http://arxiv.org/abs/1908.11325

We investigate constraints on the new gauge boson ($Z_{BL}$) mass and gauge coupling ($g_{BL}$) in the $U(1){B-L}$ extension of the standard model (SM) with an extra SM singlet Dirac fermion ($\zeta$) which plays the role of dark matter (DM). The DM particle $\zeta$ is a non-singlet under the $B-L$ symmetry with an arbitrarily chosen charge $Q$ to guarantee its stability. We focus on the small mass and small $g{BL}$ regions of the model, and find new constraints for both the cases where the DM relic abundance arises from thermal freeze-out and freeze-in mechanisms. We point out that in the thermal freeze-out case, the dark matter coupling is given by $g_{\zeta}\equiv g_{BL}Q\simeq 0.016\sqrt{m_\zeta[{\rm GeV}]}$ to reproduce the observed DM relic density and $g_{BL}\geq 2.7 \times 10^{-8} \sqrt{m_\zeta[{\rm GeV}]}$ for the DM particle to be in thermal equilibrium prior to freeze-out. In this case, the direct detection constraints put a lower bound on the $Z_{BL}$ mass ($M_{Z_{BL}}$) of about 45 MeV. We find that $Z_{BL}$ mass range up to about 2 GeV with $g_{BL}$ in this region can be probed in the FASER experiment via displaced vertex searches and combined with future improved constraints from the direct detection limits, the $B-L$ gauge extension can be tested in this parameter region. For the freeze-in scenario, there are two possibilities to reproduce the observed DM relic density: $g^2_\zeta \, g^2_{BL} + \frac{18}{37} \, g^4_\zeta \simeq 9.2 \times 10^{-24}$ for $g_{BL}\geq 2.7 \times 10^{-8} \sqrt{m_\zeta[{\rm GeV}]}$, and $g_\zeta \, g_{BL} \simeq 3.0 \times 10^{-12}$ for $g_{BL} < 2.7 \times 10^{-8} \sqrt{m_\zeta[{\rm GeV}]}$, independently of the DM mass. Even for the freeze-in case, the direct detection constraints set a lower bound on, for example, $M_{Z_{BL}} \gtrsim 70$ MeV for the DM mass of 30 GeV. We also discuss the bounds from SN1987A observations on $g_{BL}$.

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R. Mohapatra and N. Okada
Fri, 30 Aug 19
30/58

Comments: 17 pages, 8 figures