The problems and physics prospects for a $μ+μ−$ collider

In 1992, a new study of $μ+μ−$ colliders was started at a workshop at Napa, California. Subsequently, many problems have been solved except for two: (1) The best cooling system to use for the machine and (2) the real particle physics needs of such a machine. We argue here that these two issues are related and that the only compelling scientific argument today is for a $μ+μ−$ collider Higgs factory. We show that a 4-TeV collider may not even be the correct high-energy range based on the possible future observations at the LHC and the NLC and the Higgs factory. Such a collider requires very cold $μ±$ beams and will select the cooling method.