Calibrating the energy of a 50×50 GeV muon collider using spin precession

The neutral Higgs boson is expected to have a mass in the region 90–150 GeV/$c^2$ in various schemes within the minimal supersymmetric extension of the standard model. A first generation muon collider is uniquely suited to investigate the mass, width, and decay modes of the Higgs boson, since the coupling of the Higgs boson to muons is expected to be strong enough for it to be produced in the $s$ channel mode in the muon collider. Because of the narrow width of the Higgs boson, it is necessary to measure and control the energy of the individual muon bunches to a precision of a few parts in a million. We investigate the feasibility of determining the energy scale of a muon collider ring with circulating muon beams of 50 GeV energy by measuring the turn by turn variation of the energy deposited by electrons produced by the decay of the muons. This variation is caused by the existence of an average initial polarization of the muon beam and a nonzero value of $g-2$ for the muon. We demonstrate that it is feasible to determine the energy scale of the machine with this method to a few parts per million using data collected during 1000 turns.