Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 4 / 17B / b / Solution

In the pion rest frame, conservation of three-momentum makes the electron and massless neutrino momenta equal and opposite, of common magnitude $p$. Their energies obeySquaring $E_e=m_{\pi }{c}^2-pc$ and cancelling $p^2{c}^2$ givesThe electron four-momentum satisfies $p=E_{e}v/c^2$. Thus, for the physically allowed decay $m_{\pi }>m_e$,