What happens when particles collide with their anti-particles?

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What will happen when a particle collide with other particles' anti-self? For example, down quark with anti-up quark , up quark with positron etc
 
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It will scatter somehow. You can think of all kinds of elastic and inelastic collisions compatible with the conservation laws. If something is not forbidden by conservation laws, it will happen with some probability. Perhaps I don't understand right your question, but there's nothing special about anti-particles. They just undergo elastic or inelastic reactions as particles.
 
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Most mesons are a combination of a quark and an anti-quark.
 
You can see this in the decay of the charged and neutral pion decays.
The decay of the neutral pion is basically a matter-antimatter annihilation process that can be seen through the decay equation:
π0 -> γ + γ
The annihilation occurs because neutral pions always have a quark and an antiquark from the same flavor.
But you can't see this annihilation process in charged pions where the flavors are different
π± -> π0 + e± + electron neutrino/antineutrino
 
Garlic said:
π± -> π0 + e± + electron neutrino/antineutrino
That is an extremely rare decay (about 10 decays in a billion). The most common decay is ##\pi^+ \to \mu^+ \nu## and ##\pi^- \to \mu^- \bar\nu## (probability of more than 99.98%).

Free quarks do not exist, you cannot "collide" quarks. You can have them in the same meson, with implications discussed above.
 
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