Future detectability of a pseudoscalar mediator dark matter model

We investigate the maximum value of the spin-independent cross section in a dark matter (DM) model called the two-Higgs doublet model + a (THDM+a). This model can explain the observed DM energy density while evading the current strict bound from the DM direct detection experiment because the predicted cross section at the tree-level is highly suppressed by the momentum transfer. On the other hand, the loop induced scattering effects are predicted without momentum suppression and might be detectable in the future DM direct detection experiments. The predicted cross section strongly depends on the scalar quartic couplings. We derive the theoretical constraints on these parameters by studying the stability of the electroweak vacuum, and the condition for the potential bounded from below. Considering these constraints, we find that the maximum value of the predicted cross section is larger than the prospects of the LZ and XENONnT experiments and this model has the potential to explain the DM direct detection signal which might be obtained near future.