[QUE/EPP-01008]

 The values of \(mc^2\) for the pion \(\pi^+\) and muon \(\mu^+\) are 139.57MeV and 105.66 MeV respectively. Find the kinetic energy of the muon decay in \[ \pi^+ \longrightarrow \mu^+  + \nu_\mu \] assuming that the neutrino is massless. For a neutrino of finite but very small mass \(m_\nu\) show that, compared with the case of a massless neutrino, the muon momentum would be reduced by the fraction \begin{equation*}    \frac{\Delta p}{p} = - \frac{m_\nu^2(m_\pi^2+m_\mu^2)}{(m_\pi^2-m_\mu^2)^2} ~\text{MeV} \approx -\frac{m_\nu^2}{10^4}. \end{equation*} where \(m_\nu\) is neutrino mass in MeV.