Renormalization group equation analysis of a pseudoscalar portal dark matter model

We investigate the vacuum stability and perturbativity of a pseudoscalar portal dark matter model with a Dirac dark matter (DM) candidate, through the renormalization group equation analysis at one-loop order. The model has a particular feature which can evade the direct detection upper bounds measured by XENON100 and even that from planned experiment XENON1T. We first find the viable regions in the parameter space which will give rise to correct DM relic density and comply with the constraints from Higgs physics. We show that for a given mass of the pseudoscalar, the mixing angle plays no significant role in the running of the couplings. Then we study the running of the couplings for various pseudoscalar masses at mixing angle $\theta = 6^\circ$, and find the scale of validity in terms of the dark coupling, $\lambda_{d}$. Depending on our choice of the cutoff scale, the resulting viable parameter space will be determined.