Effect of Initial Particle Instability in Muon Collisions

Abstract

We study $μ^+μ^-$ collision with production of some state $F$ (for example, $F= W^+$) and $(e\barν)$ system with the effective mass, which is less than muon mass. In this case the momentum $k$, transferred from $μ$ to $e\barν$ system (virtual neutrino momentum), can be time--like. The path of integration over $k^2$ goes through the pole at $k^2=0$. It gives divergent cross section. This divergence disappears if the finite width $Γ$ of initial $μ$ is taken into account. It gives the factor $\proptoΓ^{-1}$ in cross section. The compensating factor $Γ$ appears from $μ\to e\barνν$ subprocess. The resulting cross section is finite but high enough.