(insert diagram) Here, all external particles have the same flavour. There are two distinct Feynman diagrams (insert Feynman diagrams) The first diagramt-channel corresponds directly to the only diagram for the Electron-Muon Scattering. The second diagramu-channel arises due to the presence of identical final states in the process. Note: Pauli anti-symmetry, i.e. the anti-symmetry of the two-particle wave function of two identical fermions, introduces a relative minus sign between both diagrams.
\mathcal{M}=\mathcal{M}_1-\mathcal{M}_2$$$$|\mathcal{M}|^2=|\mathcal{M}_1|^2+|\mathcal{M}_2|^2-2\text{Re}\mathcal{M}_1\mathcal{M}_2^*
- The first term is identical to the result of Electron-Muon Scattering.
- The second term will similarly consist of fermion traces.
- The third term, however, as the fermion lines in the two amplitudes connect different electrons, give rise to only one single trace with eight constituent Dirac matrices.