Michel spectrum ($f(x)=2x^2(3-2x)$)

For an unpolarized parent charged lepton undergoing a three-body leptonic V-A interaction decay, neglecting daughter masses and radiative corrections, the normalized charged-daughter energy distribution in the parent rest frame is $f(x)=2x^2(3-2x)$, where $x=2E_{\ell }^{\ast }/m_{\mathrm{parent}}$ lies in $[0,1]$. Direct integration gives ${\int }_0^{1}f(x)dx=1$ and ${\int }_0^{1}xf(x)dx=7/10$. A specified parent spin orientation also produces angular terms, so this one-variable law alone does not describe polarized samples.