Novel collider signatures in the type-I 2HDM+$a$ model

The 2HDM+$a$ model is one of the main models used in the interpretations of dark matter searches at the LHC. So far, all the 2HDM+$a$ benchmarks considered by the ATLAS and CMS experiments are limited to a type-II Yukawa sector, in which the Higgs bosons $A$, $H$, and $H^\pm$ are all constrained to be mass-degenerate and heavier than around $600 \, {\rm GeV}$. In this work, we present the first detailed study of 2HDM+$a$ models with a type-I Yukawa sector, which, for moderate values of $\tan\beta$, lift the constraints from flavour physics, allowing the extra Higgs bosons to be even lighter than the $125 \, {\rm GeV}$ Higgs boson discovered at the LHC. We discuss several benchmarks where the $A$, $H$, and $H^\pm$ states are not necessarily mass-degenerate and the signatures that arise in these models, some of which have not yet been explored at the LHC. We present the dominant channels in the studied benchmarks and the expected sensitivity in Run 2 data using truth-level analyses and discuss potential improvements in the experimental searches for Run 3.