# Muon decay correction

by Catria
Tags: correction, decay, muon
 P: 52 In my class notes, the muon decay width is: $\Gamma_\mu=\frac{G^2_F m^5_\mu}{192\pi^3}$ Yet, in Wikipedia (take that for what it's worth) it says that, once the corrections have been applied, the muon decay width takes the form: $\Gamma_\mu=\frac{G^2_F m^5_\mu}{192\pi^3}I\left(\frac{m^2_e}{m^2_\mu}\right)$ where $I(x)=1-8x-12x^2 ln(x)+8x^3+x^4$ is a correction factor. I wonder how does one arrive at that correction factor. If it is possible to get enough steps so that someone could understand its origin, as well as understanding its derivation, it would be very appreciated.