Scalar Mediated FCNC at the First Muon Collider

In the most general two-Higgs doublet model (generally referred to as Model III), tree level flavor changing neutral couplings exist. It has been noted that the most natural value for such a coupling is of the order of the geometric mean of the Yukawa couplings of the two fermions. Bounds on those couplings that involve the second and third generations, from $\tau,B,D$ and $\mu$ physics, are very weak and are not sensitive to this "natural" value. In this paper, it is pointed out that the process \mu\mu ---> \mu\tau, at a muon collider tuned to the scalar resonance, will easily reach this sensitivity if the scalar mass is below 140 GeV. Hundreds of events are expected for an integrated luminosity of an inverse femtobarn, and there appears to be no background. Failure to observe this process, if the scalar is below 140 GeV, would effectively rule out Model III.