No, in general, QED (Quantum Electrodynamics) and QCD (Quantum Chromodynamics) Feynman diagrams do not mix when calculating the matrix element squared in QED/QCD processes. This is because QED and QCD are distinct quantum field theories that describe different fundamental interactions.
In QED, the Feynman diagrams represent the interactions of photons (gauge bosons of the electromagnetic force) with charged particles, such as electrons and positrons. These diagrams involve vertices that couple the photons to the charged particles.
In QCD, the Feynman diagrams represent the interactions of gluons (gauge bosons of the strong nuclear force) and quarks. QCD Feynman diagrams involve vertices that couple gluons to quarks and interactions among gluons themselves.
When calculating the matrix element squared in QED or QCD processes, the contributions from QED diagrams are computed separately from the contributions from QCD diagrams. Each set of diagrams is evaluated independently and then combined appropriately based on the nature of the process.
However, there can be cases where QED and QCD processes can be combined, such as in processes involving both electromagnetic and strong interactions. In such cases, the combined Feynman diagrams would include both QED and QCD vertices, reflecting the interactions of photons, gluons, and charged particles.
It's worth noting that the combination of QED and QCD in a unified framework is part of the electroweak theory, which describes the electromagnetic and weak nuclear forces. The electroweak theory combines QED with the theory of weak interactions to form a unified description. In this framework, Feynman diagrams can involve both electromagnetic and weak vertices.