Roadmap to explore vectorlike quarks decaying to a new scalar or pseudoscalar

The current experimental data allow for a sub-TeV colourless weak-singlet scalar or pseudoscalar. If such a singlet field is present together with TeV-range vectorlike top and bottom partners, there is a possibility that the heavy quarks decay dominantly to the singlet state and a third-generation quark, and the singlet state decays to quark and boson pairs. Such a possibility may arise in various models but it has not been explored experimentally, especially in the context of vectorlike-quark searches. We consider some minimal models, covering the possible weak representations of the top and bottom partners, that can be mapped to many well-motivated ultraviolet-complete theories. We chart out the possible interesting and unexplored signatures of the exotic decay of vectorlike quarks and identify benchmark points representing different signal topologies for the high luminosity LHC. We perform a general scan of the parameter space with the relevant direct search bounds and find that large regions, which do not require any fine-tuning, remain open for the unexplored channels. We also perform a simple projection study in the cleanest channel and indicate how other new but experimentally challenging channels can be used to probe more regions of the parameter space.