Search for exotic Higgs boson decays H $\to$ $\mathcal{A}\mathcal{A}$ $\to$ 4$\gamma$ with events containing two merged diphotons in proton-proton collisions at $\sqrt{s}$ = 13 TeV

We present the first direct search for exotic Higgs boson decays H $\to$ $\mathcal{A}\mathcal{A}$, $\mathcal{A}$ $\to$ $\gamma \gamma$ in events with two photonlike objects. The hypothetical particle $\mathcal{A}$ is a low-mass spin-0 particle decaying promptly to a merged diphoton reconstructed as a single photonlike object. We analyze the data collected by the CMS experiment at $\sqrt{s}$ = 13 TeV corresponding to an integrated luminosity of 136 fb${}^{-1}$. No excess above the estimated background is found. We set upper limits on the branching fraction $\mathcal{B}$(H $\to$ $\mathcal{A}\mathcal{A}$ $\to$ 4$\gamma$) of (0.9-3.3) $\times$ 10${}^{-3}$ at 95% confidence level for masses of $\mathcal{A}$ in the range 0.1-1.2 GeV.