Physics motivations for a muon collider

Future muon colliders will have remarkable capability for revealing and studying physics beyond the Standard Model. A first muon collider with variable c.m.\ energy in the range \sqrt s = 100 to 500~GeV provides unique opportunities for discovery and factory-like production of Higgs bosons in the s-channel. For excellent (but achievable) machine energy resolution, the total width and \mupmum coupling of a SM-like Higgs boson with mass \lsim 2\mw (as particularly relevant to supersymmetric/GUT models) can be directly measured with substantial precision. Multiplication of measured branching ratios by the total width yields the corresponding couplings. As a result, the light CP-even SM-like Higgs of the minimal supersymmetric model can be distinguished from the Higgs of the minimal Standard Model over a larger portion of supersymmetric parameter space than otherwise possible. Scan discovery and detailed measurements of total widths and some partial widths of the heavier CP-even and CP-odd Higgs bosons of the minimal supersymmetric model are possible for Higgs masses up to the maximum \rts. The excellent energy resolution, absence of beamstrahlung and mild bremsstrahlung at the first muon collider would allow increased precision for the measurement of \mt and \mw via t\anti t and \wp\wm threshold studies. A multi-TeV \mm collider would open up the realm of physics above the 1 TeV scale. Pair production of supersymmetric particles up to masses even higher than consistent with naturalness would be possible, guaranteeing that the heavier gauginos and possibly very massive squarks would be abundantly produced and that their properties could be studied. Very importantly, the multi-TeV collider would guarantee our ability to perform a detailed study of a strongly-interactin