Scalar-Mediated Inelastic Dark Matter as a Solution to Small-Scale Structure Anomalies

TL;DR

The paper constructs a scalar-mediated inelastic dark matter model with a hard Z2 symmetry that forbids elastic tree-level scattering. By solving non-perturbative coupled-channel dynamics, it achieves velocity-dependent self-interactions with resonant enhancement that address core-cusp and diversity problems while remaining consistent with CMB, BBN, and cluster constraints. A leptophilic scalar mediator ensures rapid φ decay before BBN, and a dimension-5 dipole operator enables χ2 → χ1γ decays and yields a distinctive 1/ER recoil spectrum for future direct-detection searches. The authors identify a robust benchmark around (mχ, mφ, Δm, α) ≈ (40 GeV, 20 MeV, 100 eV, 0.01), and discuss the discovery potential in next-generation detectors, as well as possible cosmological implications from early-universe phase transitions that could generate gravitational waves.

Abstract

We propose a scalar-mediated Self-Interacting Dark Matter (SIDM) model to address small-scale structure anomalies such as the core-cusp and diversity problems. The model is composed by a leptophilic scalar mediator and a pseudo-Dirac dark matter candidate with a mass splitting of 100 eV.We imposed aA dark discrete $\mathbb{Z}_2$ symmetry forbids tree-level elastic scattering. Therefore creates kinematic threshold that suppresses scattering in ultra-faint satellite galaxies while enabling large self-interaction cross-sections in dwarf galaxies via resonant enhancement. To satisfy Big Bang Nucleosynthesis (BBN) requirements, we introduce a dimension-5 magnetic dipole operator that enable the decay of the excited state ($χ_2 \rightarrow χ_1 γ$). This operator also provides a unique, low-threshold signal for direct detection experiments, characterized by a distinct $1/E_R$ recoil spectrum. We identify a benchmark parameter space around ($m_χ\approx 40$ GeV, $m_φ\approx 20$ MeV) where non-perturbative coupled-channel dynamics successfully reconcile astrophysical observations with cosmological bounds, including CMB constraints on annihilation.

Figures (8)

• Figure 1: Feynman diagrams presenting some of the scatterings and decay processes to investigate: $\chi_1\chi_1\rightarrow\chi_2\chi_2$, the contributor to the inelastic scattering phenomenology (S1); $\chi_1N\rightarrow\chi_2N$, potential nuclear recoil in direct search experiments (S2); the possible elastic scattering below threshold (S3); $\chi_2\rightarrow\chi_1+\gamma$, the decay from excited state DM to stable state (D1); and $\phi\rightarrow e^++e^-$, decay of mediators to positron and electron pairs (D2).
• Figure 2: Combined cosmological and astrophysical constraints on the leptophilic scalar mediator $\phi$. The shaded regions indicate exclusion by: stellar cooling in Horizontal Branch/Red Giant stars (Purple) Hardy:2016kme; free-streaming cooling of SN1987A (Blue) Chang:2018rso; visible decay searches in beam-dump experiments (Green) Liu:2016qwd; and Big Bang Nucleosynthesis (BBN) disruption for lifetimes $\tau_\phi > 1$ s (Orange) Cyburt:2015mya. The gold star marks our benchmark ($m_\phi = 20$ MeV, $g_e = 10^{-6}$), which resides in the SN1987A trapping regime where scalars are trapped in the core and decays promptly ($\tau \ll 1$ s) to ensure BBN safety, while remaining below the sensitivity of past beam-dump searches.
• Figure 3: The discovery window for $M_{\chi}$and $\alpha_s$, combining bounds from relic densityPlanck2018 , non-perturbative limits,below it the non-perturbative treatment failed, and cluster exclusionRandall2008
• Figure 4: The velocity-dependent transport cross-section $\sigma_T/m$ for the scalar inelastic model (Benchmark: $m_\chi=40$ GeV, $\Delta m=100$ eV). The calculation uses the full non-perturbative Schrödinger solution. The cross-section is suppressed in the satellite regime (gray), resonates in the dwarf regime (green), and is suppressed in the cluster regime (red)
• Figure 5: Allowed parameter space from non-perturbative analysis. The color scale indicates the coupling strength $\log_{10}(\alpha)$. The points represent models that satisfy all self-interaction constraints.