Why does the cross section drop between resonances?

In summary: This is because the energy required to produce a new particle gets higher and higher the closer you get to the resonance.
  • #1
Dreak
52
0
Hello.

When you have a plot of the cross section in function of the centre of mass energy of an e+e- -> hadrons collision, you get a graph with a few peaks which are due to the resonances (ρ, ω, J/ψ...).


But I don't understand why at a resonance, the cross section goes up? Or other way around: why does the cross section drop between the resonances even though there is still hadronisation?


Same for when you take the ratio R= σ(e-e+ -> hadrons)/σ(e-e+ -> μ-μ+)
If you graph this, you get high R peaks for the resonances, but between the peaks, R stays horizontal for increasing s? Why?


I hope my question is clear? I couldn't find a clear graphic that could show my problem.
 
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  • #2
When you have a mechanical or electrical system with two resonant frequencies, why does the amplitude go down between those two frequencies?
 
  • #3
Vanadium 50 said:
When you have a mechanical or electrical system with two resonant frequencies, why does the amplitude go down between those two frequencies?

Yes, but I don't see how this can be connected with these collisions?

Isn't cross section a rate for 'probability'?
 
  • #4
If your question is the following. Why does the cross section tend to decrease between resonances?

This is to do with how virtual a process is. The cross section is inversely proportional to an amount of momentum exchange. Which makes sense, the more massive the new particles I want to create, the harder it is to produce them.

This explains the drop off. The resonances appear as there is high probability to make a pair of new particles if I tune my energy to a centre of mass corresponding to a bound state.
 
  • #5
Mathematically you probably want to look at "propagator", "relativistic breit wigner".
 
  • #6
Isn't cross section a rate for 'probability'?
The probability of an interaction is higher if the interaction can give a single particle or resonance (in addition to the multiple particles you can get at other energies, too). Apart from those peaks, it goes down with increasing energy.
 

Related to Why does the cross section drop between resonances?

1. Why does the cross section drop between resonances?

The cross section is a measure of the probability of a particle interacting with another particle. In the context of scattering experiments, it represents the likelihood of a particle being scattered in a particular direction. Between resonances, there are no energy levels that match the energy of the incoming particle, thus the probability of scattering decreases.

2. What causes the appearance of resonances in cross section graphs?

Resonances occur when the energy of the incoming particle matches the energy levels of the target particle. This leads to a high probability of interaction and a peak in the cross section graph.

3. How does the width of a resonance affect the cross section?

The width of a resonance is related to the lifetime of the excited state of the target particle. A narrow resonance indicates a longer lifetime and thus a higher probability of interaction, resulting in a higher cross section. A broader resonance, on the other hand, indicates a shorter lifetime and a lower cross section.

4. Can the cross section drop to zero between resonances?

It is possible for the cross section to drop to zero between resonances, especially if the energy of the incoming particle is significantly different from the energy levels of the target particle. This indicates that there is no possibility for interaction at that energy.

5. How do different types of particles affect the cross section between resonances?

The cross section is dependent on the properties of both the incoming particle and the target particle. Different types of particles have different energy levels and interactions, which can lead to variations in the shape and magnitude of the cross section graph between resonances.

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