Search for Dark Matter in association with a Higgs boson at the LHC: A model independent study

Astrophysical and cosmological observations strongly suggest the existence of Dark Matter\,(DM). Experiments at the Large Hadron Collider\,(LHC) have the potential to probe the particle nature of the DM. In the present work, we investigate the potential of the mono-Higgs plus Missing Transverse Energy signature at the LHC to search for a relatively light fermionic dark matter candidate using the framework of Effective Field Theory. In our study, the DM interacts with the Standard Model\,(SM) via dimension-6 and dimension-7 effective operators involving the Higgs and the gauge bosons. Although, our analysis is independent of any Ultra Violet complete dynamics of DM, such interactions can be realized in an extension of the SM where the gauge group is extended minimally by adding an extra $U(1)$. Both cut-based and Boosted Decision Tree\,(BDT) discriminators are used to estimate and optimize the signal sensitivity over the SM backgrounds, assuming an integrated luminosity of $3000~fb^{-1}$ at $\sqrt{s}=14$ TeV at the High Luminosity phase of the LHC\,(HL-LHC). It can be seen that in the best scenario, atleast $4\sigma$ significance can be achieved for relic masses upto 200 GeV, showcasing the prospects of this search at the HL-LHC. This study provides a foundation for future explorations in this direction.