  In extensions of two Higgs doublet models with vectorlike quarks and leptons
the decays of new scalars or fermions can be altered by the presence of the
other, depending on the hierarchy of new physics. If new fermions are heavier
than Higgses, their decays may be dominated by cascade decays through charged
and neutral heavy Higgs bosons. In the opposite hierarchy, the decay of a heavy
Higgs can lead to single production of vectorlike quarks and leptons when
Yukawa couplings to SM fermions are present. We explore the resulting novel
collider signatures in either case and present projected sensitivities of
future runs of the LHC to the masses and branching ratios of new fermions and
heavy Higgses. Importantly, we discuss kinematic challenges of the signatures
and suggest strategic observables which could be adopted in future analyses.
Interpreting the prospective reach of the LHC in the context of a type-II 2HDM,
we find that in the presence of vectorlike fermions heavy Higgs boson masses
slightly above 2 TeV can be explored at the HL-LHC even at low $\tan\beta$. For
heavy Higgs decays through vectorlike leptons, this reach extends to slightly
above 3 TeV for $\tan\beta \gtrsim 10$. Further, these search strategies imply
a reach for vectorlike quark and lepton masses close to 2.4 TeV and 1.5 TeV,
respectively. This article is partly based on Refs. [1-6]
