Light mediators in dark matter direct detections

In an extended effective operator framework, we investigate in detail the effects of light mediators on the event spectra of dark matter (DM)-nucleus scatterings. The presence of light mediators changes the interpretation of the current experimental data, especially the determination of DM particle mass. We show by analytic and numerical illustrations that for all the operators relevant to spin-independent scatterings, the DM particle mass allowed by the data increases significantly when the mediator particle becomes lighter. For the data of CDMS-II-Si, the allowed DM particle mass can reach $\sim 50$ GeV, depending on the type of operators, and the increase of DM particle mass saturates when the mediator mass is below $\mathcal{O}(10)$ MeV. The upper limits from other experiments such as SuperCDMS, CDMSlite, CDEX, XENON10/100, LUX, PandaX etc. all tend to be weaker toward high DM mass regions. In a combined analysis, we show that the presence of light mediators can partially relax the tension in the current results of CDMS-II-Si, SuperCDMS and LUX.