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Probing extended Higgs sector in the intensity and energy frontiers

A light Higgs that can accommodate muon g-2 anomaly can be probed in various low energy experiments, such as muon decay, charged Kaon decays, etc. I will first discuss it in a model-independent way and then provide a concrete UV model where the light scalar can be realized. The proposed muon electric dipole moment will also have a sensitivity to some part of parameter space. Lepton flavor violating decays due to the light scalar will also be discussed.  Next, I will talk about some signatures of a heavy Higgs including an enhancement of the double Higgs production rate and CP violation that can potentially be probed at the LHC or a future 100 TeV collider in models with extended Higgs sectors.