  We consider a minimal renormalizable and gauge invariant dark matter (DM)
model, in which the singlet fermion DM has only axial couplings to a new
pseudoscalar mediator. The mixing between the pseudoscalar mediator and the
standard model (SM) Higgs boson induces the interactions between the DM and SM
particles. The DM candidate in this model can provide the correct thermal relic
density and evades all direct detections, while it can produce observable
signals in indirect detection experiments due to its large annihilation cross
section. A comparative study for DM phenomenology at the LHC is conducted for
models with scalar mediators that have either scalar or pseudoscalar couplings
to SM particles and the DM. We find that the three scenarios have
distinguishable features in scalar decay branching ratio, DM pair production
cross section as well as the signal reaches at the LHC. The LHC searches for
some visible signals related to the scalar sector are also discussed.
