Search for Higgs boson pair production in the final state containing two photons and two bottom quarks in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

A search is presented for the production of a pair of Higgs bosons, where one decays into two photons and the other to two bottom quarks. Both resonant and nonresonant production mechanisms of the Higgs boson pair are investigated. The analysis is performed using proton-proton collision data from the LHC at $\sqrt{s} = 13$ TeV recorded by the CMS detector in 2016, which corresponds to an integrated luminosity of 35.9 fb$^{-1}$. The observed data are in agreement with standard model predictions. Upper limits on the production cross sections of spin-0 and spin-2 particles are set at $95\%$ confidence level, excluding a product of the production cross section and branching fraction of narrow-width particles between 0.26 and 3.67 fb for spin-0 and between 0.21 and 3.61 fb for spin-2. In addition, an upper limit on the cross section for nonresonant Higgs boson pair production is set and compared to standard model Higgs boson pair production via gluon fusion. Constraints on anomalous couplings that affect Higgs boson pair production are also determined. For the standard model hypothesis, the data exclude a product of production cross section and branching fraction larger than 1.67 fb at $95\%$ confidence level, corresponding to 19.2 times the standard model prediction.