High-energy particle colliders enable the systematic, direct and conclusive exploration of short-distance fundamental physical laws. Point-like particles such as electrons and muons are particularly suited for this purpose because their collision energy is entirely available to produce short-distance reactions. Unlike electrons, muons are sufficiently heavy to be accelerated in a ring without limitation from synchrotron radiation, allowing in line of principle for a 10 or 14 TeV energy muon collider in a ring of the same size of the LHC one, and with the same effective magnetic field.
I will report on ongoing studies about the potential of such a very high energy muon collider to advance knowledge by direct searches for new particles and by precision measurements, and I will outline future directions of theoretical and experimental investigation towards a conclusive assessment of the muon collider physics case. These studies will offer guidance and motivation to the ongoing activity on the accelerator design in the context of the newly-formed International Muon Collider Collaboration.