constraint on the magnitude of a direct coupling of two top quarks to two Higgs bosons of -2.4 (-1.7) to 2.9 (2.2) at a 95$\%$ CL. Additionally, observed (expected) 95$\%$ CL upper limits are placed on twenty effective field theory BSM benchmark scenarios ranging from 1.7 to 6.2 $(1.0\text{ to }3.9)~\mathrm{pb}$.