Every scalar-fermion vertex contracts the scalar momentum with the <Dirac current>. Between on-shell external spinors,
$$
(p'-p)_\mu\bar u(p')\gamma^\mu u(p)
=\bar u(p')(\not p'-\not p)u(p)=0,
$$
and the analogous particle-antiparticle identity also vanishes. Equivalently, the field redefinition in the previous part turns the theory into a free theory. Consequently every putative tree channel for $\psi\bar\psi\to\psi\bar\psi$ has zero amplitude and
$$
\boxed{\overline{|\mathcal M|^2}=0,
\qquad \sigma(\psi\bar\psi\to\psi\bar\psi)=0.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 301 / 2 / iv / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-301/2/iv/solution