Typical cross sections for ee-uu scattering

[alex3]

I'm numerically evaluating the differential cross sections \frac{\operatorname{d}\sigma}{\operatorname{d} \Omega} for e^{-}e^{+}\rightarrow\mu^{-}\mu^{+} scattering by integrating over \operatorname{d}\Omega = \operatorname{d}(\cos{\vartheta})\operatorname{d} \phi.

Assuming no transverse polarisation so that the integration over \phi is simply 2\pi, and also assuming no electron mass, there are three effective cross sections: one due solely to \gamma-\gamma, one due to Z^{0}-Z^{0}, and one due to the interference term of the matrix elements ((\mathcal{M}_{\gamma} + \mathcal{M}_{Z^{0}})^{2}), \gamma-Z^{0}. The photon term is the so-called QED term, while the Z boson terms are the Standard Model terms.

I'm not experienced in plotting or analysing these kinds of events, so my problem is that I'm unsure of what to expect. I know that I should see a resonance, as I am, but I'm worried that the interference term should be contributing more than what I'm seeing.

I've attached three plots, each centred around the Z^{0} mass (which I've taken as about 91.2GeV). The first is the \gamma-\gamma contribution, second the Z^{0}-Z^{0}, third the interference term \gamma-Z^{0}. The fourth plot, the combined total cross section \sigma, can be found http://cl.ly/421W1Y212L0k3h0B0S27 . (These are raw plots! Energy in GeV on x, cross section \sigma on y.)

As you can see, each contribution has a different form (which is OK), but the interference term is much smaller (~10e-3) than the dominating Z^{0}-Z^{0} term. Is this expected behaviour for these types of events?

(I should mention that the given differential cross sections are trivially solvable. I think I have coded it up correctly, but given my inexperience it would be nice to hear from someone with more competence in the field.)

 

[mfb]

That matches the actual plots for the cross section. Close to the Z peak the Z is completely dominant. Outside the interference term has some influence.