Measuring rare and exclusive Higgs boson decays into light resonances

We evaluate the LHC's potential of observing Higgs boson decays into light elementary or composite resonances through their hadronic decay channels. We focus on the Higgs boson production processes with the largest cross sections, $pp\to h$ and $pp\to h+\mathrm{jet}$, with subsequent decays $h \to ZA$ or $h\to Z\,\eta_c$, and comment on the production process $pp\to hZ$. By exploiting track-based jet substructure observables and extrapolating to $3000~\mathrm{fb}^{-1}$ we find ${\cal BR}(h \to ZA) \simeq {\cal BR}(h \to Z \eta_c) \lesssim 0.02$ at 95% CL. We interpret this limit in terms of the 2HDM Type 1. We find that searches for $h\to ZA$ are complementary to existing measurements and can constrain large parts of the currently allowed parameter space.