Dark matter actually can interact with normal matter. The only constraint is that it can't interact neither electromagnetically nor via standard strong interactions. Gravity is left, as well as the weak interactions. Many of the dark matter direct detection experiments and have been designed to target a specific class of dark matter candidates that are expected to interact via weak interactions.
At the LHC is work the same, dark matter can be produced via weak interactions, or via a fifth force if both the Standard Model particles and dark matter are sensible to a fifth force.
I hope I clarified! Otherwise please let me know! :)
Thanks I didn't know that dark matter interact via the weak force and I do hope that there is a fifth force. This will open up some new areas in physics!
Was dark matter first speculated in the LHC or during the observations of clusters of galaxies?
The idea is almost 85 years, although the word dark matter is more than 100 years old (I am actually planning to write on this in my next post. but it is not ready yet). The LHC is just one of the numerous ways to track dark matter.