# Database of scattering amplitudes

I want to check whether my result for the invariant amplitude of the electron-electron scattering (to lowest order in $\alpha$; t+u channels) is correct or not.

I can't find any reference that has the result explicitly. Can someone point out some kind of database of scattering amplitudes?

Edit: for completeness I post my result (which might have an error) $$|\mathcal{M}|^2=\frac{2e^4}{u^2t^2}\left((s^2-8m^4)[(t+u)^2+u^4+t^4]+8m^2ut(4m^2-3s)\right)$$

Update: I managed to do the calculation using CompHEP+Mathematica.

On CompHEP I selected the QED model and calculated the diagrams for $e^-e^- \rightarrow e^-e^-$ from which I get the two contributions to the process (t+u channels). Then I exported the symbolic computation of the squared diagrams to Mathematica code which gives $$\frac{2e^4}{t^2 \left(-4 m^2+s+t\right)^2} (64 m^8+16 m^6 (t-6 s)+4 m^4 \left(13 s^2+3 s t+3 t^2\right)-4 m^2 \left(3 s^3+3 s^2 t+3 s t^2+2 t^3\right)+\left(s^2+s t+t^2\right)^2)$$ where the denominator is clearly $t^2u^2$ by using $s+t+u=4m^2$ but the rest is not so trivial to put in the same form as my equation for $|\mathcal{M}|^2$. So if I substitute the value of $u$ on my first equation I get something that doesn't look anything like the second equation. Therefore my first equation is wrong.

Note: I compared the second equation with the expression for the differential cross section of the Møller scattering from a book and it is consistent.

• The basic SM cross sections (although not amplitudes, I recall) are mentioned in the Particle Data Booklet, see here. – Vibert Mar 4 '13 at 23:12

## 1 Answer

Besides textbooks such as Peskin & Schroeder, COMPHEP has some of the functionality you are looking for as well, although I have never used it for this purpose. From the overview page:

"The symbolic part of CompHEP has the following possibilities: [...] calculate analytical expressions corresponding to squared diagrams by using the fast built-in symbolic calculator;"

To test calculations against actual experimental data, most modern particle physics experiments today will submit their results to HEPDATA. You might try a search for [re e+ e- --> e+ e- and obs sig]

One of the results it: "Measurement of hadron and lepton-pair production in e+ e- collisions at s**(1/2) = 192-GeV to 208-GeV at LEP"

• Thanks, that's an good reference to keep in mind. In my case I was thinking more like a theoretical exercise. Thus for example I calculated the amplitude in terms of Mandelstam variables and wanted to check if my result is correct. The other option is to use a CAS to do the algebra for me, unfortunately I only found a package for Mathematica that does algebraic manipulations of gamma matrices but I don't have access to that software. – Prastt Mar 4 '13 at 11:25
• Hi I expanded my answer to that effect, I guess textbooks are the best source here. – luksen Mar 4 '13 at 11:43
• Thanks for pointing out COMPHEP, I'll dig it when I get some time. – Prastt Mar 4 '13 at 17:05
• @Barefeg any luck? I'd personally be interested in this answer as well. – luksen Mar 8 '13 at 18:21
• I think compHEP should do the trick but I'm having technical problems. After I square the diagrams I select algebraic manipulation and the program crashes. I'm not sure if this is because I installed from .deb package (I couldn't install it from source it gave me errors). The solution I think is to export to Reduce or Mathematica. I'll install the former and try, but from the code it generates it seems that it can calculate what I asked in the original question – Prastt Mar 10 '13 at 12:39