Hidden fermion as milli-charged dark matter in Stueckelberg Z' model

TL;DR

The paper extends the Stueckelberg $Z'$ model by introducing a hidden Dirac fermion $\chi$ that couples via a hidden $U(1)_X$, making $Z'$ broadly invisible and enabling $\chi$ to be a milli-charged dark matter candidate. The authors compute the relic density, showing that a thermal cross section $\langle \sigma v \rangle \approx 0.95 \pm 0.08$ pb can be achieved for $g_X$ of weak-like strength and $\delta \sim 0.03$, with annihilation channels including $\chi\bar{\chi} \to Z',Z,\gamma \to f\bar{f}$ and $\chi\bar{\chi} \to V_1 V_2$, and identify two branches in the $(m_\chi,m_{Z'})$ plane. They analyze indirect detection signatures, highlighting potential monochromatic gamma-ray lines from $\chi\bar{\chi}$ annihilation, especially via $\gamma Z'$ when kinematically allowed, and discuss astrophysical uncertainties via the $\overline J$ factor. Collider phenomenology is explored, showing that invisible $Z'$ decays dominate when $m_{Z'}>2m_\chi$, which relaxes Drell–Yan constraints and motivates monojet searches at the LHC and mono-photon searches at the ILC as key discovery channels. Overall, the work links hidden-sector milli-charged DM with testable astrophysical and collider signals, outlining concrete experimental probes across current and next-generation facilities.

Abstract

We augment the hidden Stueckelberg $Z'$ model by a pair of Dirac fermions in the hidden sector, in which the $Z'$ has a coupling strength comparable to weak scale coupling. We show that this hidden fermion-antifermion pair could be a milli-charged dark matter candidate with a viable relic density. Existing terrestrial and astrophysical searches on milli-charged particles do not place severe constraints on this hidden fermion. We calculate the flux of monochromatic photons coming from the Galactic center due to pair annihilation of these milli-charged particles and show that it is within reach of the next generation $γ$-ray experiments. The characteristic signature of this theoretical endeavor is that the Stueckelberg $Z'$ boson has a large invisible width decaying into the hidden fermion-antifermion pair. We show that existing Drell-Yan data do not constrain this model yet. Various channels of singly production of this $Z'$ boson at the LHC and ILC are explored.

Figures (7)

• Figure 1: (a)--(b) are contours of $\sigma v$ = $0.95 \pm 0.16$ pb (2 $\sigma$ range) in the plane of $(g_X,\, \delta)$ for various $m_{Z'}$ and $m_{\chi}$. Part (c) shows the annihilation rate $\sigma v$ versus $m_\chi$ with $m_{Z'} = 500$ GeV, $g_X = g_2$, and $\delta = 0.03$. Part (d) shows the contour of $\sigma v$ = $0.95 \pm 0.16$ pb (2 $\sigma$ range) in the $(m_\chi, m_{Z'})$ plane.
• Figure 2: The resulting photon flux from annihilation processes $\chi \bar{\chi} \to \gamma \gamma$, $\gamma Z$, and $\gamma Z'$. We have used typical values of ${\overline J} =100$, $\Delta \Omega = 10^{-3}$, and the present value of $v \approx 10^{-3}$.
• Figure 3: Branching ratios for $Z'$ with $g_X= g_2$, $\delta = 0.03$, and $m_\chi = 60$ GeV.
• Figure 4: Comparison with the DELPHI data on the mono-photon production. The theory prediction is for $g_X = g_2$ and $\delta = 0.03$.
• Figure 5: Drell-Yan cross sections $p \bar{p} \to Z' \to e^- e^+$ versus $m_{Z'}$ for $g_X = g_2$ and $\delta = 0.03$. We also show the 95% C.L. upper limits on $\sigma(Z')\cdot B(Z' \to e^- e^+)$ from the CDF preliminary results cdf-z.