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To keep it simple: We think quarks interact through “colour charges”, the forces obey the “quantum chromodynamics”. That is pretty much like positive and negative charge, but in 3 directions and not only 2.

If you solve the underlying math you can find that radiation of particles should be supressed in a cone shaped area in the direction of their movement. That’s the dead-cone

If you can experimentally verify that this cone exists that confirms the underlying theory (colour charges can’t be measured directly, so we need this kind of indirect proof)