Here are a few suggestions from Stephane Tjampens:
I know you are very familiar with the phenomenology of Hadron Physics, but this is not the case of most of the students and researchers! So, your notebook starts already, at least to me, with already 'complicated cases'. It would also be interesting to link the examples with real-life resonances found in the PDG.
I would have started at a more basic level, and would have increased the complexity step-by-step:
one pole one channel to show one finds the BW
one pole one channel but with a background amplitude to show that the resonance pole is no more the BW peak position! [most people in LHCb don't know this.]
one pole two channels to illustrate the Flatté lineshape [eg, a0(980) to KK and pi eta]
two poles one channel (your example 3) to illustrate the main feature of the K-Matrix: Unitarity
etc.
A thornier issue is that in general the K-matrix poles are not the T-matrix poles
Here are a few suggestions from Stephane Tjampens:
I know you are very familiar with the phenomenology of Hadron Physics, but this is not the case of most of the students and researchers! So, your notebook starts already, at least to me, with already 'complicated cases'. It would also be interesting to link the examples with real-life resonances found in the PDG.
I would have started at a more basic level, and would have increased the complexity step-by-step:
A thornier issue is that in general the K-matrix poles are not the T-matrix poles