Exploring muonphilic dark matter with the $Z_2$-even mediator at muon colliders

TL;DR

This study investigates muonphilic dark matter with a $Z_2$-even mediator at a future $3$ TeV muon collider, aiming to explain the Galactic Center GeV excess while fitting relic abundance and evading direct-detection constraints. It analyzes seven renormalizable $Z_2$-even mediator models with DM spins ${\\chi}$, ${S}$, or ${X^\\mu}$, focusing on non-resonant parameter regions and three collider search channels: visible on-shell mediator decays, invisible on-shell mediator decays, and mono-photon production via off-shell mediators. Using a full signal-background pipeline (FeynRules, MadGraph5_aMC@NLO, Pythia8, Delphes) and a cut-based analysis, the paper projects 95% CL exclusions across mediator masses from $20$ GeV to $1.5$ TeV, showing that a muon collider can probe significant portions of the viable GCE-compatible parameter space with sensitivities down to $g_D g_f \sim O(10^{-5})$ (visible), $M_{D\phi} g_f \sim O(10^{-6}-10^{-5})$ (scalar/vector DM, visible), and complementary reach in the other channels. The results demonstrate the collider’s unique capability to directly test the muonphilic DM hypothesis, providing precision measurements of the DM–muon coupling and mediator mass that complement indirect detection and direct-detection constraints, even when accounting for a conservative $5\%$ background systematic. Overall, the work establishes a future muon collider as a powerful probe of muon-specific DM explanations for the GCE and related relic-density considerations.

Abstract

The Galactic Center GeV Excess (GCE) remains a compelling but enigmatic signal from the inner region of our galaxy. Muonphilic dark matter (DM), which couples exclusively to muons via a new mediator, provides a viable explanation for the GCE and relic density while naturally evading constraints from direct detection, collider searches and other multi-messenger observations. Based on the viable non-resonant parameter space identified in previous global fits, we perform a comprehensive study exploring the prospects for discovering such muonphilic DM in the context of a future $3$ TeV muon collider, focusing on simplified models with a $Z_2$-even mediator. Three distinct search strategies are investigated: visible on-shell mediator decays ($μ^{+}μ^{-}γ$ final state), invisible on-shell mediator decays (mono-photon plus missing energy), and mono-photon production via off-shell mediators. Through a detailed signal-background analysis using cut-and-count methods, we project the exclusion limits at $95\%$ confidence level for seven representative models across a wide range of mediator masses. Our results demonstrate that the projected limits cover a significant portion of the viable parameter space that explains the GCE, establishing a muon collider as a decisive machine for testing the muonphilic DM hypothesis.

Figures (12)

• Figure 1: The parameter space for relevant simplified muonphilic DM models with $M < 2m_D$, based on Ref. Abdughani:2021oit, is shown here. The left panel depicts $\mathcal{L}_3$, $\mathcal{L}_4$ and $\mathcal{L}_8$, while the right panel covers $\mathcal{L}_9$, $\mathcal{L}_{10}$, $\mathcal{L}_{13}$ and $\mathcal{L}_{14}$. For comparison, three benchmark ratios of mediator to DM mass are displayed: $M/m_D = 1.1$ (black-solid), $M/m_D = 1.5$ (blue-dashed) and $M/m_D = 1.9$ (red-dotted).
• Figure 2: Visible on-shell mediator decays of the $\mathcal{L}_3$ model, representative kinematic distributions include photon energy $E({\gamma})$ (top-left), photon pseudorapidity $\eta({\gamma})$ (top-right), $\mu^-$ transverse momentum $p_T(\mu^-)$ (middle-left), $\mu^-$ pseudorapidity $\eta(\mu^-)$ (middle-right), $\Delta R$ of a muon pair (bottom-left), and invariant mass $M(\mu^+\mu^-)$ of a muon pair (bottom-right) for signal-1 ($M = 50$ GeV, blue-dotted line), signal-2 ($M = 500$ GeV, green-dotted line), signal-3 ($M = 900$ GeV, black-dotted line), signal-4 ($M = 1300$ GeV, purple-dotted line) and background (red-solid line).
• Figure 3: In the invisible on-shell mediator decay scenario ($M/m_D=2.5$) of the $\mathcal{L}_3$ model, representative kinematic distributions include photon energy $E({\gamma})$ (top-left), missing transverse energy ${\:/\!\!\!\! E}_T$ (top-right), missing energy ${\:/\!\!\!\! E}$ (bottom-left), and the ratio of $P_T(\gamma)/{\:/\!\!\!\! E}$ (bottom-right) for signal-1 ($M = 50$ GeV, blue-dotted line), signal-2 ($M = 500$ GeV, green-dotted line), signal-3 ($M = 900$ GeV, black-dotted line), signal-4 ($M = 1300$ GeV, purple-dotted line) and background (red-solid line).
• Figure 4: In the off-shell mediator scenario of the $\mathcal{L}_3$ model with $m_D=20$ GeV, representative kinematic distributions include photon energy $E({\gamma})$ (top-left), missing transverse energy ${\:/\!\!\!\! E}_T$ (top-right), missing energy ${\:/\!\!\!\! E}$ (bottom-left), and the ratio of $P_T(\gamma)/{\:/\!\!\!\! E}$ (bottom-right) for signal-1 ($M/m_D=1.1$, blue-dotted line), signal-2 ($M/m_D=1.5$, green-dotted line), signal-3 ($M/m_D=1.9$, black-dotted line), and background (red-solid line).
• Figure 5: Similar to Fig. \ref{['fig:L3_20_offshell']}, but for the $\mathcal{L}_3$ model with $m_D = 100$ GeV.