# Typical cross sections for ee-uu scattering

## Main Question or Discussion Point

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 [Broken]. (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.)

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