Reviving $Z^\prime$ Portal Dark Matter with Conversion Mechanism

TL;DR

This work examines a $Z'$ portal dark matter model based on gauged $U(1)_{B-L}$ featuring two nearly degenerate dark fermions, $\tilde{\chi}_1$ and $\tilde{\chi}_2$, with a small mixing term $\delta m$ that yields mass eigenstates $\chi_1$ (DM) and $\chi_2$. With a compressed spectrum, relic density can be controlled by coscattering $\chi_2f\to\chi_1f$, conversion $\chi_2\chi_i\to\chi_1\chi_j$, and coannihilation $\chi_1\chi_2\to f\bar{f}$, while a small mixing angle $\theta$ suppresses the $Z'$ coupling of DM, producing distinctive collider and cosmological signatures. The paper analyzes two production regimes—resonance (where $m_{Z'}$ is near the $2m_{\chi_2}$ threshold) and secluded (where $m_{Z'}<m_{\chi_{1,2}}$)—and performs a comprehensive scan of the parameter space using micrOMEGAs to calculate relic densities and phenomenology. It finds that conversion is favored under current collider and cosmological constraints in both scenarios, while coscattering is heavily constrained in the resonance case but gains visibility in the secluded case. The results emphasize the complementary roles of collider searches, direct/indirect detection, and CMB observations in testing these novel DM production mechanisms and outline promising regions for future experiments.

Abstract

In many new physics models with extended gauge symmetry, the new gauge boson $Z'$ could mediate the interactions between the dark matter and standard model particles. For the conventional $Z^\prime$ portal dark matter, the collider and the direct detection constraints typically pose a significant challenge. To address this pressing issue, we present in this paper a new benchmark model based on the gauged $U(1)_{B-L}$ symmetry, which introduces a Dirac dark fermion $\tildeχ_1$ and a heavier partner $\tildeχ_2$ with zero and nonzero $U(1)_{B-L}$ charge, respectively. Including the mass term $δm \bar{\tildeχ}_1\tildeχ_2$ results in the dark fermions $χ_1$ and $χ_2$ in the mass eigenstate, where the lighter one $χ_1$ is regarded as the dark matter candidate. Various intriguing processes for the relic density arise with the compressed mass spectrum $m_{χ_1}\simeq m_{χ_2}$, such as the coscattering $χ_2f\toχ_1f$, the conversion $χ_2χ_i\toχ_1χ_j$, and the coannihilation $χ_1χ_2\to f\bar{f}$ processes. Suppressed by the small mixing angle $θ$ between the dark fermions, the small effective gauge coupling of dark matter $χ_1$ to the gauge boson $Z'$ is one distinct feature of this model, rendering phenomenology in many aspects more promising. In this paper, we investigate the production of dark matter through new mechanisms within the frameworks of resonance and secluded scenarios. The impacts of phenomenological constraints from collider, dark matter, and cosmology are also taken into account. We report that the conversion mechanism is both favored by the resonance and secluded scenarios under current constraints.

Figures (10)

• Figure 1: The evolutions of various abundances $Y_i$ for (a) coscattering, (b) conversion , and (c) coannihilation benchmarks in the resonance scenario. The subfigures (d), (e), and (f) on the right correspond to the thermal rates of various reaction processes in three different phases. We fix $\Delta_\chi=10^{-2}$, $r_{Z^\prime}=2$ and $\theta=5\times10^{-4}$. The solid green and red lines in (a)-(c) represent the abundance of $\chi_1$ and $\chi_2$, meanwhile the dashed lines are their thermal equilibrium. Purple dotdashed cruve is the observation of DM $\Omega_{\chi_1}h^2=0.12$Planck:2018vyg. In subfigures (d)-(f), the black vertical dashed line corresponds to the thermal decoupling temperature when $Y_{\chi_1}/Y_{\chi_1}^{\rm eq}=2.5$, and the horizontal black line is $\Gamma_i=\mathcal{H}$. Moreover, $\chi_i \chi_2\to \chi_j \chi_1$ is the sum of conversion channels $\chi_2\chi_2\to\chi_1\chi_1$, $\chi_1\chi_2\to\chi_1\chi_1$ and $\chi_2\chi_2\to\chi_1\chi_2$.
• Figure 2: Constraints on the $m_{Z^\prime}-g^\prime$ parameter space in the resonance scenario. Panels (a)-(d) correspond to different selections with fixed parameters. Each panel features red, green, and blue lines representing three distinct benchmarks, all of which are consistent with DM observation. The solid, dashed, and dot-dashed parts on each line correspond to coscattering, conversion, and coannihilation phases, respectively. The gray shaded area indicates the current exclusion on $Z^\prime$ by various colliders. The future sensitivities of Belle II, FCC-ee, CMS, and ATLAS are illustrated by the orange, pink, and purple dashed lines, respectively. The orange shaded areas appearing in (b), (c) and (d) indicate the promising coannihilation region that can be probed by future CMB on long lived $\chi_2$.
• Figure 3: The constraints of direct detection experiments in the resonance scenario. The fixed parameters in subfigures (a)-(d), as well as the selections of benchmarks in each panel, are consistent with those presented in Figure \ref{['FIG:fig2']}. The solid, dashed, and dot-dashed components of each benchmark line still correspond to coscattering, conversion, and coannihilation phases. The orange region and dashed line represent the results of current and future direct detection experiments.
• Figure 4: The constraints of indirect detection experiments in the resonance scenario. The legends of panels (a)-(d) and markers of benchmark lines are consistent with those in Figure \ref{['FIG:fig2']}. The purple region is not permitted by the existing constraints of indirect detection experiments, meanwhile the projected sensitivity of future experiments is represented as a purple dashed line.
• Figure 5: Cosmological constraints on long-lived $\chi_2$ in the resonance scenario. The horizontal axis represents the lifespan of $\chi_2$, while the vertical axis indicates the relative relic density. Here, $f_e$ is the branching ratio of $\chi_2$ decay to $e^+e^-$ final state, and $\epsilon=(m_{\chi_2}^2-m_{\chi_1}^2)/2m_{\chi_2}^2$ is the fraction of the energy of $\chi_2$ that has been transferred to electron. The legends of panels (a)-(d) and markers of benchmark lines are consistent with those in Figure \ref{['FIG:fig2']}. The gray area is excluded by BBN, and the orange dashed line represents the future CMB results.