Pion electron-to-muon decay ratio (source code)

= Pion electron-to-muon decay ratio
{title2=$R_{e/\mu}=\frac{m_e^2}{m_\mu^2}\left(\frac{1-m_e^2/M_\pi^2}{1-m_\mu^2/M_\pi^2}\right)^2$}

At tree level with universal <weak charged current> coupling and massless neutrinos, the <leptonic pseudoscalar decay width> gives the displayed ratio. The <pion decay constant>, Fermi constant and common quark mixing coefficient cancel. The charged-lepton mass factor is <helicity suppression>: a spin-zero parent cannot emit the two massless helicities selected by the chiral weak interaction. The ratio tests this suppression and lepton universality; scalar or pseudoscalar four-fermion interactions can modify it. Radiative corrections must be included for a precision comparison.