Typical cross sections for ee-uu scattering

In summary, the speaker is discussing the differential cross sections for e^{-}e^{+}\rightarrow\mu^{-}\mu^{+} scattering and the contributions from different particles. They mention that there should be a resonance at the Z mass and provide plots showing the contributions from \gamma-\gamma, Z^{0}-Z^{0}, and the interference term \gamma-Z^{0}. They express concern that the interference term may be smaller than expected and ask for confirmation from someone with more expertise. The expert responds that the plots match the expected behavior, with the Z being dominant near its peak and the interference term having some influence outside of the peak.
  • #1
alex3
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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].

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 . (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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  • #2
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.
 

FAQ: Typical cross sections for ee-uu scattering

1. What is the significance of typical cross sections for ee-uu scattering?

Typical cross sections for ee-uu scattering are important in understanding the behavior and interactions of particles in the subatomic world. They provide a measure of the probability of a specific scattering process occurring and can be used to test and validate theories about the fundamental forces of nature.

2. How are typical cross sections for ee-uu scattering calculated?

Typical cross sections for ee-uu scattering are typically calculated using quantum field theory, which describes the interactions of particles at the subatomic level. These calculations involve complex mathematical equations and are often done using computer simulations.

3. What factors affect the value of typical cross sections for ee-uu scattering?

Several factors can influence the value of typical cross sections for ee-uu scattering, including the energy of the colliding particles, the types of particles involved, and the strength of the fundamental forces involved in the scattering process.

4. Can the value of typical cross sections for ee-uu scattering change over time?

Yes, the value of typical cross sections for ee-uu scattering can change over time as our understanding of subatomic particles and their interactions evolves. As new data is collected and new theories are developed, the calculations and values of typical cross sections may be refined.

5. How are typical cross sections for ee-uu scattering used in experimental particle physics?

In experimental particle physics, typical cross sections for ee-uu scattering are used as a benchmark for comparing the results of experiments. By comparing the measured cross sections to the predicted values, researchers can validate or disprove theories about the fundamental forces and particles in the universe.

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