Given the probabilistic nature of quantum mechanics, it’s not even possible to define.
Suppose that you have two quarks interacting, and for simplicity let’s say that they’re an up and an anti-up. You know that an up and an anti-up go into the interaction, and an up and an anti-up come out of the interaction. Well, there’s a few ways that could happen. The two particles could get close to each other, exchange a vector boson (a particle that carries a force) such as a photon or gluon, and then go apart again. In that case, presumably you’d say that you still have the original particles. Alternately, the two particles could annihilate into a vector boson, and then after some short time that vector boson could turn into a new quark-antiquark pair. In that case, presumably you’d say that you don’t have the same particles you started with. Or you could have more complicated interactions, involving multiple vector bosons, but let’s not worry about that.
So, given any individual interaction, can you say which one of those two possibilities happened? In fact, so far as we can tell, what actually happens in any interaction is all of them, each with varying amplitudes. The particles both are and are not the original particles, and it doesn’t matter.