Constraining Effective Self Interactions of Fermionic Dark Matter

The idea of Dark Matter (DM) with self interaction was invoked to resolve a number of discrepancies between the simulation based predictions by collisionless cold DM and the astrophysical observations on galactic and subgalactic scales. Evidences for self interaction would have striking implications for particle nature of DM. In order to reconcile such astrophysical observations for self interaction with particle properties for DM, we consider the general scenario of self interacting Dirac fermionic DM, $\chi$. Also since the exact particle physics model for DM is yet to be probed, we simply adopt the effective model independent framework for DM self interaction which occurs via the most general effective 4-fermion operators invariant under both Lorentz and CPT transformations. From the thorough investigation of the interrelations among the parameters in this framework, namely, the effective DM self couplings ($G_{i}$), DM mass ($m_{\chi}$) and relative velocity ($v_{\rm rel}$), it can be inferred that $G_{i}$ decrease with increasing $m_{\chi}$ for a given DM self interaction strength. Moreover, for few types of effective operators the values of $G_{i}$ fall off with increasing $v_{\rm rel}$ while they remain roughly constant for a wide range of $v_{\rm rel}$ for other cases. In addition, the parameter space in this framework is constrained by the claimed observational results of ${\sigma \over m_{\chi}}$ on cluster scales (Abell 3827, Bullet Cluster) after averaging the DM self interaction cross sections over DM velocity distribution in the cluster. This puts interesting constraints on the values of effective DM self couplings for different fermionic DM masses for various effective operators (scalar, vector, etc.) of DM self interactions in this scenario. Some other implications of DM effective self interaction are also discussed in this model independent framework.