Combination of searches for Higgs boson pair production in proton-proton collisions at $\sqrt{s} = 13~\mathrm{TeV}$

This document describes the combination of searches for Higgs boson pair production in proton-proton collisions at $\sqrt{s} = 13~\mathrm{TeV}$ performed by the CMS Collaboration using an integrated luminosity of $35.9~\mathrm{fb}^{-1}$ collected at the LHC in 2016. Four different final states are considered, with one Higgs boson decaying into a $b\bar{b}$ pair and the other decaying into $\gamma\gamma$, $\tau\tau$, $b\bar{b}$, or a pair of vector bosons. Limits are set on the Higgs boson pair production cross section. The $95\%$ confidence level observed (expected) upper limit on the production cross section is found to be 21.8 (12.4) times the standard model value. A search for heavy narrow width resonances (X) decaying to Higgs boson pairs is also performed in the mass range $250 < M_X < 3000~\mathrm{GeV}$. No evidence of a signal is observed and upper limits are set on the resonance production cross section.