This isn't a homework problem. I am preparing for a particle physics exam and although I understand the theoretical side of field theory, I have little idea how to approach practical scattering questions like these. THE PROBLEM: Dark matter might be observed at the LHC with monojet and monophoton signals, which proceed via the parton processes: Q aQ → χχϒ Q aQ → χχg where Q is a quark, aQ is an anti-quark, χ is the dark matter candidate, γ is a photon, g is a gluon. Explain why the cross sections of the two processes are related by σ(Q aQ → χχϒ) = A σ(Q aQ → χχg) where A is a numerical coefficient. EXTRA: It would be great if someone could explain how to determine A for a particular process; e.g. σ(Qred aQred → χχϒ) = A σ(Qred aQred → χχϒ). ATTEMPT: Using QCD and QED Feynman rules to determine the Feynman amplitude, the only difference is in the quark-gluon vs. quark-photon vertex. These terms only contribute constant terms so the equations are equal except for a proportionality constant.