Dark Matter signals at the LHC from a 3HDM

We analyse new signals of Dark Matter (DM) at the Large Hadron Collider (LHC) in a 3-Higgs Doublet Model (3HDM) where only one doublet acquires a Vacuum Expectation Value (VEV), preserving a parity $Z_2$. The other two doublets are inert and do not develop a VEV, leading to a dark scalar sector controlled by $Z_2$, with the lightest CP-even dark scalar $H_1$ being the DM candidate. This leads to the loop induced decay of the next-to-lightest scalar, $H_2\to H_{1}f\overline{f}$ ($f=u,d,c,s,b,e,\mu ,\tau$), mediated by both dark CP-odd and charged scalars. This is a smoking-gun signal of the 3HDM since it is not allowed in the 2HDM with one inert doublet and is expected to be important when $H_2$ and $H_1$ are close in mass. In practice, this signature can be observed in the cascade decay of the SM-like Higgs boson, $h\to H_1{H}_2\to H_1{H}_{1}f\overline{f}$ into two DM particles and di-leptons/di-jets, where $h$ is produced from either gluon-gluon Fusion (ggF) or Vector Boson Fusion (VBF). However, this signal competes with the tree-level channel $q\overline{q}\to H_1{H}_1{Z}^{\ast }\to H_1{H}_{1}f\overline{f}$. We devise some benchmarks, compliant with collider, DM and cosmological data, for which the interplay between these modes is discussed. In particular, we show that the resulting detector signature, ${\overline{)E}}_{T}f\overline{f}$, with invariant mass of $f\overline{f}$ much smaller than $m_Z$, can potentially be extracted already during Run 2 and 3. For example, the $H_2\to H_1{\gamma }^{\ast }$ and ${\gamma }^{\ast }\to e^{+}{e}^{-}$ case will give a spectacular QED mono-shower signal.