Constraints on dark matter interactions from the first results of DarkSide-50

In an extended effective operator framework of isospin violating interactions with light mediators, we investigate the compatibility of the candidate signal of the CDMS-II-Si with the latest constraints from DarkSide-50 and XENON-1T, etc. We show that the constraints from DarkSide-50 which utilizes Argon as the target is complementary to that from XENON-1T which utilizes Xenon. Combining the results of the two experiments, we find that for isospin violating interaction with light mediator there is no parameter space which can be compatible with the positive signals from CDMS-II-Si. As a concrete example of this framework, we investigate the dark photon model in detail. We obtain the combined limits on the dark matter mass $m_{\chi}$, the dark photon mass $m_{A'}$, and the kinetic mixing parameter $\varepsilon$ in the dark photon model. The DarkSide-50 gives more stringent upper limits in the region of mediator mass from 0.001 to 1 GeV, for $m_{\chi} \lesssim 6$ GeV in the ($m_{A'}$,$\varepsilon$) plane, and more stringent constraints for $m_{\chi}\lesssim 8$ GeV and $\varepsilon \thicksim 10^{-8}$ in the ($m_{\chi}$,$m_{A'}$) plane.