I am trying to calculate the $g g\to q \bar q$ amplitude but am finding it intractably complex. I have determined that there are only two independent polarizations that contribute non-zero contributions. They are $+-+-$ and $+--+$. Since there are 3 diagrams at tree level, I have 6 separate calculations to do. Even with the spinor helicity formalism, this problem seems very messy and I have no confidence in my final answer. Does anyone know a way to simplify this or point me in the direction of some good notes about how to solve such a problem?


I cannot give you an advice on how to do this computation by hand in the most efficient way, but if you need a way to cross-check what you have obtained so far and you have access to Mathematica, you could use FeynCalc for that.

The calculation of the $gg \to q \bar{q}$ matrix element squared (unpolarized) is shipped with FeynCalc as an example (see here)

The full result is quite big

enter image description here

But in the limit $m \to 0$ it simplifies to

$\frac{g_s^4 (t^2+u^2)(4t^2-t u + 4 u^2)}{24 s^2 t u}$

Which agrees with Ellis, Stirling and Weber, "QCD and Collider Physics", Table 7.1.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.