Dark Matter Constraints on Low Mass and Weakly Coupled B-L Gauge Boson

Abstract

We investigate constraints on the new $B-L$ gauge boson ($Z_{BL}$) mass and coupling ($g_{BL}$) in a $U(1{)}_{B-L}$ extension of the standard model (SM) with an SM singlet Dirac fermion ($\zeta$) as dark matter (DM). The DM particle $\zeta$ has an arbitrary $B-L$ charge $Q$ chosen to guarantee its stability. We focus on the small $Z_{BL}$ mass and small $g_{BL}$ regions of the model, and find new constraints for the cases where the DM relic abundance arises from thermal freeze-out as well as freeze-in mechanisms. In the thermal freeze-out case, the DM coupling is given by $g_{\zeta }\equiv g_{BL}Q\simeq 0.016\sqrt{m_{\zeta }[\mathrm{GeV}]}$ to reproduce the observed DM relic density and $g_{BL}\ge 2.7\times 10^{-8}\sqrt{m_{\zeta }[\mathrm{GeV}]}$ for the DM particle to be in thermal equilibrium prior to freeze-out. Combined with the direct and indirect DM detection constraints, we find that the allowed mass regions are limited to be $m_{\zeta }\gtrsim 200$ GeV and $M_{Z_{BL}}\gtrsim 10$ GeV. We then discuss the lower $g_{BL}$ values where the freeze-in scenario operates and find the following relic density constraints on parameters depending on the $g_{BL}$ range and dark matter mass: Case (A): for $g_{BL}\ge 2.7\times 10^{-8}\sqrt{m_{\zeta }[\mathrm{GeV}]}$, one has $g_{\zeta }^2{g}_{BL}^2+\frac{0.82}{1.2}{g}_{\zeta }^4\simeq 8.2\times 10^{-24}$ and Case (B): for $g_{BL}<2.7\times 10^{-8}\sqrt{m_{\zeta }[\mathrm{GeV}]}$, there are two separate constraints depending on $m_{\zeta }$. Case (B1): for $m_{\zeta }\lesssim 2.5\mathrm{TeV}$, we find $g_{\zeta }^2{g}_{BL}^2\simeq 8.2\times 10^{-24}\left(\frac{m_{\zeta }}{2.5\mathrm{TeV}}\right)$ and case (B2): for $m_{\zeta }\gtrsim 2.5$ TeV, we have $g_{\zeta }^2{g}_{BL}^2\simeq 8.2\times 10^{-24}$. For this case, we display the various parameter regions of the model that can be probed by a variety of ``Lifetime Frontier" experiments such as FASER, FASER2, Belle II, SHiP and LDMX.

27 pages, 8 figures, the version to be published in Phys. Rev. D

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