We explore a simple extension to the Standard Model containing two gauge singlets: a Dirac fermion and a real pseudoscalar. In some regions of the parameter space both singlets are stable without the necessity of additional symmetries, then becoming a possible two-component dark matter model. We study the relic abundance production via freeze-out, with the latter determined by annihilations, conversions and semi-annihilations. Experimental constraints from invisible Higgs decay, dark matter relic abundance and direct/indirect detection are studied. We found three viable regions of the parameter space, and the model is sensitive to indirect searches.

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