Standard Model and Beyond · Problem 2.19

Lie Groups, Lie Algebras, and Symmetries

Physics — Particle Physics · electron-pion-elastic-scattering

Problem

Consider

e^-(\vec{k}_1)\pi^+(\vec{p}_1) \to e^-(\vec{k}_2)\pi^+(\vec{p}_2)

elastic scattering. Show that the spin-averaged differential cross section in the pion rest frame is

\frac{d\bar{\sigma}}{d\cos\theta_L} = \frac{\pi\alpha^2\cos^2\frac{\theta_L}{2}}{2k_1^2\sin^4\frac{\theta_L}{2}\left[1 + \frac{2k_1}{m_\pi}\sin^2\frac{\theta_L}{2}\right]},

where

\theta_L

is the electron scattering angle and we have neglected the electron mass. Hint: use (2.224).