Eur. Phys. J. C (2022) 82: 864
https://doi.org/10.1140/epjc/s10052-022-10801-3

Regular Article - Theoretical Physics

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

¹ Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Via Orabona 4, 70126, Bari, Italy
² Department of Physics and Astronomy, University of Alabama, 35487, Tuscaloosa, AL, USA
³ Physics Department, Washington College, 21620, Chestertown, MD, USA
⁴ Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, 19716, Newark, DE, USA

^d draut@udel.edu

Received: 6 January 2022
Accepted: 14 September 2022
Published online: 3 October 2022

Abstract

We consider a $U{(1)}_{B-L}$ model with a $Z^{\prime }$ portal Dirac fermion dark matter (DM) $\chi$ 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 $\chi$ 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, $m_{\chi }\simeq m_{Z^{\prime }}/2$, where $m_{\chi }$ is the DM mass. For the freeze-in scenario, we focus on $m_{\chi }\ll m_{Z^{\prime }}$. We show that for a fixed value of $m_{Z^{\prime }}$, $g_{\mathit{BL}}$ 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 $g_{\mathit{BL}}$ 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 $g_{\mathit{BL}}$ values are found to be much smaller than that in the freeze-out case.