Search for Higgs boson decays into two spin-0 particles in the $bb\mu\mu$ final state with the ATLAS detector in $pp$ collisions at $\sqrt{s}=13$ TeV

This note presents a search for decays of the Higgs boson with a mass of 125 GeV to a pair of new spin-0 particles, $H\rightarrow aa$, where one $a$-boson decays to a $b$-quark pair and the other to a muon pair. The search uses 139~fb$^{-1}$ of the LHC proton--proton collision data at a centre-of-mass energy of $\sqrt{s}$=13 TeV recorded by the ATLAS experiment between 2015 and 2018. A narrow dimuon resonance is searched for in the invariant mass spectrum between 16 GeV and 62 GeV. The largest excess of events above the Standard Model backgrounds is observed at an invariant dimuon mass of 52 GeV and corresponds to a local (global) significance of $3.3 \sigma$ ($1.7 \sigma$). Upper limits at 95\% confidence level are placed on the branching ratio of the Higgs boson to the $bb\mu\mu$ final state, $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$, and are in the range $(0.22-4) \times10^{-4}$, depending on the signal mass hypothesis.