[Paper Review] Hidden Fermion in Stueckelberg Z' Models as Milli-charged Dark Matter

Kingman Cheung, Tzu-Chiang Yuan|ArXiv.org|Oct 10, 2007

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper proposes a hidden Dirac fermion in a Stueckelberg $Z'$ model as a viable milli-charged dark matter candidate with a relic density consistent with WMAP data. The $Z'$ boson acquires a large invisible width via decay into the fermion pair, enabling detectable monojet+missing energy signals at the LHC and single-photon+missing energy at the ILC, while the fermion pair annihilation produces a monochromatic gamma-ray line near the Galactic center, potentially observable in next-generation gamma-ray experiments.

ABSTRACT

The hidden Stueckelberg Z' model is augmented by a pair of Dirac fermions. If the Z' has a coupling strength comparable to weak scale coupling, one can show that this hidden fermion-antifermion pair could be a milli-charged dark matter candidate with a viable relic density. Monochromatic photon flux coming from the Galactic center due to pair annihilation of these milli-charged particles is calculated and is shown to be within reach of the next generation gamma-ray experiments. Characteristic collider signature of this theoretical endeavor is that the Stueckelberg Z' boson has a large invisible width decaying into the hidden fermion-antifermion pair if kinematically allowed. Singly production of this Z' boson at the LHC and ILC are studied.

Motivation & Objective

• To explore the phenomenology of a hidden Dirac fermion-antifermion pair in a Stueckelberg $Z'$ model as a dark matter candidate.
• To investigate the cosmological viability of the hidden fermion as a milli-charged dark matter candidate with a relic density matching WMAP observations.
• To examine collider signatures of the $Z'$ boson decaying into the hidden fermion pair, particularly large invisible widths and monojet/mono-photon signals.
• To assess the detectability of a monochromatic gamma-ray line from $ar{ u} u$ annihilation at the Galactic center using next-generation gamma-ray experiments.
• To determine the compatibility of the model with existing electroweak precision data and collider constraints.

Proposed method

• Augment the Stueckelberg $Z'$ model with a pair of Dirac fermions, introducing a non-zero hidden current $\mathcal{J}_X^\mu = \bar{\chi}\gamma^\mu Q_X^\chi \chi$.
• Diagonalize the neutral gauge boson mass matrix to derive mixing angles and compute effective couplings of the hidden fermion to the photon, $Z$, and $Z'$ bosons.
• Calculate the $Z'$ invisible width via $Z' \to \chi\bar{\chi}$, showing it becomes GeV-scale when kinematically allowed, contrasting with the typical MeV-scale width in models with $\mathcal{J}_X = 0$.
• Compute the relic density of the hidden fermion using thermal freeze-out, showing it matches WMAP constraints when $g_X Q_X^\chi \sim g_2$.
• Evaluate the monochromatic photon flux from $\chi\bar{\chi} \to Z'\gamma$ and $\gamma\gamma$ processes at the Galactic center, using the $J$-factor from dark matter halo profiles.
• Simulate collider signals: $pp \to Z' + \text{jet} \to \chi\bar{\chi} + \text{jet}$ at the LHC and $e^+e^- \to Z'\gamma \to \chi\bar{\chi} + \gamma$ at the ILC, applying realistic cuts on jet and photon energy.

Experimental results

Research questions

• RQ1 Can a hidden Dirac fermion in a Stueckelberg $Z'$ model serve as a viable milli-charged dark matter candidate with a relic density consistent with WMAP data?
• RQ2 What are the collider signatures of the $Z'$ boson when it decays into a pair of hidden fermions, particularly in terms of large invisible widths and monojet/mono-photon signals?
• RQ3 To what extent can the monochromatic gamma-ray line from $\chi\bar{\chi}$ annihilation at the Galactic center be detected by future gamma-ray experiments?
• RQ4 How does the inclusion of a non-zero hidden current affect the $Z'$ width and its phenomenological constraints from LEP and Tevatron data?
• RQ5 What are the implications of the $Z'$ having a dominant invisible decay mode into $\chi\bar{\chi}$ for searches at the LHC and ILC?

Key findings

• The hidden fermion acquires a milli-charge $\epsilon^\chi_\gamma / e \sim 10^{-3}$ due to mixing with the photon, making it a viable milli-charged dark matter candidate.
• The $Z'$ boson has a large invisible width of order GeV when $Z' \to \chi\bar{\chi}$ is kinematically allowed, significantly increasing its detectability at colliders compared to narrow $Z'$ models.
• The relic density of the hidden fermion is consistent with WMAP data when $g_X Q_X^\chi \sim g_2$, indicating a viable thermal dark matter candidate.
• The monochromatic photon flux from $\chi\bar{\chi} \to Z'\gamma$ can reach $1.9 \times (\text{TeV}/m_\chi)^2 \times (10^{-14} - 10^{-13})\ \text{cm}^{-2}\text{s}^{-1}$ for $m_\chi < 300\ \text{GeV}$, placing it within the sensitivity range of GLAST and HESS2.
• The LHC signal $pp \to Z' + \text{jet} \to \chi\bar{\chi} + \text{jet}$ with monojet + missing energy is viable for $m_{Z'} \sim 300\ \text{GeV}$ and $m_\chi \sim 60\ \text{GeV}$, with cross sections above the discovery threshold.
• The ILC signal $e^+e^- \to Z'\gamma \to \chi\bar{\chi} + \gamma$ has a detectable cross section for $m_{Z'} \sim 300\ \text{GeV}$ and $\sqrt{s} = 1.5\ \text{TeV}$, with $E_\gamma > 10\ \text{GeV}$ and $\cos\theta_\gamma \in (-1,1)$, making it a promising probe of the model.