Particle physics - exercises

In summary, the question asks for the ratio of the scattering cross sections for hadron and muon production, just above and below the threshold for quark production, in the case of the exchange of photons. The Breit-Wigner formula applies in the region of a resonance, while the cross section for photon production away from resonances is given by the formula: \sigma \sim \frac{4 \pi}{3} (\hbar c^2)^2 C \frac{Q_{f} \alpha^2}{E^2}. The ratio can be calculated by summing over the charges of all the quarks involved in hadron production.
  • #1
Uncle_John
15
0

Homework Statement


Calculate the ratio of scattering cross sections for hadron and muon production
[itex] \sigma(e^{+} e^{-} \rightarrow hadrons) / \sigma(e^{+} e^{-} \rightarrow \mu^{+}\mu{-})[/itex],
just underneath and just a bit above the treshold for quark production [itex]t \bar{t}[/itex]
(Note only the exchange of the photons)

Homework Equations



Equation for cross section(i think):

[itex]\sigma = \frac{K}{(M_{invariant} - M)^2 c^4 + (\frac{\Gamma}{2})^2} [/itex]
What represents the [itex]\Gamma[/itex] in this equation?
How do i calculate the treshold for above productions

Any help appreciated
 
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  • #2
Looking at the [itex]t\overline{t}[/itex] production from:
[itex]\gamma \rightarrow t\overline{t}[/itex]

so minimum [itex]E_{\gamma} = 2m_{t}c^2[/itex]

But still I don't see how can i get data to calculate [itex]\Gamma [/itex] and [itex]M[/itex] in formula for cross section
 
  • #3
The equation you have given for the cross section is the Breit-Wigner formula which applies in the region of a resonance (e.g. when the centre of mass energy is just enough to create a charmonium state such as the J/Psi).

I think the ratio you are being asked for is for production away from resonances. In this case the cross section for the photon diagram is:

[tex]
\sigma \sim \frac{4 \pi}{3} (\hbar c^2)^2 C \frac{Q_{f} \alpha^2}{E^2}
[/tex]

Where C is the colour factor and Qf is the charge of the fermion involved. For hadron production you need to some over the the charges of all the quarks which can be produced at the energy you are considering (hence the difference in cross section above and below the threshold for t).
 

FAQ: Particle physics - exercises

1. What is particle physics?

Particle physics is the branch of physics that studies the smallest building blocks of matter and the forces that govern their interactions. It involves studying particles such as electrons, protons, and neutrons, as well as smaller particles like quarks and leptons.

2. Why is particle physics important?

Particle physics helps us understand the fundamental nature of the universe and the laws that govern it. It also has practical applications in fields such as medicine, energy production, and technology development.

3. What are some common exercises in particle physics?

Some common exercises in particle physics include calculating the behavior and interactions of particles in different scenarios, analyzing data from particle accelerator experiments, and solving equations to describe the behavior of particles.

4. What are some key concepts in particle physics?

Some key concepts in particle physics include matter and antimatter, forces such as gravity and the strong and weak nuclear forces, and the Standard Model which describes the fundamental particles and their interactions.

5. How does particle physics relate to other branches of science?

Particle physics is closely related to other branches of physics, such as quantum mechanics and relativity, as it deals with the behavior of particles on a tiny scale. It also has connections to cosmology, as the study of particles and their interactions helps us understand the origins and evolution of the universe.

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