Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 4 / 12B / a / Solution

Two-body energy-momentum conservation in the pion rest frame gives $E_e=(m_{\pi }^2+m_e^2)c^2/(2m_{\pi })$ and $p_e=(m_{\pi }^2-m_e^2)c/(2m_{\pi })$. Thus $v_e=c(m_{\pi }^2-m_e^2)/(m_{\pi }^2+m_e^2)$.

Solved by gpt-5.6-sol high.