Dark coloured scalars impact on single and di-Higgs production at the LHC

The search for Dark Matter (DM) at colliders is primarily pursued via the detection of missing energy in particular final states. These searches are based on the production
and decay processes where final states include DM particles and at least one Standard Model (SM) particle. DM will then reveal itself as missing energy. An alternative form to get a hint of a dark sector is via loop contribution to SM processes. In this case, it is not even relevant if the new particles have their origin in the dark sector of the model. In this work we discuss the impact of an arbitrary number of coloured scalars with Z$_2$ -odd parity in single Higgs and double Higgs production at the Large Hadron Collider (LHC), and we show their complementarity. We determine the range of variation of the corrections relative to the SM for an arbitrary number of coloured scalars n. We discuss the cases n = 1 and n = 2 for a specific model in more detail, which includes direct searches at the LHC. We also find that the electroweak
observable T parameter imposes significant restrictions on the difference of the heavy coloured scalar masses.