Effective Dark Matter Model: Relic density, CDMS II, Fermi LAT and LHC

TL;DR

This work develops an effective field theory approach to dark matter interactions with the Standard Model by introducing a DM field D and a set of dimension-6 operators that couple D to SM fields at a heavy scale $\Lambda$. It maps the viable parameter space by enforcing the observed relic density $\Omega_{DM}h^{2}$ and confronts direct detection constraints from CDMS II/XENON, indirect gamma-ray data from Fermi-LAT, and LHC prospects across fermionic, scalar, and vector DM scenarios, deriving operator-specific relationships between $m_{D}$ and $\Lambda$ and predicting collider signatures such as mono-photon and mono-jet channels. The results show that fermionic DM can simultaneously satisfy relic, direct/indirect, and collider constraints with TeV-scale $\Lambda$ and $m_{\chi}$ in the few hundred GeV to multi-TeV range, while scalar and vector DM face tighter restrictions, with vector DM being largely excluded if CDMS II hints hold. The study demonstrates the power of a unified EFT framework to connect cosmological relic abundance with multi-messenger and collider observables, guiding UV completions and informing search strategies at the LHC and future detectors.

Abstract

The Cryogenic Dark Matter Search recently announced the observation of two signal events with a 77% confidence level. Although statistically inconclusive, it is nevertheless suggestive. In this work we present a model-independent analysis on the implication of a positive signal in dark matter scattering off nuclei. Assuming the interaction between (scalar, fermion or vector) dark matter and the standard model induced by unknown new physics at the scale $Λ$, we examine various dimension-6 tree-level induced operators and constrain them using the current experimental data, e.g. the WMAP data of the relic abundance, CDMS II direct detection of the spin-independent scattering, and indirect detection data (Fermi LAT cosmic gamma-ray), etc. Finally, the LHC reach is also explored.

Figures (22)

• Figure 1: Pictorial illustration of our EFT model, in which the SM particles interact with the (unknown) DM particles through the new physics which appears at the scale $\Lambda$.
• Figure 2: Feynman diagrams for $\chi\bar{\chi}$ annihilations. Blobs denote the effective vertices induced by the dim-6 operators.
• Figure 3: Allowed parameter set $\left(m_{\chi},\Lambda\right)$ for a universal coupling constant $\alpha$ when DM is a fermion. The upper (lower) boundary of each band corresponds to the upper (lower) limit of $\Omega_{DM}h^{2}$.
• Figure 4: Prediction of the fermionic DM-nucleon cross sections with respect to $m_{\chi}$ and $\Lambda$ for allowed parameter set given in Fig. \ref{['fig:fermion']}; (a, b) for the spin-independent DM search; (c, d) for the spin-dependent DM search. The red (green, blue) band denotes the cross section for $\alpha_{\chi q}^{L}=1$ ($\alpha_{\chi q}^{R}=1$, $\alpha_{\phi\chi}=1$), respectively, when one operator is considered at a time. The gray shaded region denotes the cross sections when all these three operators contribute, which corresponds to the black band in Fig. \ref{['fig:fermion']}; see the text for details. In the upper panel, the blue-solid (red-solid) line labels the upper limit ($90\%$ confidence level) on the SI DM-nucleon scattering cross section from the current XENON10 (CDMS II 2009) direct search, respectively. The black-dashed line denotes the near term expected sensitivity from the CDMS II experiment, whereas the blue-dotted (red-dotted) line represents the longer term projection for the Super-CDMS Phase-A (Phase-C), respectively.
• Figure 5: (a) Predicted gamma-ray spectra for the annihilation of fermionic DM $\chi$ (solid lines) with the NFW density profile. The Fermi LAT observation (Galactic background) is also presented by the red-box (grey-solid line); (b) Comparison between the DM signal plus background and the Fermi LAT observation. Note that a common boost factor of 20 is applied to all the DM signals; (c) The comparison between the DM signal with the difference of Fermi LAT observation and background. The different boost factors are adopted for different DM masses so that the DM signal will not exceed the data.