Effect of Initial Particle Instability in Muon Collisions

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We study μ+μ- collision with production of some state F (for example, F= W+) and (eν) system with the effective mass, which is less than muon mass. In this case the momentum k, transferred from μ to eν system (virtual neutrino momentum), can be time--like. The path of integration over k² goes through the pole at k²=0. It gives divergent cross section. This divergence disappears if the finite width Γ of initial μ is taken into account. It gives the factor ∝Γ⁻¹ in cross section. The compensating factor Γ appears from μ→ eνν subprocess. The resulting cross section is finite but high enough.