Searching for exotic production of Higgs boson + $X$ to map out new physics

We propose leveraging our proficiency for detecting Higgs resonances by using the Higgs as a tagging object for new heavy physics. In particular, we argue that searches for exotic Higgs production from decays of color-singlet fields with electroweak charges could beat current searches at the Large Hadron Collider which look for their decays to vectors. As an example, we study the production and decay of vectorlike leptons which admit Yukawa couplings with Standard Model leptons. We find that bounds from run 2 searches are consistent with anywhere from hundreds to many thousands of Higgses having been produced in their decays over the same period, depending on the representation. Dedicated searches for these signatures may thus be able to significantly improve our reach at the electroweak energy frontier.