Differential cross section with invariant matrix element

[allenowen]

Homework Statement

Calculate the differential cross section for A+B---> C+D with an invariant matrix element

Homework Equations

See attachment

The Attempt at a Solution

I have no idea how to even begin this problem. The course I am taking is an undergraduate course in intermediate modern physics, but for some reason the professor thinks it is appropriate to introduce graduate level material to people who may not have had quantum mechanics yet. The professor, when asked how to work these problems, proceeds to ignore my concerns and talk about something else unrelated. Then seemed surprised no one knows how to solve it.

I don't have LaTex, so I am attaching the homework pdf to this. I don't want someone to work this for me, just help me get started, and maybe help when I get stuck later.

 

[fzero]

I suspect that you were given a formula for $$d\sigma/d(\cos\theta)$$ in terms of $$|\mathcal{M}|^2$$ in class and are not expected to derive it on your own. Then the meat of the problem would seem to be simplifying the expression that you get using that matrix element by writing the 4-momenta in the center-of-mass frame. You should obtain a formula in terms of the center-of-mass energy and the scattering angle. Possibly also the initial 3-momenta, I haven't tried working it out.

You should check your notes and text for more information and come back with questions.

 

[allenowen]

There isn't a text and the notes the instructor gave are incomplete. He started to explain it, then went off on a tangent and never explained how we are to approach this problem. He has tried to turn this junior level course into an upper level graduate course.