Numerically analyzing self-interacting dark matter

We consider the scenario of self-interacting dark matter(SIDM) with a light mediator in a model-independent way, which can alleviate two long-standing issues of the small scale cosmology namely cusp vs. core and too-big-to-fail. A Yukawa potential is chosen to achieve mediator exchange between DM particles as part of their self-interactions. The dynamics of self-interacting transfer cross-section are studied for a range of mediator mass($m_Z'$). Also, a relationship is established between the cross-section and DM particles' relative velocity, which ensures the solution to the DM crisis at small scales. Our obtained numerical results are efficient compared to the earlier works in the context that a lesser number of $\ell$ modes have been used by us to achieve the same level of accuracy in the cross-section calculations. For a better understanding of the SIDM parameter space, we perform an analytical analysis on the dependence of transfer cross-section over the other important SIDM parameters using a Hulth\'{e}n potential which is similar in its behavior to Yukawa potential. A detailed evolution of particle dynamics using the Boltzmann equation and the effect of Sommerfeld enhancement on such calculations has also been studied here. We also provide a minimal anomaly-free leptophilic extension of the standard model, that can incorporate SIDM and its mediator candidate in the framework.