Physics Potential and Motivations for a Muon Collider

The discovery of the Higgs particle is demanding a detailed knowledge of the properties of this fundamental component of the Standard Model. From the available data however, it cannot be concluded yet that we have found the SM Higgs boson and not one of the scalars postulated within the possible extensions of the SM. It is shown that a Higgs factory through a muon collider is particularly appropriate for precision studies of the properties of this particle. However sizable QED radiative effects — of order of 50% — must be carefully taken into account for a precise measurement of the leptonic and total widths of the Higgs particle. The results presented here are mainly based on a recent work in collaboration of Tao Han and Zhen Liu.