Freeze-in production of fermionic dark matter with pseudo-scalar and phenomenological aspects

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