Strong constraints of LUX-2016 results on the natural NMSSM

Given the fact that the relatively light Higgsino mass $\mu$ favored in natural supersymmetry usually results in a sizable scattering cross section between the neutralino dark matter and the nucleon, we study the impact of the recently updated direct detection bounds from LUX experiment, including both Spin Independent (SI) and Spin Dependent (SD) measurements, on the parameter space of natural Next-to-Minimal Supersymmetric Standard Model (nNMSSM). Different from the common impression that the SI bound is stronger than the SD one, we find that the SD bound is complementary to the SI bound and in some cases much more powerful than the latter in limiting the nNMSSM scenarios. After considering the LUX results, nNMSSM is severely limited, e.g. for the peculiar scenarios of the NMSSM where the next-to-lightest CP-even Higgs corresponds to the $125 {\rm GeV}$ Higgs boson discovered at the LHC, the samples obtained in our random scan are excluded by more than $85\%$. By contrast, the monojet search at the LHC Run-I can not exclude any sample of nNMSSM. We also investigate the current status of nNMSSM and conclude that, although the parameter points with low fine tuning are still attainable, they are distributed in some isolated parameter islands which are difficult to get. Future dark matter direct search experiments such as XENON-1T will provide a better test of nNMSSM.