I'm numerically evaluating the differential cross sections [itex]\frac{\operatorname{d}\sigma}{\operatorname{d} \Omega}[/itex] for [itex]e^{-}e^{+}\rightarrow\mu^{-}\mu^{+}[/itex] scattering by integrating over [itex]\operatorname{d}\Omega = \operatorname{d}(\cos{\vartheta})\operatorname{d} \phi[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Assuming no transverse polarisation so that the integration over [itex]\phi[/itex] is simply [itex]2\pi[/itex], and also assuming no electron mass, there are three effective cross sections: one due solely to [itex]\gamma-\gamma[/itex], one due to [itex]Z^{0}-Z^{0}[/itex], and one due to the interference term of the matrix elements ([itex](\mathcal{M}_{\gamma} + \mathcal{M}_{Z^{0}})^{2}[/itex]), [itex]\gamma-Z^{0}[/itex]. 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 [itex]Z^{0}[/itex] mass (which I've taken as about 91.2GeV). The first is the [itex]\gamma-\gamma[/itex] contribution, second the [itex]Z^{0}-Z^{0}[/itex], third the interference term [itex]\gamma-Z^{0}[/itex]. The fourth plot, the combined total cross section [itex]\sigma[/itex], can be found http://cl.ly/421W1Y212L0k3h0B0S27 [Broken]. (These are raw plots! Energy in GeV on [itex]x[/itex], cross section [itex]\sigma[/itex] on [itex]y[/itex].)

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 [itex]Z^{0}-Z^{0}[/itex] 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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# Typical cross sections for ee-uu scattering

Can you offer guidance or do you also need help?

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