Freeze-in production of Fermionic Dark Matter with Pseudo-scalar and Phenomenological Aspects

In this paper, we study freeze-in production of fermionic dark matter with a pseudo scalar as the mediator between dark sector and Standard Model (SM). While the fermionic DM is non-thermal, we will explain two scenarios in which production of pseudo-scalar particles are either thermal or non thermal. We'll present elaborate discussion to derive yield quantity and relic density and illustrate these values for the different range of model parameters. We'll investigate constraints on parameters space coming from invisible Higgs decay at LHC. For the case of extremely small couplings and zero mixing between SM Higgs field with pseudo scalar field which pseudo scalar boson can play role of DM, we will justify recent observation of merging galaxies with a case of self-interacting DM. We'll show that influence of DM annihilation in this case, would provide a better fit to the AMS-02 data of positron flux.