Chapter 5: Bright muon beams and muon colliders

The muon collider offers a path toward high-energy, high-luminosity lepton collisions that extends beyond the expected reach of electron-positron colliders and would be competitive in physics reach with proton colliders at the highest energies. Nonetheless, several challenging elements of muon collider technology must be more fully addressed to achieve a maturity level commensurate with linear colliders. In this chapter, the potential benefits of a muon collider in terms of cost, sustainability and timescale are outlined. The major remaining technical challenges are described and an R&D; programme is outlined. This programme, assuming suitable funding, will enable the next Update of the European Strategy for Particle Physics to make informed decisions regarding the future R&D; path for lepton colliders.