Resonance Concept in Particle Physics: What, Why, How

[Deepak247]

What is the true concept of resonance in particle physics? can particle production happen via resonance? how?

 

[DrDu]

In scattering theory, one observes the interaction of two or more particles which are initially and also after the scattering event separated far from each other. There are various constructs which describe the probability that the particles interact with each other (get scattered) and not only pass by each other, like the cross section or the scattering matrix. This probability depends on the energy of the particles and also on the geometry of the (possible) collisison. Now if this scattering probability increases strongly at or near a certain energy, then one speaks of a resonance. A possible mechanism (but not the only one) for a resonance is the intermediate formation of a compound particle which decays again after some time, setting free again the scattering particles (or other ones).

 

[A. Neumaier]

Now if this scattering probability increases strongly at or near a certain energy, then one speaks of a resonance. A possible mechanism (but not the only one) for a resonance is the intermediate formation of a compound particle which decays again after some time, setting free again the scattering particles (or other ones).

Typically, such a resonance peak is accompanied by a pole of the associated green's function in the nonphysical sheet, a complex number whose real part defines the resonance energy, and whose imaginary part denotes (up to a constant factor) the decay rate of an associated unstable particle.

 

[DrDu]

An experimentalist would probably infer the lifetime $$\tau$$ directly from the half width $$\Delta E$$ of the resonance using the time energy uncertainty relation $$\tau \approx h/\Delta E$$ if no theoretician is around.
I tried to find an interpretive picture:
http://www.google.de/imgres?imgurl=...&ndsp=20&tbs=isch:1&ei=DT5VTdSnK4r2sgbS1uy4DQ