How do you know that a particle is strongly interacting?

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when physicists discovered particles other than nucleons, before the quark model, how did they know they are "strongly" interacting, is it the half-life?
 
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Yes, half-life i.e. decay width (and in general strength of interaction, i.e. scattering cross section, but that doesn not apply to outgoing particles, of course)
 
No, not the half-life, it has to do with production. Particles are typically produced via strong interaction and decay via weak interaction. Strong interactions have a characteristic time scale of 10-23 sec, whereas most decays are 10-13 sec or thereabouts.

However the shortest lived known particle, the top quark, decays into a W boson and a bottom quark with an estimated lifetime of 5×10−25 sec. Even this is a semi-weak interaction.
 
I think we are not talking about quarks but e.g. hadrons.

How do you distinguish a meson and its decay channels from a myon or tau lepton? or from a neutrino? especially when you are capturing data from cosmic radiation? via half-life of the paricle; production is not under control.
 
Ok, here's a question for you. I have a particle with a mass of 1.8 GeV and an observed lifetime of 3 x 10-13 sec. From the relationship that you believe exists connecting a particle's lifetime with its strong interactions, tell me whether you think this particle is a hadron or a lepton.
 
I cannot distinguish whether it's a hadron or a lepton, but I can GUESS that it decays only weakly.
 
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