We study the fermionic dark matter ( DM ) particle interacting with Standard Model quarks via a light pseudoscalar mediator .
We consider separately the scenarios for which the DM-pseudoscalar coupling is CP conserving or CP violating .
We show that taking a contact interaction is not suitable , even when the mediator has a mass of the same order of magnitude as the typical momentum transfer at the direct-detection experiments , such that the allowed DAMA region is excluded or considerably modified by the correct relic density requirement .
The DAMA result seems to indicate that the CP -violating interaction is dominant at direct searches .
We find that , if the proton-to-neutron effective coupling ratio is -60 \sim - 40 , the exclusion limits set by SuperCDMS , XENON100 , and LUX are highly suppressed , and the DAMA signal can thus be easily reconciled with these null measurements .
For this model , the allowed region determined by the DAMA signal and correct relic density can successfully satisfy the conditions required by the thermal equilibrium , big bang nucleosynthesis , and DM self-interactions .
The results of future measurements on flavor physics will provide important constraints on the related models .
Precise measurements performed by COUPP , PICASSO , SIMPLE and KIMS should be able to test this model in the near future .