Eur. Phys. J. C (2025) 85: 1224
https://doi.org/10.1140/epjc/s10052-025-14972-7

Regular Article - Theoretical Physics

Dark matter, leptogenesis and $Z^{\prime }$ in the $B-L$ model

Institute of Theoretical Physics, School of Physics, Dalian University of Technology, No.2 Linggong Road, 116024, Dalian, Liaoning, People’s Republic of China

^a qxx@dlut.edu.cn
^b haosun@dlut.edu.cn

Received: 28 July 2025
Accepted: 19 October 2025
Published online: 30 October 2025

Abstract

We discuss the interplay between dark matter, leptogenesis and a new gauge boson $Z^{\prime }$ in the $B-L$ model. A fermion dark matter $\chi$ carrying $U{(1)}_{B-L}$ charge is introduced to the model but not coupling with other particles. We consider the Freeze-out and Freeze-in mechanisms, and obtain the correct relic density respectively. We have scanned the feasible parameter space and found that the dark matter direct detection experiments imposed the most stringent constraints on the parameter space. The constraint on the parameter space places a limit on the mass of dark matter with $m_{\chi }\approx 1/2M_{Z^{\prime }}$ within a narrow region in the case of the Freeze-out scenario, and we can obtain the right baryon asymmetry result in the case of $m_{\chi }\subset [654$ GeV, 664 GeV]. For the Freeze-in scenario, we have a much broader parameter space for $m_{\chi }$ and $M_{Z^{\prime }}$ but $g_{\mathit{BL}}$ is restricted at ${10}^{-5}$ level for $Q=0.1$. In both scenarios, $g_{\mathit{BL}}-M_{Z^{\prime }}$ is limited within a narrow region by the dark matter relic density, direct detection and baryon asymmetry constraints.