when physicists discovered particles other than nucleons, before the quark model, how did they know they are "strongly" interacting, is it the half-life?
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.