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In the search for the BSM signals at high-energy colliders, rare events play a crucial role.
We consider two cases, one for the fermiophobic Higgs boson with a high cutoff scale and the other for the lepton flavor violation phenomenon associated with the Z and Higgs bosons.
A fermiophobic Higgs boson appears in type-I two-Higgs-doublet model. Notably, the parameter space with a high cutoff scale yields different signatures than the current search modes.
We will show that two distinctive modes can probe the signal with high sensitivity at the HL-LHC. The second topic is the LFV in the Z and Higgs sectors.
Our meticulous investigation reveals the remarkable suitability of electron-proton colliders, harnessing advantages such as negligible pileups, minimal QCD backgrounds, and suppressed positron-related backgrounds. Through a dedicated signal-background analysis with the boosted decision tree algorithm, we demonstrate that the LHeC with the total integrated luminosity of 1/ab can put significantly lower 2σ bounds than the HL- LHC