Tree scattering in Yukawa theory (source code)

= Tree scattering in Yukawa theory
{title2=$\mathcal L_{\rm int}=-g\bar\psi\phi\psi$}

For a real scalar coupled through $-g\bar\psi\phi\psi$, the scalar-fermion <Feynman vertex> is $-ig$. Two-fermion scattering has scalar exchange in the $t$ and $u$ channels with a relative minus from exchanging identical external fermions. Fermion-antifermion scattering has $t$ exchange and $s$ annihilation, again with a relative fermionic minus for a fixed state ordering. Fermion-scalar scattering has the two orderings along one open fermion line, using internal momenta $p_1+p_2$ and $p_1-p_4$; these have the same sign. The <Mandelstam variables> specify the propagator denominators.