  Models in which dark matter particles communicate with the visible sector
through a pseudoscalar mediator are well-motivated both from a theoretical and
from a phenomenological standpoint. With direct detection bounds being
typically subleading in such scenarios, the main constraints stem either from
collider searches for dark matter, or from indirect detection experiments.
However, LHC searches for the mediator particles themselves can not only
compete with -- or even supersede -- the reach of direct collider dark matter
probes, but they can also test scenarios in which traditional monojet searches
become irrelevant, especially when the mediator cannot decay on-shell into dark
matter particles or its decay is suppressed. In this work we perform a detailed
analysis of a pseudoscalar-mediated dark matter simplified model, taking into
account a large set of collider constraints and concentrating on the parameter
space regions favoured by cosmological and astrophysical data. We find that
mediator masses above 100-200~GeV are essentially excluded by LHC searches in
the case of large couplings to the top quark, while forthcoming collider and
astrophysical measurements will further constrain the available parameter
space.
