Self Interacting Dark Matter and Dirac neutrinos via Lepton Quarticity

In this paper, we put forward a connection between the self-interacting dark matter and the Dirac nature of neutrinos. Our exploration involves a $Z_4 \otimes Z_4'$ discrete symmetry, wherein the Dirac neutrino mass is produced through a type-I seesaw mechanism. This symmetry not only contributes to the generation of the Dirac neutrino mass but also facilitates the realization of self-interacting dark matter with a light mediator that can alleviate small-scale anomalies of the $\Lambda {\rm CDM}$ while being consistent with the latter at large scales, as suggested by astrophysical observations. Thus the stability of the DM and Dirac nature of neutrinos are shown to stem from the same underlying symmetry. The model also features additional relativistic degrees of freedom $\Delta N_{\rm eff}$ of either thermal or non-thermal origin, within the reach of cosmic microwave background (CMB) experiment providing a complementary probe in addition to the detection prospects of DM.