Abstract
We study the pair production of the long-lived mediator particles from the decay of the SM Higgs boson and their subsequent decay into standard model particles. We compute the projected sensitivity, both model-independently and with a minimal model, of using the muon spectrometer of the CMS detector at the HL-LHC experiment for ggF, VBF, and Vh production modes of the Higgs boson and various decay modes of the mediator particle, along with dedicated detectors for LLP searches like CODEX-b and MATHUSLA. Subsequently, we study the improvement with the FCC-hh detector at the 100\,TeV collider experiment for such long-lived mediators, again focusing on the muon spectrometer. We propose dedicated LLP detector designs for the 100\,TeV collider experiment, DELIGHT (\textbf{De}tector for \textbf{l}ong-l\textbf{i}ved particles at hi\textbf{gh} energy of 100\,\textbf{T}eV), and study their sensitivities.
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