Ultra-Heavy Dark Matter Through Exponential Production Mechanism

Exponential production of dark matter has been introduced recently as one of the alternatives to the widely studied thermal production of dark matter scenarios. This non-thermal production mechanism leads to the exponential growth in the abundance of the dark matter ($χ$) through its scatterings with the bath particle ($ξ$), viz. $χ+ ξ\to χ+ χ$. In our framework, we consider a scalar dark matter $χ$ charged under $Z_3$ symmetry and bath particle $ξ$ to be standard model singlet and determine the maximum mass of the dark matter using the criteria of perturbativity. We find that dark matter has an upper mass around the ballpark of $\mathcal{O}(10^{15})$ GeV for the cases when the bath particle mass is similar to the dark matter mass. The computations are largely performed with minimal model dependence and will hold in any scenario where the renormalizable couplings driving the exponential growth effectively reduce to $χ^3ξ$ interactions. Thus, in exponential production of dark matter, we have a possibility of an ultra-heavy dark matter with large couplings, making the scenario phenomenologically interesting. Later, we extend the simplified dark matter model to a UV-complete Dirac Type-I seesaw model where the $Z_3$ symmetry is obtained as a residual unbroken subgroup of a global $U(1)_{B-L}$ symmetry, providing a natural connection with the neutrino sector.