Search for a new resonance decaying to two scalars in the final state with two bottom quarks and two photons in proton-proton collisions at $\sqrt{s}=13\,\mathrm{TeV}$

A search for new resonances in the final state with two bottom quarks and two photons is presented, using CERN LHC proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13~\mathrm{TeV}$, and corresponding to an integrated luminosity of $138~\mathrm{fb}^{-1}$. The resonance $\mathrm{X}$ decays into either a pair of the standard model Higgs bosons $\mathrm{HH}$, or an $\mathrm{H}$ and a new scalar $\mathrm{Y}$ having a mass $m_{\mathrm{Y}} < m_{\mathrm{X}} - m_{\mathrm{H}}$. A model-independent analysis is performed with a narrow-width approximation for $\mathrm{X}$ in the mass range $260~\mathrm{GeV} - 1~\mathrm{TeV}$ (for the $\mathrm{HH}$ decay) and $300~\mathrm{GeV} - 1~\mathrm{TeV}$ (for the $\mathrm{HY}$ decay), covering a mass range of $90< m_{\mathrm{Y}} <800~\mathrm{GeV}$. The upper limits at $95\%$ confidence level on the product of the production cross section of spin-0 $\mathrm{X}$ and its decay branching fraction to $\mathrm{HH}$ are observed to be within $0.82 - 0.07~\mathrm{fb}$, while the corresponding expected limits are $0.74 - 0.08~\mathrm{fb}$, depending upon the considered mass range in $m_{\mathrm{X}}$. For the $\mathrm{X}$ decaying to $\mathrm{HY}$, the observed limits lie in the range $0.90 - 0.04~\mathrm{fb}$ whereas the expected limits are $0.79 - 0.05~\mathrm{fb}$, with the considered mass ranges in $m_{\mathrm{X}}$ and $m_{\mathrm{Y}}$. The largest deviation from background-only hypothesis with local (global) significance of 3.8 (2.8) standard deviations is observed for $m_{\mathrm{X}}= 650~\mathrm{GeV}$ and $m_{\mathrm{Y}}= 90~\mathrm{GeV}$. The $\mathrm{HH}$ limits are compared with predictions in the warped extra dimensional model. The $\mathrm{HY}$ limits are interpreted with the next-to-minimal supersymmetric standard model and the two-real-scalar-singlet model. $$\textit{This document has been revised with respect to the version dated July 8th, 2022.}$$