The Higgs and WIMP DM Lamp Posts for New Weak Scale Physics: EFT Perspectives and the NMSSM

I will show, via effective field theory (EFT) techniques, that obtaining an observationally consistent relic density while evading stringent direct detection limits and maintaining $h_{125}$ phenomenology in an extended Higgs sector can be easily achieved. I will then map such an EFT to the low energy limit of the NMSSM with the Higgsinos integrated out. Both the singlino and the singlet-like CP-odd and even scalars in the NMSSM may play a relevant role in such a scenario, while being difficult to probe via conventional searches. The singlet sector of the general NMSSM can be mapped on to a 2HDM+S, and I will discuss prospects of probing this at the LHC using signatures such as mono-Higgs and mono-Z. This proceeding is mostly based on Refs. arXiv:1712.09873 and arXiv:1808.02667.