Griffiths Introduction to Elementary Particles · Problem 6.9

Quantum Electrodynamics — David J. Griffiths

Physics — QFT · scattering-cross-section

Problem

Consider the collision

1 + 2 \to 3 + 4

in the lab frame (2 at rest), with particles 3 and 4 massless. Obtain the formula for the differential cross section.

\left[Answer: \frac{d\sigma}{d\Omega} = \left(\frac{\hbar}{8\pi}\right)^2 \frac{S|\mathcal{M}|^2 |\mathbf{p}_3|}{m_2 |\mathbf{p}_1| c (E_1 + m_2 c^2 - |\mathbf{p}_1| c \cos\theta)}\right]