Search for exotic Higgs boson decays H $\to$$\mathcal{AA}$ with $\mathcal{AA}$$\to$$γγ$ in events with a semi-merged topology in proton-proton collisions at $\sqrt{s}$ = 13 TeV

A search for exotic Higgs boson decays H $\to$$\mathcal{AA}$, with $\mathcal{A}$$\to$$γγ$ is presented, using events with a semi-merged topology. One of the hypothetical particles, $\mathcal{A}$, is assumed to decay promptly into a semi-merged diphoton system reconstructed as a single photon-like object, while the other $\mathcal{A}$ decays into two resolved photons. The search is performed using proton-proton collision data collected by the CMS experiment at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The data agree with the standard model background expectation. Upper limits are set on the product of the Higgs boson production cross section and the branching fraction, $σ$(pp $\to$ H)$\mathcal{B}$(H $\to$$\mathcal{AA}$$\to$ 4$γ$), which range from 0.264 to 0.005 pb at 95% confidence level, for $\mathcal{A}$ masses in the range 1 $\lt$ $m_\mathcal{A}$ $\lt$ 15 GeV. These limits are the most stringent to date in the 1$-$5 GeV $m_\mathcal{A}$ range.