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I'm trying to understand the difference in cross section between top-quark pair production and pair production of scalar top quarks (top squarks) as predicted by Supersymmetry. Assume the mass of the scalar top quark were the same as that of the top quark (roughly 173 GeV).

Let us focus on one of the Feynman diagrams contributing to the production at a hadron collider with a gluon in the s-channel, $pp\to g\to t \bar t$ and $pp\to g\to \tilde t \tilde {t^*}$, with $p$ being a parton $q$ or $g$. The cross section for the latter is smaller by about an order of magnitude compared to the first. What is the reason for that?

Part of the explanation and thus a follow-up question might be: The vertex factor for $gqq$ is $\frac{-ig_s}{2}\lambda^\alpha\gamma^\mu$, with the strong coupling $g_s$, gamma matrix $\gamma$ and color matrix $\lambda^\alpha$. For $g\tilde q\tilde q$, it is $-ig_s\lambda^\alpha(p_i + p_f)^\mu$), with $p_{i,f}$ the 4-momenta of the squarks. Why is there a dependence on the 4-momenta in one case (scalars) but not the other (fermions)?

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