New constraints and discovery potential for Higgs to Higgs cascade decays through vectorlike leptons

One of the cleanest signatures of a heavy Higgs boson in models with vectorlike leptons is $H\to e_4^\pm \ell^\mp \to h\ell^+\ell^-$ which, in two Higgs doublet model type-II, can even be the dominant decay mode of heavy Higgses. Among the decay modes of the standard model like Higgs boson, $h$, we consider $b \bar b$ and $\gamma \gamma$ as representative channels with sizable and negligible background, respectively. We obtained new model independent limits on production cross section for this process from recasting existing experimental searches and interpret them within the two Higgs doublet model. In addition, we show that these limits can be improved by about two orders of magnitude with appropriate selection cuts immediately with existing data sets. We also discuss expected sensitivities with integrated luminosity up to 3 ab$^{-1}$ and present a brief overview of other channels.