Standard Model and Beyond · Problem 2.18

Lie Groups, Lie Algebras, and Symmetries

Physics — Particle Physics · yukawa-fermion-scalar-cross-section

Problem

Suppose a fermion

\psi

of mass

m

interacts with a Hermitian scalar

\phi

of mass

\mu

with

\mathcal{L}_I = h\bar{\psi}\psi\phi,

where

h

is small. (a) Calculate the spin-averaged differential cross section for

\psi(\vec{p}_1)\psi(\vec{p}_2) \to \psi(\vec{p}_3)\psi(\vec{p}_4)

in the CM in terms of the invariants

s

t

, and

u

. (b) Specialize to

m = \mu = 0

. Show that the scattering is isotropic in that limit and calculate the total cross section.