Weakly interacting massive particles are a widely well-probed dark matter candidate by the dark matter direct detection experiments. Theoretically, there are a large number of ultraviolet completed models that consist of a weakly interacting massive particle dark matter. The variety of models makes the comparison with the direct detection data complicated and often non-trivial. To overcome this, in the non-relativistic limit, the effective theory was developed in the literature which works very well to significantly reduce the complexity of dark matter-nucleon interactions and to better study the nuclear response functions. In the effective theory framework for a spin-1/2 dark matter, we combine three independent likelihood functions from the latest PandaX, LUX, and XENON1T data, and give a joint limit on each effective coupling. The astrophysical uncertainties of the dark matter distribution are also included in the likelihood. We further discuss the isospin violating cases of the interactions. Finally, for both dimension-five and dimension-six effective theories above the electroweak scale, we give updated limits of the new physics mass scales.

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The cosmic electron energy spectrum recently observed by the DAMPE experiment exhibits two interesting features, including a break around 0.9 TeV and a sharp resonance near 1.4 TeV. In this analysis, we propose a dark matter explanation to both exotic features seen by DAMPE. In our model, dark matter annihilates in the galaxy via two different channels that lead to both a narrow resonance spectrum near 1.4 TeV and electron excess events over an extended energy range thus generating the break structure around TeV. The two annihilation channels are mediated by two gauge bosons that interact both with dark matter and with the standard model fermions. Dark matter annihilations through the s-channel process mediated by the heavier boson produce monoenergetic electron-positron pairs leading to the resonance excess. The lighter boson has a mass smaller than the dark matter such that they can be on-shell produced in dark matter annihilations in the galaxy; the lighter bosons in the final state subsequently decay to generate the extended excess events due to the smeared electron energy spectrum in this process. We further analyze constraints from various experiments, including HESS, Fermi, AMS, and LHC, to the parameter space of the model where both excess events can be accounted for. In order to interpret the two new features in the DAMPE data, dark matter annihilation cross sections in the current galaxy are typically much larger than the canonical thermal cross section needed for the correct dark matter relic abundance. This discrepancy, however, is remedied by the nonperturbative Sommerfeld enhancement because of the existence of a lighter mediator in the model.where we use R = 3.5 kpc, α = 2, β = 2 and γ = 0 [63]. The value of ρ s in all the above profiles are chosen such that the local DM density is normalized to ρ χ (8.5 kpc) = 0.39 GeV/cm 3 . We compute the HESS J-factors for these DM profiles using Eq. (6.2) J NFW = 2.25 × 10 21 GeV 2 /cm 5 , J E = 4.41 × 10 21 GeV 2 /cm 5 , J iso = 7.23 × 10 19 GeV 2 /cm 5 .(A.4)HESS collaboration [54] provides the J-factors for two profiles: J NFW = 2.67×10 21 GeV 2 /cm 5 and J E = 4.92 × 10 21 GeV 2 /cm 5 . Thus our calculation here yields slightly smaller J-factors than HESS. We use the J NFW and J E values provided by HESS [54] in the rescaling method to be described in Appendix (B). Because the J-factor for the isothermal profile is not given explicitly by HESS [54], we use our calculated J iso value in the analysis.

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