Light $Z^{\prime }$ and Dirac fermion dark matter in the $B-L$ model

Abstract

We consider a $U(1{)}_{B-L}$ model with a $Z^{\prime }$ portal Dirac fermion dark matter (DM) $\ddot{I}‡$ of low mass which couples very weakly to the $B-L$ gauge boson $Z^{\prime }$. An arbitrary $B-L$ charge $Q\ne \pm 1,\pm 3$ of the DM $\ddot{I}‡$ ensures its stability. Motivated by the sensitivity reach of forthcoming "Lifetime Frontier" experiments, we focus on the $Z^{\prime }$ mass, $m_{Z^{\prime }}$, in the sub-GeV to few GeV range. To evaluate the DM relic abundance, we examine both the freeze-out and freeze-in DM scenarios. For the freeze-out scenario, we show that the observed DM abundance is reproduced near the $Z^{\prime }$ resonance, $m_{\ddot{I}}‡\simeq m_{Z^{\prime }}/2$, where $m_{\ddot{I}}‡$ is the DM mass. For the freeze-in scenario, we focus on $m_{\ddot{I}}‡\ll m_{Z^{\prime }}$. We show that for a fixed value of $m_{Z^{\prime }}$, $g_{BL}$ values roughly scale as $1/Q$ to reproduce the observed DM abundance. For various $Q$ values in the range between $10^{-6}$ and $10^2$, we show that the gauge coupling values $g_{BL}$ needed to reproduce the observed DM abundance lie in the search reach of future planned and/or proposed experiments such as FASER, Belle-II, LDMX, and SHiP. In the freeze-in case, the $Q$ values to realize observable $g_{BL}$ values are found to be much smaller than that in the freeze-out case.

14 pages, 3 figures, revised section III with new Figure 1