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 $g_{\zeta}\equiv g_{BL}Q\simeq0.016\sqrt{m_\zeta[{\rm GeV}]}$ 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. 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 $g_{BL}\geq 2.7\times10^{-8}\sqrt{m_\zeta[{\rm GeV}]}$, one has $g^2_\zeta\,g^2_{BL}+\frac{0.82}{1.2}\,g^4_\zeta\simeq 8.2\times10^{-24}$ and Case (B): for $g_{BL} < 2.7 \times 10^{-8} \sqrt{m_\zeta[{\rm GeV}]}$, there are two separate constraints depending on $m_\zeta$. Case (B1): for $m_\zeta\lesssim 2.5{\rm TeV}$, we find $g_\zeta^2\,g_{BL}^2\simeq 8.2\times10^{-24}\,\left( \frac{m_\zeta}{2.5\,{\rm TeV}} \right)$ 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.
Highlights
Extensions of the standard model (SM) with Uð1ÞB−L as a possible new symmetry of electroweak interactions are well motivated due to their connections to the neutrino mass [1,2] and have recently attracted a great deal of attention
We have considered an extension of the standard model with the gauged Uð1ÞB−L symmetry and a Dirac fermion with arbitrary B − L charge which plays the role of dark matter
The B − L symmetry is broken by a B − L 1⁄4 2 Higgs field so that ZBL picks up a mass and it leads to the seesaw mechanism for neutrino masses
Summary
Extensions of the standard model (SM) with Uð1ÞB−L as a possible new symmetry of electroweak interactions are well motivated due to their connections to the neutrino mass [1,2] and have recently attracted a great deal of attention. We consider the following two gauge coupling parameter ranges of the theory: (i) one where the DM relic density arises via thermal freeze-out, and (ii) the second case where the couplings, gBL and gζ, are so small that the DM particle ζ was never in thermal equilibrium in the early universe with. Early For universe requires the freeze-in case, that we find that the product gBLgζ ≈ 2.9 × 10−12 to satisfy the constraint of the DM relic density This result is independent of the dark matter mass as long as mζ ≳ 2.5 TeV ≫ MZBL. Thermal freeze-out of the dark matter and the constraints on the relevant model parameters from it We combine it with the already existing indirect detection constraints to find new allowed regions for the DM mass for different MZBL values. VI with a discussion of implications of our results and some additional comments
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