Why does the cross section drop between resonances?

[Dreak]

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.

 

[Vanadium 50]

When you have a mechanical or electrical system with two resonant frequencies, why does the amplitude go down between those two frequencies?

 

[Dreak]

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'?

 

[RGevo]

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.

 

[RGevo]

Mathematically you probably want to look at "propagator", "relativistic breit wigner".

 

[mfb]

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.